SPEX Reference Manual
Jelle Kaastra
Rolf Mewe, Ton Raassen & Jelle de Plaa
Version 3.04.00
December 8, 2017
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Contents
Recent changes to the manual 7
1 Introduction 11
1.1 General description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3 SPEXACT: The SPEX Atomic Code & Tables . . . . . . . . . . . . . . . . . . . 13
1.3.1 Main version number definition . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4 Changes introduced in SPEX 3.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4.1 Changes in version 3.01 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4.2 Changes in version 3.02.00 . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.4.3 Changes in version 3.03.00 . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.4.4 Changes in version 3.04.00 . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.5 Document structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.6 Additional information and documents . . . . . . . . . . . . . . . . . . . . . . . . 17
1.6.1 SPEX Cookbook: Examples . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.6.2 Physical background of spectral models . . . . . . . . . . . . . . . . . . . 17
2 Spectral Fitting 19
2.1 Spectral Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Sectors and regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.2 Sky sectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.3 Detector regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3 Different types of spectral components . . . . . . . . . . . . . . . . . . . . . . . . 22
3 Syntax overview 23
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 Abundance: standard abundances . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3 Ascdump: ascii output of plasma properties . . . . . . . . . . . . . . . . . . . . . 25
3.4 Bin: rebin the spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.5 Calculate: evaluate the spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4 CONTENTS
3.6 Comp: create, delete and relate spectral components . . . . . . . . . . . . . . . . 28
3.7 Data: read response file and spectrum . . . . . . . . . . . . . . . . . . . . . . . . 30
3.8 DEM: differential emission measure analysis . . . . . . . . . . . . . . . . . . . . 31
3.9 Distance: set the source distance . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.10 Egrid: define model energy grids . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.11 Elim: set flux energy limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.12 Error: Calculate the errors of the fitted parameters . . . . . . . . . . . . . . . . . 37
3.13 Fit: spectral fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.14 Ibal: set type of ionisation balance . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.15 Ignore: ignoring part of the spectrum . . . . . . . . . . . . . . . . . . . . . . . . 41
3.16 Ion: select ions for the plasma models . . . . . . . . . . . . . . . . . . . . . . . . 42
3.17 Log: Making and using command files . . . . . . . . . . . . . . . . . . . . . . . . 44
3.18 Menu: Menu settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.19 Model: show the current spectral model . . . . . . . . . . . . . . . . . . . . . . . 46
3.20 Multiply: scaling of the response matrix . . . . . . . . . . . . . . . . . . . . . . . 46
3.21 Obin: optimal rebinning of the data . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.22 Par: Input and output of model parameters . . . . . . . . . . . . . . . . . . . . . 47
3.23 Plot: Plotting data and models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.24 Quit: finish the program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.25 Sector: creating, copying and deleting of a sector . . . . . . . . . . . . . . . . . . 55
3.26 Shiftplot: shift the plotted spectrum for display purposes . . . . . . . . . . . . . 55
3.27 Simulate: Simulation of data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.28 Step: Grid search for spectral fits . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.29 Syserr: systematic errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.30 System: call system executables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.31 Use: reuse part of the spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.32 Var: various settings for the plasma models . . . . . . . . . . . . . . . . . . . . . 61
3.32.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.32.2 Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.32.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.33 Vbin: variable rebinning of the data . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.34 Watch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4 Spectral Models 65
4.1 Overview of spectral components . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2 Absm: Morrison & McCammon absorption model . . . . . . . . . . . . . . . . . . 66
4.3 Amol: oxygen edge molecules absorption model . . . . . . . . . . . . . . . . . . . 66
4.4 Bb: blackbody model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.5 Cf: isobaric cooling flow differential emission measure model . . . . . . . . . . . . 69
4.6 Cie: collisional ionisation equilibrium model . . . . . . . . . . . . . . . . . . . . . 70
CONTENTS 5
4.6.1 Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.6.2 Line broadening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.6.3 Density effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.6.4 Non-thermal electron distributions . . . . . . . . . . . . . . . . . . . . . . 71
4.6.5 Abundances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.6.6 Parameter description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.7 Comt: comptonisation model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.7.1 Some modifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.8 CX: model for charge exchange plasmas . . . . . . . . . . . . . . . . . . . . . . . 73
4.8.1 Charge exchange cross sections . . . . . . . . . . . . . . . . . . . . . . . . 73
4.8.2 Parameter description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.9 Dabs: dust absorption model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.10 Dbb: disk blackbody model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.11 Delt: delta line model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.12 Dem: differential emission measure model . . . . . . . . . . . . . . . . . . . . . . 77
4.13 Dust: dust scattering model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.14 Ebv: Galactic interstellar extinction model . . . . . . . . . . . . . . . . . . . . . 78
4.15 Etau: simple transmission model . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.16 Euve: EUVE absorption model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.17 File: model read from a file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.18 Gaus: gaussian line model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.19 Hot: collisional ionisation equilibrium absorption model . . . . . . . . . . . . . . 80
4.20 Hyd: model with user-own hydrodynamical simulation . . . . . . . . . . . . . . . 81
4.21 Knak: segmented power law transmission model . . . . . . . . . . . . . . . . . . 82
4.22 Laor: relativistic line broadening model . . . . . . . . . . . . . . . . . . . . . . . 83
4.23 Line: transmission model for a single spectral line . . . . . . . . . . . . . . . . . . 83
4.24 Lpro: spatial broadening model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.25 Mbb: modified blackbody model . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.26 Musr: User defined multiplicative model . . . . . . . . . . . . . . . . . . . . . . . 86
4.27 Neij: non-equilibrium ionisation jump model . . . . . . . . . . . . . . . . . . . . 87
4.28 Pdem: DEM models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.29 Pion: SPEX photoionised plasma model . . . . . . . . . . . . . . . . . . . . . . . 89
4.29.1 Emission from the pion model . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.29.2 More options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.29.3 Model parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.30 Pow: power law model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.31 Reds: redshift model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.32 Refl: reflection model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.33 Rrc: radiative recombination continuum model . . . . . . . . . . . . . . . . . . . 95
6 CONTENTS
4.34 Slab: thin slab absorption model . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.35 Spln: spline continuum model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.36 User: User defined model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.37 Vblo: rectangular velocity broadening model . . . . . . . . . . . . . . . . . . . . 99
4.38 Vgau: gaussian velocity broadening model . . . . . . . . . . . . . . . . . . . . . . 99
4.39 Vpro: velocity profile broadening model . . . . . . . . . . . . . . . . . . . . . . . 100
4.40 Warm: continuous photoionised absorption model . . . . . . . . . . . . . . . . . . 100
4.41 Wdem: power law differential emission measure model . . . . . . . . . . . . . . . 101
4.42 Xabs: photoionised absorption model . . . . . . . . . . . . . . . . . . . . . . . . . 102
5 More about spectral models 105
5.1 Plasma model in SPEX 3.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.1.1 The core of the plasma model . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.1.2 Ions for which updated calculations are available . . . . . . . . . . . . . . 106
5.2 Absorption models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.2.2 Thomson scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.2.3 Different types of absorption models . . . . . . . . . . . . . . . . . . . . . 111
5.2.4 Dynamical model for the absorbers . . . . . . . . . . . . . . . . . . . . . . 112
5.3 Atomic database for the absorbers . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.3.1 K-shell transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.3.2 L-shell transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.3.3 M-shell transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.4 Non-equilibrium ionisation (NEI) calculations . . . . . . . . . . . . . . . . . . . . 115
5.5 Non-thermal electron distributions . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.6 Supernova remnant (SNR) models . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6 More about plotting 119
6.1 Plot devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.2 Plot types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.3 Plot colours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
6.4 Plot line types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
6.5 Plot text . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.5.1 Font types (font) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.5.2 Font heights (fh) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.5.3 Special characters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.6 Plot captions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.7 Plot symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.8 Plot axis units and scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.8.1 Plot axis units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
CONTENTS 7
6.8.2 Plot axis scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
7 Auxilary programs 131
7.1 Trafo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.1.1 File formats spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.1.2 File formats responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.1.3 Multiple spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.1.4 How to use trafo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.2 Xabsinput . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
7.3 RGS fluxcombine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
7.3.1 Option 1: combining RGS spectra of the same detector and spectral order 138
7.3.2 Option 2: combine spectra of RGS1, RGS2 and first and second order of
both (4 spectra) into one spectrum . . . . . . . . . . . . . . . . . . . . . . 140
7.4 RGS fmat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
7.5 Hydro driver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
7.6 Rgsvprof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
7.6.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
7.7 Stepcontour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
8 Response matrices 145
8.1 Optimal definition of respons matrices . . . . . . . . . . . . . . . . . . . . . . . . 145
8.2 Proposed file formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
8.2.1 Proposed response format . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
8.2.2 Proposed spectral file format . . . . . . . . . . . . . . . . . . . . . . . . . 146
9 Installation 153
9.1 Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
9.1.1 Installation on Linux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
9.1.2 Installation on Mac OSX . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
10 Acknowledgements 155
8 CONTENTS
Recent changes to the manual
Date Version Changes
December 2017 3.04.00 Minor updates to the manual:
Updates to the pion model documentation
Updates to the C-stat documentation
Update to the stepcontour program documentation
November 2016 3.03.00 Minor updates to the manual:
Minor updates to var, hyd, amol and pion
August 2016 3.02.00 Minor updates to the manual:
Introduced SPEXACT naming and versioning
April 2016 3.01.00 Minor updates to the manual:
Update of the refl model description
Update of the pion model description
Update of the cx model description
Update of the ascdump and ions command description
January 2016 3.00.00 Full revision of the manual with a.o.:
New Chapter 1, Introduction
New Chapter 2, Spectral Fitting and Code
Refences list updated
New model descriptions added for new models
10 CONTENTS
Chapter 1
Introduction
1.1 General description
This document gives a background of the use of the software package SPEctral X-ray and UV
modelling and analysis, SPEX . In the last decades SRON-Utrecht has developed this software
package for the computation and modelling of X-ray and EUV spectra. SPEX encompasses a
number of subroutines for the computation of emergent spectra of optically thin plasmas such
as stellar coronal loop structures and supernova remnants (also including transient ionization
effects), photo-ionized plasmas, and optically thick plasmas. A synthetic spectra program that
convolves the calculated input spectra with representative instrumental response functions and
a subroutine for Differential Emission Measure modelling is available.
SPEX includes more than a million lines from 30 (from H to Zn) different chemical elements
in the far UV and X-ray band. These lines are produced by excitation from electron impact,
radiative and dielectronic recombination and by innershell excitation and ionization. In addition
to the lines the code calculates the contributions from continuum radiation due to free-free, freebound,
and two-photon emission and includes several absorption models.
Current developments are pointed to extend the work to photoionized plasmas and charge exchange
processes. This will be needed since it became evident that those processes play an
important role in X-ray sources and emitting regions. Moreover, atomic physics has improved
considerably during the last decade, and the advent of a new series of satellites with high sensitivity
and spectral resolution like Hitomi or Athena, strongly demands the availability of spectral
code with higher accuracy and more detail.
1.2 History
Starting in the early seventies (Mewe 1972) Rolf Mewe and his colleagues of the Space Research
Laboratory in Utrecht started developing a spectral code for the X-ray emission of optically
thin plasmas. A milestone was reached in 1985 and 1986, when two papers describing the line
emission (Mewe et al. 1985) and continuum emission (Mewe et al. 1986) were published. This
spectral code, often abbreviated as the Mewe-Gronenschild code, together with the code by
Raymond & Smith (1977) served for many years as the basis for many X-ray spectroscopic
papers.
At the beginning of the eighties the code was extended with non-equilibrium ionization balance
12 Introduction
calculations (Gronenschild & Mewe 1982), and motivated by the work on supernova remnants
done in Leiden by Fred Jansen and Jelle Kaastra vastly improved. The need for a faster code in
order to be able to do spectral fitting to these non-equilibrium spectra of supernova remnants
motivated us to improve the performance of the code. Then in 1992 an update of in particular the
continuum calculation appeared, and this updated and faster computer code was implemented
at HEASARC in the XSPEC package, at which time it was baptized as meka code, after the
two main authors of this version, Mewe and Kaastra.
Around the same time (early 1992) 1we started the SPEX project, with the intention to improve,
update and extend also the line emission part of the code. In addition, we intended to make
it more useful by having spectral simulation and fitting options attached to it, as well as more
illustrative graphical and tabular output from the program, which helps to understand the
physics of the sources being studied. Also different extensions like hydrodynamical models for
supernova remnants, and differential emission measure analysis techniques were foreseen.
Figure 1.1: Mewe, Kaastra & Liedahl preparing the mekal model. Photo by Hans Nieuwenhuijzen,
1996.
In 1994 the first version of SPEX became public, with the re-written meka code as working horse
in the core of the software package. A year before the ASCA satellite had been launched, and
in one of the first X-ray spectra of a cluster of galaxies, the Centaurus clusters, the observed
spectrum did not match neither the predicted meka calculations nor the results of other codes
like the Raymond & Smith code (Fabian et al. 1994). In particular the Fe-L 4 − 2 to 3 − 2
blend ratio did not match the observations. Around the same time, Duane Liedahl was able to
produce better results for the Fe- L complex using the HULLAC atomic code, and by joining
forces an update of the meka code, now named mekal, after the three authors, was released
(Mewe, Kaastra & Liedahl 1995). This code was both included in the SPEX package as well as
a model in the XSPEC package. Apart form the update and extension of the iron L complex,
it also contained an improvement of the 300 − 2000 ˚A band, triggered by the EUVE spectra of
stellar coronae, an update for the Fe VIII to Fe XVI ions, plus addition of DR satellites for Mg
XI. Also the ionization balance for iron was updated using the results of Arnaud & Raymond
(1992).
Already around 1996 we started developing version 2.0 of the code, with a transition from
olf fortran77 compilers to modern fortran90, allowing much more flexibility using dynamical
memory, modules etc. Also the original menu-driven structure was replaced by a command
1
The oldest program files that we can trace back dates from 5 February 1991
1.3 SPEXACT: The SPEX Atomic Code & Tables 13
structure. Stimulated by the availability of high-resolution spectra taken by Chandra and XMMNwton
the code was gradually extended and improved, although the availability of these new
data also slowed down the development due to manpower limitations.
Driven by the need to further improve on the atomic data because of the more detailed spectra
that become available, in January 2016 version 3.0 of the software has been launched.
1.3 SPEXACT: The SPEX Atomic Code & Tables
The SPEX package is a spectral fitting program with integrated models that are mostly based
on one atomic database and a set of routines to calculate all the atomic processes in the plasma.
Although the development of the atomic database and code is performed mostly in parallel
with the other SPEX development, it can sometimes be confusing which version of the atomic
database was actually used in an analysis. Especially after the major update of the atomic
database in SPEX 3.0 and the option to calculate models using the ’old’ database and routines
from SPEX 2.0, there is a need to name and version the ’core’ routines of SPEX separately.
This has become SPEXACT (SPEX Atomic Code & Tables). In principle, models calculated
using the same SPEXACT version should produce the same results.
Please note that the SPEXACT database and routines are an integrated part of SPEX and are
not distributed separately.
1.3.1 Main version number definition
SPEXACT v1: Is essentially the MEKAL model that was developed in the 1980’s and is
distributed with Xspec. This model is no longer developed or supported, but can be regarded
as the first version of SPEXACT. It is no longer included in SPEX.
SPEXACT v2: In SPEX version 1 & 2, the original MEKAL model was extended and updated
into SPEX. The version number of this SPEXACT version is the same as the version number of
SPEX when it was released. For example, the SPEXACT version in SPEX version 2.04.00 is also
2.04.00. In SPEX version 3, these routines are still the default and are used in var calc old
mode.
SPEXACT v3: These are the newly developed atomic database and corresponding routines
that were officially released with SPEX version 3.00.00. This database and its routines are not
(yet) the default in SPEX but can be used when the var calc new command is given. The
second number in the SPEXACT version is the same as the SPEX version it was released in.
The third number can in principle be different from the SPEX version and indicates the minor
version of the database.
1.4 Changes introduced in SPEX 3.0
What is new in SPEX version 3.00 compared to SPEX 2.06? Most of the changes are actually
“under the hood” of the SPEX program and are only noticed when model fits are compared,
but we also provide useful new model additions. A more detailed overview of the changes in the
plasma models can be found in Section 5.1. The most important changes are summarized here:
• The first version of the new atomic database prepared by Ton Raassen is included in this
release. It contains hundreds of thousands of energy levels from hydrogen to zinc. The
14 Introduction
new database is not yet enabled by default (see command var calc new). Using the new
line database requires more memory and CPU time then before, which may not be needed
in every case. Enable the new line list if you need more accuracy, for example when you
fit high-resolution spectra.
• We have optimized the calculation of the radiative recombination, di-electronic recombination,
two-photon, and proton excitation processes to be able to calculate a spectrum
from the new atomic data within a reasonable time. The results from full calculations were
approximated by functions that can be calculated much faster, which allows the fitting of
complicated spectra with models containing a large range of physical parameters of the
plasma.
• The photo-ionization model pion has been substantially improved. It is now possible to
model several absorption layers with including their radiative transfer. Also the emission
part is implemented. However, use with care since this model is still experimental.
• We included natural & Voigt broadening to SPEX emission models.
• We introduce a new charge exchange model (cx) developed by Gu et al. (2016).
• We added the ebv component in SPEX to model interstellar extinction.
• There are now interfaces to include your own model in SPEX . Use com user for additive
models and com musr for multiplicative models. Examples of how to use this model
component are shown in the revised SPEX Cookbook. It also allows you to call Xspec
models from SPEX .
• We added a line emission/absorption model with a Voigt profile (com line) to model
individual lines.
• Contour plots of χ2 values from the steppar command can now be plotted using the
stepcontour task. The steppar command can now export the results to an ASCII file
that stepcontour can convert into a quick contour plot (or QDP file).
• The SPEX syntax has been slightly changed. From now on, all ranges can be written
with a ’:’ in between to improve the consistency of the syntax. For example, changing the
X axis of a plot can now be written as: plot rx 0.1:10. Affected commands are plot,
egrid, elim, dem chireg, step axis, and par ... range. If possible, the old syntax
was also kept alive. Check the manual for details.
• C-statistics, the Bryans et al. (2009) ionization balance and the proto-solar abundances by
Lodders et al. (2009) are now the default in SPEX. The abundance table and the ionisation
balance can now be queried using the commands abun show and ibal show, respectively.
1.4.1 Changes in version 3.01
• To optimize for calculation speed, in the new line list, one can select ions that should be
calculated the old way (ions old) or the new way (ions new). The syntax is the same
as the ions ignore and ions use commands.
• Added sorting option to the command asc ter ... line to sort lines based on emissivity.
1.4 Changes introduced in SPEX 3.0 15
• In version 3.00.00 (using the new line database, var calc new), we had also included
dielectronic satellite lines of He-like ions of the type 1s2 => 2s 2p2, which actually are
trielectronic recombination lines. The 2s 2p2 levels decay rapidly through radiation of
a photon (2p to 1s transition) to the 1s 2s 2p level, which decays further by a similar
transition to the 1s2 2s ground state of Li-like iron. Therefore, our model predicts relatively
strong satellite lines from these transitions, stronger than present in corresponding EBIT
spectra. We have resolved this issue by for this moment omitting transitions from these
triply excited states from the calculations. Note they were/are absent in SPEX version
2.0 or all APEC versions.
• The new CIE model did not reproduce the x/y line ratio in He-like iron very well. The
x & y lines are the two intercombination lines in this ion. We traced this problem down
to some confusion caused by different notations for line levels. The NIST database, the
Cowan code, Chianti use different notations for the same transition: some use 1s2s(3S)2p
2P1/2, others 1s2s(1S)2p 2P1/2 for the same transition (same if you compare the values of
the corresponding energy levels). Some others couple the 2s and 2p electrons first, leading
to P states, and then attach the 1s electron to it, leading to again different notations.
This confusion led to an interchange of collisonal and radiative rates between some levels,
thereby affecting the x/y line intensities. This has now been fixed.
• The innershell levels and related auger and radiative transitions for Fe XIX to Fe XXIII
are added using the data from Palmeri et al. (2003a).
1.4.2 Changes in version 3.02.00
• Updated pion model (details will be described soon).
• Re-installed the tri-electronic recombination transistions (details will be described soon).
• Introduced the SPEXACT naming and versioning for the atomic code and tables in SPEX.
1.4.3 Changes in version 3.03.00
In SPEX 3.03.00:
• Fixed bug related to opening many fits files.
• Fixed bug in data merge regarding the deallocation of the derivative array.
• Fixed bug in the calculation of the average exposure time in data show.
In SPEXACT 3.03.00:
• Fixed bug in generation of atomic data files.
• Added Auger rates for O V, Ne VII, Fe XIII.
• Ionization limits added for Mg IX, Si XI, S XIII, Ar XV.
• Atomic data extended including autoionisation for Be-like ions.
16 Introduction
• Added correction for auto-ionization for excitation and inner-shell ionisation to doubly
excited levels.
• Update and bugfix for CX model (H-H collision).
• Updated ionisation balance for U16.
1.4.4 Changes in version 3.04.00
In SPEX 3.04.00:
• The ionisation balance is now by default Urdampilleta et al. (2017). The actual data did
not change, but the paper was published in 2017. The command ibal u16 still works,
but gives a warning message that the actual command is ibal u17 from now on.
• Fixed bug in stepcontour program related to logarithmic grids.
In SPEXACT 3.04.00:
• Fixed bugs in the CIE, NEIJ, CX and PION models.
• Included radiative recombination cooling following Mao et al. (2017).
• Updates of PION model.
• Updated Auger rates for Be-like to C-like Fe.
• Ni XXI of the O-like added and some Fe ions extended.
• Now we multiply the emission measure by ne/nH in the pion model. This will result in
typically 20% more emission from the pion model.
• Added the tmod option to the pion model (see 4.29), allowing to set the temperature and
not solve for energy balance (useful for hot stars, the WHIM etc.).
• Allowed to use multiple solutions in the pion model (fmod and soln parameters).
• Allowed for external heating source in the pion model (exth parameter).
• Extended the pion model with all elements from Z=1 to Z=30.
• Fe XX levels modified to Nist5.
• Bug fix: Now we use the proper argument 2 (y) in the call to the integrated Voigt function
sivf. The Lorentzian component is now 2x narrower than before, which does affect the
CIE emission spectra. It does not affect ”old” xabs, hot calculations etc.
• Extended data for Fe XXI, Fe XXII, and Fe XXIII.
1.5 Document structure 17
1.5 Document structure
This document has been divided in the following sections:
• Chapter 1, is an introduction of SPEX Reference Manual contents.
• Chapter 2, is a brief explanation of spectral fitting philosphy, the initial information needed
and code used in SPEX .
• Chapter 3, lists the main syntax used in SPEX .
• Chapter 4, contains an overview of all spectral components and models.
• Chapter 5, explains additional spectral models.
• Chapter 6, describes the tool used for plotting.
• Chapter 7, lists the auxiliary programs needed in some cases for using SPEX .
• Chapter 8, includes guidelines about how to construct a proper response matrix .
• Chapter 9, gives some instructions to test SPEX after the installation.
• Chapter 10, contains the acknowlegements.
1.6 Additional information and documents
1.6.1 SPEX Cookbook: Examples
In addition to the current manual, we have updated the SPEX cookbook, which contains several
useful hints and examples of how to analyse X-ray spectra. The HTML version of the cookbook
can be found at http://var.sron.nl/SPEX-doc/cookbook or find it in the manual section of
the SPEX web site: http://www.sron.nl/spex
1.6.2 Physical background of spectral models
Apart from Chapter 5 of this manual, other books and documents that describe the physical
backgrounds are also available.
The fundamentals of the SPEX code are summarized in SRON/SPEX/TRPB01, which can
be downloaded from the SPEX website: https://www.sron.nl/astrophysics-spex/physics.
The documents below describe the basics of the main emission processes in the older MEKAL
code and the basics of multi-temperature analysis:
• Ionization and Energy balance in Collisionally and Photoionized Plasmas
(SRON/SPEX/TRPB02)
• Continuum Radiation Processes (SRON/SPEX/TRPB03)
• Line Excitation Processes (SRON/SPEX/TRPB04)
• Differential Emission Measure Analysis (SRON/SPEX/TRPB05)
18 Introduction
Updates on the physics and application of these older codes can be found in the books Kaastra
(2008) and Kaastra & Paerels (2011).
The official SPEX website is:
http://www.sron.nl/spex
Chapter 2
Spectral Fitting
2.1 Spectral Modelling
To infer relevant physical parameters from observed X-ray spectra, physical models are needed.
The models need to calculate the expected X-ray spectrum based on physical parameters, like the
electron temperature, emission measure and density distributions, ion and elemental abundances,
mass motions, and the nature of the ambient radiation field. Unfortunately, the physical models
cannot be compared directly to the measured spectra, because the instruments used to obtain
the spectra change the spectrum for example by adding background components (instrument
noise), change the continuum shape due to the sensitivity of the mirror (effective area), and blur
spectral lines due to the instruments spectral resolution.
To take these instrumental components into account, the usual procedure is to apply a forward
modelling technique by convolving theoretical model spectra with the instrumental response
and to vary the model parameters in order to optimize the fit of the model to the observational
data. A common approach is to consider first a simplified plasma model for the X-ray source,
neglecting much of the complexity of the temperature and density structure and of the effects
of opacity, and to synthesize such models into successively more sophisticated approximations
of the source model.
In Figure 2.1 we give in a processing flow diagram schematically the process of spectral modelling
for the case of optically thin coronal plasmas. The synthetic spectra program is fed with
input parameters from the spectral model (atomic data for ionization and line and continuum
excitation), the instrumental model, and from the assumed plasma model for the source. The
synthetic spectra code generates spectra which can be compared to the observations and tested
by means of statistical fitting procedures.
2.2 Sectors and regions
2.2.1 Introduction
In many cases an observer analysis the observed spectrum of a single X-ray source. There are
however situations with more complex geometries.
Example 1: An extended source, where the spectrum may be extracted from different regions
of the detector, but where these spectra need to be analysed simultaneously due to the overlap
20 Spectral Fitting
Figure 2.1: Processing Flow Diagram for Spectral Modelling of optically thin plasmas (from Mewe
1992).
2.2 Sectors and regions 21
in point-spread function from one region to the other. This situation is e.g. encountered in the
analysis of cluster data with ASCA or BeppoSAX.
Example 2: For the RGS detector of XMM-Newton, the actual data-space in the dispersion
direction is actually two-dimensional: the position z where a photon lands on the detector and
its energy or pulse height E as measured with the CCD detector. X-ray sources that are extended
in the direction of the dispersion axis φ are characterised by spectra that are a function of both
the energy E and off-axis angle φ. The sky photon distribution as a function of (φ,E) is then
mapped onto the (z,E)-plane. By defining appropriate regions in both planes and evaluating
the correct (overlapping) responses, one may analyse extended sources.
Example 3: One may also fit simultaneously several time-dependent spectra using the same
response, e.g. data obtained during a stellar flare.
It is relatively easy to model all these situations (provided that the instrument is understood
sufficiently, of course), as we show below.
2.2.2 Sky sectors
First, the relevant part of the sky is subdivided into sectors, each sector corresponding to a
particular region of the source, for example a circular annulus centered around the core of a
cluster, or an arbitrarily shaped piece of a supernova remnant, etc.
A sector may also be a point-like region on the sky. For example if there is a bright point source
superimposed upon the diffuse emission of the cluster, we can define two sectors: an extended
sector for the cluster emission, and a point-like sector for the point source. Both sectors might
even overlap, as this example shows!
Another example: the two nearby components of the close binary α Centauri observed with
the XMM -Newton instruments, with overlapping point-spread-functions of both components.
In that case we would have two point-like sky sectors, each sector corresponding to one of the
double star’s components.
The model spectrum for each sky sector may and will be different in general. For example, in
the case of an AGN superimposed upon a cluster of galaxies, one might model the spectrum of
the point-like AGN sector using a power law, and the spectrum from the surrounding cluster
emission using a thermal plasma model.
2.2.3 Detector regions
The observed count rate spectra are extracted in practice in different regions of the detector.
It is necessary here to distinguish clearly the (sky) sectors and (detector) regions. A detector
region for the XMM EPIC camera would be for example a rectangular box, spanning a certain
number of pixels in the x- and y-directions. It may also be a circular or annular extraction region
centered around a particular pixel of the detector, or whatever spatial filter is desired. For the
XMM RGS it could be a specific ”banana” part of the detector-coordinate CCD pulse-height
plane (z,E).
Note that the detector regions need not to coincide with the sky sectors, neither should their
number to be equal! A good example of this is again the example of an AGN superimposed
upon a cluster of galaxies. The sky sector corresponding to the AGN is simply a point, while,
for a finite instrumental psf, its extraction region at the detector is for example a circular region
centered around the pixel corresponding to the sky position of the source.
22 Spectral Fitting
Also, one could observe the same source with a number of different instruments and analyse the
data simultaneously. In this case one would have only one sky sector but more detector regions,
namely one for each participating instrument.
2.3 Different types of spectral components
In a spectral model SPEX uses three different types of components, called additive, multiplicative,
and hybrid components respectively. Additive components have a normalisation that
determines the flux level. Multiplicative components operate on additive components. The pion
model is a hybrid model that models both the absorption and emission from an intervening slab
of plasma. A delta line or a power law are typical examples of additive components. Interstellar
absorption is a typical example of a multiplicative component.
The redshift component is treated as a multiplicative component, since it operates on additive
components.
Additive components can be divided into two classes: simple components (like power law, blackbody
etc.) and plasma components, that use our atomic code. For the plasma components it is
possible to plot or list specific properties, while for the simple models this is not applicable.
Multiplicative components can be divided into 3 classes. First, there are the absorption-type
components, like interstellar absorption. These components simply are an energy-dependent
multiplication of the original source spectrum. SPEX has both simple absorption components
as well as absorption components based upon our plasma code. The second class consists of
shifts: redshift (either due to Doppler shifts or due to cosmology) is the prototype of this. The
third class consists of convolution-type operators. An example is Gaussian velocity broadening.
For more information about the currently defined spectral components in SPEX, see chapter 4.
Chapter 3
Syntax overview
3.1 Introduction
This chapter contains a brief explanation of the most relevant syntax used in SPEX. Each
subchapter is divided in an overview, an explanation of the use of syntax followed by some
practical examples.
3.2 Abundance: standard abundances
Overview
For the plasma models, a default set of abundances is used. All abundances are calculated relative
to those standard values. The current default abundance set are the proto-Solar abundances
of Lodders et al. (2009). Note that in older versions of SPEX, Anders & Grevesse (1989) was
the default. In particular, we recommend to use the proto-Solar (= Solar system) abundances
for most applications, as the Solar photospheric abundance has been affected by nucleosynthesis
(burning of H to He) and settlement in the Sun during its lifetime. The following abundances
(Table 3.1) can be used in SPEX:
Table 3.1: Standard abundance sets
Abbrevation Reference
reset default (= Lodders et al. 2009)
ag Anders & Grevesse (1989)
allen Allen (1973)
ra Ross & Aller (1976)
grevesse Grevesse et al. (1992)
gs Grevesse & Sauval (1998))
lodders Lodders proto-Solar (Lodders 2003)
solar Lodders Solar photospheric (Lodders 2003))
For the case of Grevesse & Sauval (1998) we adopted their meteoritic values (in general more
accurate than the photospheric values, but in most cases consistent), except for He (slightly
enhanced in the solar photosphere due to element migration at the bottom of the convection
zone), C, N and O (largely escaped from meteorites) Ne and Ar (noble gases).
24 Syntax overview
In Table 3.2 we show the values of the standard abundances. They are expressed in logarithmic
units, with hydrogen by definition 12.0. For Allen (1973) the value for boron is just an upper
limit.
Table 3.2: Abundances for the standard sets
Z elem Default AG Allen RA Grevesse GS Lodders solar
1 H 12.000 12.00 12.00 12.00 12.00 12.00 12.00 12.00
2 He 10.987 10.99 10.93 10.80 10.97 10.99 10.98 10.90
3 Li 3.331 1.16 0.70 1.00 1.16 3.31 3.35 3.28
4 Be 1.373 1.15 1.10 1.15 1.15 1.42 1.48 1.41
5 B 2.860 2.6 <3.0 2.11 2.6 2.79 2.85 2.78
6 C 8.443 8.56 8.52 8.62 8.55 8.52 8.46 8.39
7 N 7.912 8.05 7.96 7.94 7.97 7.92 7.90 7.83
8 O 8.782 8.93 8.82 8.84 8.87 8.83 8.76 8.69
9 F 4.491 4.56 4.60 4.56 4.56 4.48 4.53 4.46
10 Ne 8.103 8.09 7.92 7.47 8.08 8.08 7.95 7.87
11 Na 6.347 6.33 6.25 6.28 6.33 6.32 6.37 6.30
12 Mg 7.599 7.58 7.42 7.59 7.58 7.58 7.62 7.55
13 Al 6.513 6.47 6.39 6.52 6.47 6.49 6.54 6.46
14 Si 7.586 7.55 7.52 7.65 7.55 7.56 7.61 7.54
15 P 5.505 5.45 5.52 5.50 5.45 5.56 5.54 5.46
16 S 7.210 7.21 7.20 7.20 7.21 7.20 7.26 7.19
17 Cl 5.299 5.5 5.60 5.50 5.5 5.28 5.33 5.26
18 Ar 6.553 6.56 6.90 6.01 6.52 6.40 6.62 6.55
19 K 5.161 5.12 4.95 5.16 5.12 5.13 5.18 5.11
20 Ca 6.367 6.36 6.30 6.35 6.36 6.35 6.41 6.34
21 Sc 3.123 1.10 1.22 1.04 3.20 3.10 3.15 3.07
22 Ti 4.979 4.99 5.13 5.05 5.02 4.94 5.00 4.92
23 V 4.042 4.00 4.40 4.02 4.00 4.02 4.07 4.00
24 Cr 5.703 5.67 5.85 5.71 5.67 5.69 5.72 5.65
25 Mn 5.551 5.39 5.40 5.42 5.39 5.53 5.58 5.50
26 Fe 7.514 7.67 7.60 7.50 7.51 7.50 7.54 7.47
27 Co 4.957 4.92 5.10 4.90 4.92 4.91 4.98 4.91
28 Ni 6.276 6.25 6.30 6.28 6.25 6.25 6.29 6.22
29 Cu 4.319 4.21 4.50 4.06 4.21 4.29 4.34 4.26
30 Zn 4.700 4.60 4.20 4.45 4.60 4.67 4.70 4.63
Warning: For Allen (1973) the value for boron is just an upper limit.
The current active solar abundance table can be shown using the command abundance show.
Syntax
The following syntax rules apply:
abundance #a - Set the standard abundances to the values of reference #a in the table above.
abundance show - Show the currently active abundance table.
3.3 Ascdump: ascii output of plasma properties 25
Examples
abundance gs - change the standard abundances to the set of Grevesse & Sauval (1998)
abundance reset - reset the abundances to the standard set
abundance show - show the currently active abundance table
3.3 Ascdump: ascii output of plasma properties
Overview
One of the drivers in developing SPEX is the desire to be able to get insight into the astrophysics
of X-ray sources, beyond merely deriving a set of best-fit parameters like temperature or
abundances. The general user might be interested to know ionic concentrations, recombination
rates etc. In order to facilitate this SPEX contains options for ascii-output.
Ascii-output of plasma properties can be obtained for any spectral component that uses the
basic plasma code of SPEX; for all other components (like power law spectra, gaussian lines,
etc.) this sophistication is not needed and therefore not included. There is a choice of properties
that can be displayed, and the user can either display these properties on the screen or write it
to file.
The possible output types are listed below. Depending on the specific spectral model, not all
types are allowed for each spectral component. The keyword in front of each item is the one
that should be used for the appropriate syntax.
plas: basic plasma properties like temperature, electron density etc.
abun: elemental abundances and average charge per element.
icon: ion concentrations, both with respect to Hydrogen and the relevant elemental abundance.
rate: total ionization, recombination and charge-transfer rates specified per ion.
rion: ionization rates per atomic subshell, specified according to the different contributing pro-
cesses.
pop: the occupation numbers as well as upwards/downwards loss and gain rates to all quantum
levels included.
lev: the contributions to the pouplation of the energy levels by various processes: positive for
gain, negative for loss
elex: the collisional excitation and de-excitation rates for each level, due to collisions with
electrons.
prex: the collisional excitation and de-excitation rates for each level, due to collisions with
protons.
rad: the radiative transition rates from each level.
two: the two-photon emission transition rates from each level.
26 Syntax overview
grid: the energy and wavelength grid used in the last evaluation of the spectrum.
clin: the continuum, line and total spectrum for each energy bin for the last plasma layer of
the model.
line: the line energy and wavelength, as well as the total line emission (photons/s) for each
line contributing to the spectrum, for the last plasma layer of the model. Also given
is the natural line width and the Doppler broadening (including thermal and turbulent
broadening), expressed as a FWHM in keV. Optionally, the results can be sorted according
to various columns as follows (first description, between brackets the acronym): energy
(ener), wavelength (wav), ion (ion), line power (powe), natural line width (wid).
con: list of the ions that contribute to the free-free, free-bound and two-photon continuum
emission, followed by the free-free, free-bound, two-photon and total continuum spectrum,
for the last plasma layer of the model.
tcl: the continuum, line and total spectrum for each energy bin added for all plasma layers of
the model.
tlin: the line energy and wavelength, as well as the total line emission (photons/s) for each line
contributing to the spectrum, added for all plasma layers of the model.
tcon: list of the ions that contribute to the free-free, free-bound and two-photon continuum
emission, followed by the free-free, free-bound, two-photon and total continuum spectrum,
added for all plasma layers of the model.
cnts: the number of counts produced by each line. Needs an instrument to be defined before.
nei: the history of ionisation parameter and temperature in NEI calculations.
snr: hydrodynamical and other properties of the supernova remnant (only for supernova remnant
models such as Sedov, Chevalier etc.).
heat: plasma heating rates (only for photoionized plasmas).
ebal: the energy balance contributions of each layer (only for photoionized plasmas).
dem: the emission measure distribution (for the pdem model)
col: the ionic column densities for the hot, pion, slab, xabs and warm models
tran: the transmission and equivalent width of absorption lines and absorption edges for the
hot, pion, slab, xabs and warm models. Optionally, the results (lines only) can be sorted
according to various columns as follows (first description, between brackets the acronym):
energy (ener), wavelength (wav), ion (ion), optical depth at line center (tau), equivalent
width in keV (ewk), equivalent width in ˚A (ewa), Voigt a parameter (avo).
warm: the column densities, effective ionization parameters and temperatures of the warm
model
3.4 Bin: rebin the spectrum 27
Syntax
The following syntax rules apply for ascii output:
ascdump terminal #i1 #i2 #a - Dump the output for sky sector #i1 and component #i2 to
the terminal screen; the type of output is described by the parameter #a which is listed in the
table above.
ascdump file #a1 #i1 #i2 #a2 - As above, but output written to a file with its name given
by the parameter #a1. The suffix ”.asc” will be appended automatically to this filename.
ascdump terminal #i1 #i2 #a1 sort #a2 - Dump the output for sky sector #i1 and component
#i2 to the terminal screen; the type of output is described by the parameter #a1 which
is listed in the table above; the results are sorted according to parameter #a2. Sorting is only
possible for the ”line” and ”tran” options; see there for allowed entries.
ascdump file #a1 #i1 #i2 #a2 - As above, but output written to a file with its name given
by the parameter #a1. The suffix ”.asc” will be appended automatically to this filename.
Warning: Any existing files with the same name will be overwritten. Warning: Sorting
only possible for the line and tran options.
Examples
ascdump terminal 3 2 icon - dumps the ion concentrations of component 2 of sky sector 3 to
the terminal screen.
ascdump file mydump 3 2 icon - dumps the ion concentrations of component 2 of sky sector
3 to a file named mydump.asc.
ascdump terminal 3 2 line sort pow - dumps the emission line power of component 2 of sky
sector 3 to the terminal screen, sorted according to line strength.
3.4 Bin: rebin the spectrum
Overview
This command rebins the data (thus both the spectrum file and the response file) in a manner
as described in Sect. 3.7. The range to be rebinned can be specified either as a channel range
(no units required) or in eiter any of the following units: keV, eV, Rydberg, Joule, Hertz, ˚A,
nanometer, with the following abbrevations: kev, ev, ryd, j, hz, ang, nm.
Syntax
The following syntax rules apply:
bin #r #i - This is the simplest syntax allowed. One needs to give the range, #r, over at least
the input data channels one wants to rebin. If one wants to rebin the whole input file the range
must be at least the whole range over data channels (but a greater number is also allowed). #i
is then the factor by which the data will be rebinned.
bin [instrument #i1] [region #i2] #r #i - Here one can also specify the instrument and
region to be used in the binning. This syntax is necessary if multiple instruments or regions are
28 Syntax overview
used in the data input.
bin [instrument #i1] [region #i2] #r #i [unit #a] - In addition to the above here one
can also specify the units in which the binning range is given. The units can be eV, ˚A, or any
of the other units specified above.
Examples
bin 1:10000 10 - Rebins the input data channel 1:10000 by a factor of 10.
bin instrument 1 1:10000 10 - Rebins the data from the first instrument as above.
bin 1:40 10 unit a - Rebins the input data between 1 and 40 ˚A by a factor of 10.
3.5 Calculate: evaluate the spectrum
Overview
This command evaluates the current model spectrum. When one or more instruments are
present, it also calculates the model folded through the instrument. Whenever the user has
modified the model or its parameters manually, and wants to plot the spectrum or display
model parameters like the flux in a given energy band, this command should be executed first
(otherwise the spectrum is not updated). On the other hand, if a spectral fit is done (by typing
the ”fit” command) the spectrum will be updated automatically and the calculate command
needs not to be given.
Syntax
The following syntax rules apply:
calc - Evaluates the spectral model.
Examples
calc - Evaluates the spectral model.
3.6 Comp: create, delete and relate spectral components
Overview
In fitting or evaluating a spectrum, one needs to build up a model made out of at least 1
component. This set of commands can create a new component in the model, as well as delete
any component. Usually we distinguish two types of spectral components in SPEX.
The additive components correspond to emission components, such as a power law, a Gaussian
emission line, a collisional ionization equilibrium (CIE) component, etc.
3.6 Comp: create, delete and relate spectral components 29
The second class (dubbed here multiplicative components for ease) consists of operations to be
applied to the additive components. Examples are truly multiplicative operations, such as the
Galactic absorption, where the model spectrum of any additive component should be multiplied
by the transmission of the absorbing interstellar medium, warm absorbers etc. Other operations
contained in this class are redshifts, convolutions with certain velocity profiles, etc.
The user needs to define in SPEX which multiplicative component should be applied to which
additive components, and in which order. The order is important as operations are not always
communative. This setting is also done with this component command.
If multiple sectors are present in the spectral model or response matrix (see Sect. 2.2) then
one has to specify the spectral components and their relation for each sector. The possible
components to the model are listed and described in Sect. 4.
Note that the order that you define the components is not important. However, for each sector,
the components are numbered starting from 1, and these numbers should be used when relating
the multiplicative components to the additive components.
If you want to see the model components and the way they are related, type ”model show”.
Warning: If in any of the commands as listed above you omit the sector number or sector
number range, the operation will be done for all sectors that are present. For example, having
3 sectors, the ”comp pow” command will define a power law component for each of the three
sectors. If you only want to define/delete/relate the component for one sector, you should specify
the sector number(s). In the very common case that you have only one sector you can always
omit the sector numbers.
Warning: After deleting a component, all components are re-numbered! So if you have
components 1,2,3 for example as pow, cie, gaus, and you type ”comp del 2”, you are left with
1=pow, 2=gaus.
Syntax
The following syntax rules apply:
comp [#i:] #a - Creates a component #a as part of the model for the (optional) sector range
#i:
comp delete [#i1:] #i2: - Deletes the components with number from range #i2: for sector
range (optional) #i1. See also the warning above
comp relation [#i1:] #i2: #i3,...,#in - Apply multiplicative components #i3, . . . , #in
(numbers) in this order, to the additive components given in the range #i2: of sectors in the
range #i1 (optional). Note that the multiplicative components must be separated by a ”,”
Examples
comp pow - Creates a power-law component for modeling the spectrum for all sectors that are
present.
comp 2 pow - Same as above, but now the component is created for sector 2.
comp 4:6 pow - Create the power law for sectors 4, 5 and 6
com abs - Creates a Morrison & McCammon absorption component.
comp delete 2 - Deletes the second created component. For example, if you have 1 = pow, 2
= cie and 3 = gaus, this command delets the cie component and renumbers 1 = pow, 2 = gaus
30 Syntax overview
comp del 1:2 - In the example above, this will delete the pow and cie components and renumbers
now 1 = gaus
comp del 4:6 2 - If the above three component model (pow, cie, gaus) would be defined for 8
sectors (numbered 1–8), then this command deletes the cie component (nr. 2) for sectors 4–6
only.
comp rel 1 2 - Apply component 2 to component 1. For example, if you have defined before
with ”comp pow” and ”comp ”abs” a power law and galactic absorption, the this command tells
you to apply component 2 (abs) to component 1 (pow).
comp rel 1 5,3,4 - Taking component 1 a power law (pow), component 3 a redshift operation
(reds), component 4 galactic absorption (abs) and component 5 a warm absorber (warm), this
command has the effect that the power law spectrum is multiplied first by the transmission of
the warm absorber (5=warm), then redshifted (3=reds) and finally multiplied by the transmission
of our galaxy (4=abs). Note that the order is always from the source to the observer!
comp rel 1:2 5,3,4 - Taking component 1 a power law (pow), component 2 a gaussian line
(gaus), and 3–5 as above, this model applies multiplicative components 5, 3 and 4 (in that orer)
to the emission spectra of both component 1 (pow) and 2 (cie).
comp rel 7:8 1:2 5,3,4 - As above, but only for sectors 7 and 8 (if those are defined).
comp rel 3 0 - Remove all relations from component 3.
3.7 Data: read response file and spectrum
Overview
In order to fit an observed spectrum, SPEX needs a spectral data file and a response matrix.
These data are stored in FITS format, tailored for SPEX (see section 8.2). The data files need
not necessarily be located in the same directory, one can also give a pathname plus filename in
this command.
Warning: Filenames should be entered in the data command without their extension. For
the files response.res and spectrum.spo, the data command would look like: data response
spectrum.
Syntax
The following syntax rules apply:
data #a1 #a2 - Read response matrix #a1 and spectrum #a2
data delete instrument #i - Remove instrument #i from the data set
data merge sum #i: - Merge instruments in range #i: to a single spectrum and response matrix,
by adding the data and matrices
data merge aver #i: - Merge instruments in range #i: to a single spectrum and response
matrix, by averaging the data and matrices
data save #i #a [overwrite] - Save data #a from instrument #i with the option to overwrite
the existent file. SPEX automatically tags the .spo extension to the given file name. No
response file is saved.
data show - Shows the data input given, as well as the count (rates) for source and background,
the energy range for which there is data the response groups and data channels. Also the integration
time and the standard plotting options are given.
3.8 DEM: differential emission measure analysis 31
Examples
data mosresp mosspec - read a spectral response file named mosresp.res and the corresponding
spectral file mosspec.spo. Hint, although 2 different names are used here for ease of understanding,
it is eased if the spectrum and response file have the same name, with the appropriate
extension.
data delete instrument 1 - delete the first instrument
data merge aver 3:5 - merge instruments 3–5 into a single new instrument 3 (replacing the
old instrument 3), by averaging the spectra. Spectra 3–5 could be spectra taken with the same
instrument at different epochs.
data merge sum 1:2 - add spectra of instruments 1–2 into a single new instrument 1 (replacing
the old instrument 1), by adding the spectra. Useful for example in combining XMM-Newton
MOS1 and MOS2 spectra.
data save 1 mydata - Saves the data from instrument 1 in the working directory under the
filename of mydata.spo
data /mydir/data/mosresp /mydir/data/mosspec - read the spectrum and response from the
directory /mydir/data/
3.8 DEM: differential emission measure analysis
Overview
SPEX offers the opportunity to do a differential emission measure analysis. This is an effective
way to model multi-temperature plasmas in the case of continuous temperature distributions or
a large number of discrete temperature components.
The spectral model can only have one additive component: the DEM component that corresponds
to a multi-temperature structure. There are no restrictions to the number of multiplicative
components. For a description of the DEM analysis method see document SRON/SPEX/TRPB05
(in the documentation for version 1.0 of SPEX), Mewe et al. (1994), Mewe et al. (1995) and
Kaastra et al. (1996b).
SPEX has 5 different dem analysis methods implemented, as listed shortly below. We refer to
the above papers for more details.
1. reg – Regularization method (minimizes second order derivative of the DEM; advantage:
produces error bars; disadvantage: needs fine-tuning with a regularization parameter and
can produce negative emission measures.
2. clean – Clean method: uses the clean method that is widely used in radio astronomy.
Useful for ”spiky emission measure distributions.
3. poly – Polynomial method: approximates the DEM by a polynomial in the log T −− log Y
plane, where Y is the emission measure. Works well if the DEM is smooth.
4. mult – Multi-temperature method: tries to fit the DEM to the sum of Gaussian components
as a function of log T. Good for discrete and slightly broadened components, but may not
32 Syntax overview
always converge.
5. gene – Genetic algorithm: using a genetic algorithm try to find the best solution. Advantage:
rather robust for avoiding local subminima.Disadvantage: may require a lot of cpu
time, and each run produces slightly different results (due to randomization).
In practice to use the DEM methods the user should do the following steps:
1. Read and prepare the spectral data that should be analysed
2. Define the dem model with the ”comp dem” command
3. Define any multiplicative models (absorption, redshifts, etc.) that should be applied to
the additive model
4. Define the parameters of the dem model: number of temperature bins, temperature range,
abundances etc.
5. give the ”dem lib” command to create a library of isothermal spectra.
6. do the dem method of choice (each one of the five methods outlined above)
7. For different abundances or parameters of any of the spectral components, first the ”dem
lib” command must be re-issued!
Syntax
The following syntax rules apply:
dem lib - Create the basic DEM library of isothermal spectra
dem reg auto - Do DEM analysis using the regularization method, using an automatic search
of the optimum regularization parameter. It determines the regularisation parameter R in such
a way that χ2(R) = χ2(0)[1 + s 2/(n − nT] where the scaling factor s = 1, n is the number
of spectral bins in the data set and nT is the number of temperature components in the DEM
library.
dem reg auto #r - As above, but for the scaling factor s set to #r.
dem reg #r - Do DEM analysis using the regularization method, using a fixed regularization
parameter R =#r.
dem chireg #r1:#r2 #i - Do a grid search over the regularization parameter R, with #i steps
and R distributed logarithmically between #r1 and #r2. Useful to scan the χ2(R) curve whenever
it is complicated and to see how much ”penalty’ (negative DEM values) there are for each
value of R.
dem clean - Do DEM analysis using the clean method
dem poly #i - Do DEM analysis using the polynomial method, where #i is the degree of the
polynomial
dem mult #i - Do DEM analysis using the multi-temperature method, where #i is the number
of broad components
dem gene #i1 #i2 - Do DEM analysis using the genetic algorithm, using a population size
given by #i1 (maximum value 1024) and #i2 is the number of generations (no limit, in practice
after ∼100 generations not much change in the solution. Experiment with these numbers for
your practical case.
3.9 Distance: set the source distance 33
dem read #a - Read a DEM distribution from a file named #a which automatically gets the
extension ”.dem”. It is an ascii file with at least two columns, the first column is the temperature
in keV and the second column the differential emission measure, in units of 1064 m−3 keV−1.
The maximum number of data points in this file is 8192. Temperature should be in increasing
order. The data will be interpolated to match the temperature grid defined in the dem model
(which is set by the user).
dem save #a - Save the DEM to a file #a with extension ”.dem”. The same format as above is
used for the file. A third column has the corresponding error bars on the DEM as determined
by the DEM method used (not always relevant or well defined, exept for the regularization
method).
dem smooth #r - Smoothes a DEM previously determined by any DEM method using a block
filter/ Here #r is the full width of the filter expressed in 10 log T. Note that this smoothing will
in principle worsen the χ2 of the solution, but it is sometimes useful to ”wash out” some residual
noise in the DEM distribution, preserving total emission measure.
Examples
dem lib - create the DEM library
dem reg auto - use the automatic regularization method
dem reg 10. - use a regularization parameter of R = 10 in the regularization method
dem chireg 1.e-5:1.e5 11 - do a grid search using 11 regularisation parameters R given by
10−5, 10−4, 0.001, 0.01, 0.1, 1, 10, 100, 1000, 104, 105.
dem clean - use the clean method
dem poly 7 - use a 7th degree polynomial method
dem gene 512 128 - use the genetic algorithm with a population of 512 and 128 generations
dem save mydem - save the current dem on a file named mydem.dem
dem read modeldem - read the dem from a file named modeldem.dem
dem smooth 0.3 - smooth the DEM to a temperature width of 0.3 in 10 log T (approximately a
factor of 2 in temperature range).
Recommended citation: Mewe et al. (1995).
3.9 Distance: set the source distance
Overview
One of the main principles of SPEX is that spectral models are in principle calculated at the
location of the X-ray source. Once the spectrum has been evaluated, the flux received at Earth
can be calculated. In order to do that, the distance of the source must be set.
SPEX allows for the simultaneous analysis of multiple sky sectors. In each sector, a different
spectral model might be set up, including a different distance. For example, a foreground object
that coincides partially with the primary X-ray source has a different distance value.
The user can specify the distance in a number of different units. Allowed distance units are
shown in the table below.
The default unit of 1022 m is internally used in all calculations in SPEX. The reason is that with
34 Syntax overview
Table 3.3: SPEX distance units
Abbrevation Unit
spex internal SPEX units of 1022 m (this is the default)
m meter
au Astronomical Unit, 1.49597892 1011 m
ly lightyear, 9.46073047 1015 m
pc parsec, 3.085678 1016 m
kpc kpc, kiloparsec, 3.085678 1019 m
mpc Mpc, Megaparsec, 3.085678 1022 m
z redshift units for the given cosmological parameters
cz recession velocity in km/s for the given cosmological parameters
this scaling all calculations ranging from solar flares to clusters of galaxies can be done with
single precision arithmetic, without causing underflow or overflow. For the last two units (z and
cz), it is necessary to specify a cosmological model. Currently this model is simply described by
H0, Ωm (matter density), ΩΛ (cosmological constant related density), and Ωr (radiation density).
At startup, the values are:
H0: 70 km/s/Mpc ,
Ωm: 0.3 ,
ΩΛ: 0.7 ,
Ωr: 0.0
i.e. a flat model with cosmological constant. However, the user can specify other values of the
cosmological parameters. Note that the distance is in this case the luminosity distance.
Note that the previous defaults for SPEX (H0 = 50, q0 = 0.5) can be obtained by putting
H0 = 50, Ωm = 1, ΩΛ = 0 and Ωr = 0.
Warning: when H0 or any of the Ω is changed, the luminosity distance will not change, but the
equivalent redshift of the source is adjusted. For example, setting the distance first to z=1 with
the default H0=70 km/s/Mpc results into a distance of 2.039 1026 m. When H0 is then changed
to 100 km/s/Mpc, the distance is still 2.168 1026 m, but the redshift is adjusted to 1.3342.
Warning: In the output also the light travel time is given. This should not be confused with
the (luminosity) distance in light years, which is simply calculated from the luminosity distance
in m!
Syntax
The following syntax rules apply to setting the distance:
distance [sector #i:] #r [#a] - set the distance to the value #r in the unit #a. This
optional distance unit may be omittted. In that case it is assumed that the distance unit is
the default SPEX unit of 1022 m. The distance is set for the sky sector range #i:. When the
optional sector range is omitted, the distance is set for all sectors.
distance show - displays the distance in various units for all sectors.
distance h0 #r - sets the Hubble constant H0 to the value #r.
3.10 Egrid: define model energy grids 35
distance om #r - sets the Ωm parameter to the value #r.
distance ol #r - sets the ΩΛ parameter to the value #r.
distance or #r - sets the Ωr parameter to the value #r.
Examples
distance 2 - sets the distance to 2 default units, i.e. to 2E22 m.
distance 12.0 pc - sets the distance for all sectors to 12 pc.
distance sector 3 0.03 z - sets the distance for sector 3 to a redshift of 0.03.
distance sector 2 : 4 50 ly - sets the distance for sectors 2-4 to 50 lightyear.
distance h0 50. - sets the Hubble constant to 50 km/s/Mpc.
distance om 0.27 - sets the matter density parameter Ωm to 0.27
distance show - displays the distances for all sectors, see the example below for the output
format.
SPEX> di 100 mpc
Distances assuming H0 = 70.0 km/s/Mpc, Omega_m = 0.300 Omega_Lambda = 0.700 Omega_r = 0.000
Sector m A.U. ly pc kpc Mpc redshift cz age(yr)
----------------------------------------------------------------------------------------------
1 3.086E+24 2.063E+13 3.262E+08 1.000E+08 1.000E+05 100.0000 0.0229 6878.7 3.152E+08
----------------------------------------------------------------------------------------------
3.10 Egrid: define model energy grids
Overview
SPEX operates essentially in two modes: with an observational data set (read using the data commands),
or without data, i.e. theoretical model spectra. In the first case, the energy grid neede to evaluate the
spectra is taken directly from the data set. In the second case, the user can choose his own energy grid.
The energy grid can be a linear grid, a logarithmic grid or an arbitrary grid read from an ascii-file. It
is also possible to save the current energy grid, whatever that may be. In case of a linear or logarithmic
grid, the lower and upper limit, as well as the number of bins or the step size must be given.
The following units can be used for the energy or wavelength: keV (the default), eV, Ryd, J, Hz, ˚A, nm.
When the energy grid is read or written from an ascii-file, the file must have the extension ”.egr”, and
contains the bin boundaries in keV, starting from the lower limit of the first bin and ending with the
upper limit for the last bin. Thus, the file has 1 entry more than the number of bins! In general, the
energy grid must be increasing in energy and it is not allowed that two neighbouring boundaries have
the same value.
Finally, the default energy grid at startup of SPEX is a logarithmic grid between 0.001 and 100 keV,
with 8192 energy bins.
Syntax
The following syntax rules apply:
egrid lin #r1:#r2 #i [#a] - Create a linear energy grid between #r1 and #r2, in units given by #a
(as listed above). If no unit is given, it is assumed that the limits are in keV. The number of energy bins
is given by #i
36 Syntax overview
egrid lin #r1:#r2 step #r3 [#a] - as above, but do not prescribe the number of bins, but the bin
width #r3. In case the difference between upper and lower energy is not a multiple of the bin width, the
upper boundary of the last bin will be taken as close as possible to the upper boundary (but cannot be
equal to it).
egrid log #r1:#r2 #i [#a] - Create a logarithmic energy grid between #r1 and #r2, in units given by
#a (as listed above). If no unit is given, it is assumed that the limits are in keV. The number of energy
bins is given by #i
egrid log #r1:#r2 step #r3 [#a] - as above, but do not prescribe the number of bins, but the bin
width (in log E) #r3.
egrid read #a - Read the energy grid from file #a.egr
egrid save #a - Save the current energy grid to file #a.egr
Warning: The lower limit of the energy grid must be positive, and the upper limit must always be larger
than the lower limit.
Examples
egrid lin 5:38 step 0.02 a - create a linear energy grid between 5 − 38 ˚A, with a step size of 0.02 ˚A.
egrid log 2:10 1000 - create a logarithmic energy grid with 1000 bins between 2 − 10 keV.
egrid log 2:10 1000 ev - create a logarithmic energy grid with 1000 bins between 0.002 − 0.010 keV.
egrid read mygrid - read the energy grid from the file mygrid.egr.
egrid save mygrid - save the current energy grid to file mygrid.egr.
3.11 Elim: set flux energy limits
Overview
SPEX offers the opportunity to calculate the model flux in a given energy interval for the current spectral
model. This information can be viewed when the model parameters are shown (see section 3.22).
For each additive component of the model, the following quantities are listed:
the observed photon number flux (photons m−2
s−1
) at earth, including any effects of galactic absorption
etc.
the observed energy flux (W m−2
) at earth, including any effects of galactic absorption etc.
the intrinsic number of photons emitted at the source, not diluted by any absorption etc., in photons s−1
.
the intrinsic luminosity emitted at the source, not diluted by any absorption etc., in W.
The following units can be used to designate the energy or wavelength range: keV (the default), eV, Ryd,
J, Hz, ˚A, nm.
Syntax
The following syntax rules apply:
elim #r1:#r2 [#a] - Determine the flux between #r1 #r2, in units given by #a, and as listed above.
The default at startup is 2 − 10 keV. If no unit is given, it is assumed that the limits are in keV.
Warning: When new units or limits are chosen, the spectrum must be re-evaluated (e.g. by giving the
”calc” comand) in order to determine the new fluxes.
3.12 Error: Calculate the errors of the fitted parameters 37
Warning: The lower limit must be positive, and the upper limit must always be larger than the lower
limit.
Examples
elim 0.5:4.5 - give fluxes between 0.5 and 4.5 keV
elim 500:4500 ev - give fluxes between 500 and 4500 eV (same result as above)
elim 5:38 a - give fluxes in the 5 to 38 ˚A wavelength band
3.12 Error: Calculate the errors of the fitted parameters
Overview
This command calculates the error on a certain parameter or parameter range, if that parameter is free
(thawn). Standard the 1σ error is calculated, which is equivalent to a 68 % confidence level. So ∆χ2
is
equal to 1 for a single parameter error. The ∆χ2
value can be set, such that for instance 90 % errors are
determined (see Table 3.4 for ∆χ2
values with their corresponding confidence levels).
SPEX determines the error bounds by iteratively modifying the parameter of interest and calculating χ2
as a function of the parameter. During this process the other free parameters of the model may vary.
The iteration stops when χ2
= χ2
min + ∆χ2
, where ∆χ2
is a parameter that can be set separately. The
iteration steps are displayed. It is advised to check them, because sometimes the fit at a trial parameter
converges to a different solution branch, therefore creating a discontinuous jump in χ2
. In those situations
it is better to find the error bounds by varying the search parameter by hand.
Note that SPEX remembers the parameter range for which you did your lat error search. This saves you
often typing in sector numbers or component numbers if you keep the same spectral component for your
next error search.
If the error search reveals a new minimum in χ2
space that was not found in the fit, SPEXwill save
the parameters of this new minimum in the file spex_lower_chi.com. After the error search these
parameters can be set through the command log exe spex_lower_chi, in order to direct the model to
the new minimum. Note that in the file spex_lower_chi.com the parameter for which the error was
calculated is ”frozen”.
Warning: A parameter must have the status ”thawn” in order to be able to determine its errors.
Warning: The first time that you use the error command, you need to provide the sector number before
it is remembered by SPEX. For example, error 1 1 norm
Syntax
The following syntax rules apply:
error [[[#i1:] #i2:] #a:] - Determine the error bars for the parameters specified by the sector
range #i1: (optional), component range #i2 (optional) and parameter range #a: (optional). If not specified,
the range for the last call will be used. On startup, this is the first parameter of the first component
of the first sector.
error dchi #r - This command changes the ∆χ2
, to the value #r. Default at startup and recommended
value to use is 1, for other confidence levels see Table 3.4.
error start #r - This command gives an initial guess of the error bar, from where to start searching the
relevant error. This can be helpful for determining the errors on normalization parameters, as otherwise
SPEX may from a rather small value. To return to the initial situation, put #r=0 (automatic error
search).
38 Syntax overview
Table 3.4: ∆χ2 as a function of confidence level, P, and degrees of freedom, ν.
ν
P 1 2 3 4 5 6
68.3% 1.00 2.30 3.53 4.72 5.89 7.04
90% 2.71 4.61 6.25 7.78 9.24 10.6
95.4% 4.00 6.17 8.02 9.70 11.3 12.8
99% 6.63 9.21 11.3 13.3 15.1 16.8
99.99% 15.1 18.4 21.1 13.5 25.7 27.8
Examples
error norm - Find the error for the normalization of the current component
error 2:3 norm:gamm - determines the error on all free parameters between ”norm” and ”gamm” for
components 2:3
error start 0.01 - Start calculating the error beginning with an initial guess of 0.01
error dchi 2.71 - Calculate from now onwards the 90 % error, for 1 degree of freedom. (Not recommended,
use standard 68 % errors instead!)
3.13 Fit: spectral fitting
Overview
With this command one fits the spectral model to the data. Only parameters that are thawn are changed
during the fitting process. Options allow you to do a weighted fit (according to the model or the data),
have the fit parameters and plot printed and updated during the fit, and limit the number of iterations
done.
At the moment SPEX uses two types of fit statistic, χ2
and C-stat. We first treat the χ2
statistic,
because historically that has been most widely used. However, in the present version of SPEX C-stat is
the default because in the far majority of the cases it gives more robust results.
Chi-squared fitting
First we make a few remarks about proper data weighting. χ2
is usually calculated as the sum over all
data bins i of (Ni − si)2
/σ2
i , i.e.
χ2
=
n
i=1
(Ni − si)2
σ2
i
, (3.1)
where Ni is the observed number of source plus background counts, si the expected number of source
plus background counts of the fitted model, and for Poissonian statistics usually one takes σ2
i = Ni.
Take care that the spectral bins contain sufficient counts (either source or background), recommended
is e.g. to use at least ∼10 counts per bin. If this is not the case, first rebin the data set whenever you
have a ”continuum” spectrum. For line spectra you cannot do this of course without loosing important
information! Note however that this method has inaccuracies if Ni is less than ∼100.
Wheaton et al. (1995) have shown that the classical χ2
method becomes inaccurate for spectra with
less than ∼ 100 counts per bin. This is not due to the approximation of the Poisson statistic by a
normal distribution, but due to using the observed number of counts Ni as weights in the calculation of
3.13 Fit: spectral fitting 39
χ2
. Wheaton et al. (1995) showed that the problem can be resolved by using instead σ2
i = si, i.e. the
expected number of counts from the best fit model.
The option ”fit weight model” allows to use these modified weights. By selecting it, the expected number
of counts (both source plus background) of the current spectral model is used onwards in calculating the
fit statistic. Wheaton et al. (1995) suggest to do the following 3-step process, which we also recommend
to the user of SPEX who uses this option:
1. first fit the spectrum using the data errors as weights (the default of SPEX).
2. After completing this fit, select the ”fit weight model” option and do again a fit
3. then repeat this step once more by again selecting ”fit weight model” in order to replace si of the
first step by si of the second step in the weights. The result should now have been converged (under
the assumption that the fitted model gives a reasonable description of the data, if your spectral
model is way off you are in trouble anyway!).
C-stat
There is yet another option to try for spectral fitting with low count rate statistics and that is maximum
likelyhood fitting. It can be shown that a good alternative to χ2
in that limit is
C = 2
n
i=1
si − Ni + Ni ln(Ni/si). (3.2)
This is strictly valid in the limit of Poissonian statistics. If you have a background subtracted spectrum,
take care that the subtracted number of background counts is properly stored in the spectral data file,
so that raw number of counts can be reconstructed.
This statistic was originally proposed in some other form by Cash (1979) and in the present form sometimes
attributed to Castor. However, it appears that it was already introduced and well explained by
Baker & Cousins (1984).
Warning: Note that for a spectrum with many counts per bin C → χ2
, but if the predicted number of
counts per bin is small, the expected value for C can be substantially smaller than the number of bins n.
To help the user to see if a C-value corresponds to an acceptable fit, SPEX gives, after spectral fitting,
the expected value of C and its r.m.s. spread, based on the best-fit model. Both quantities are simply
determined by adding the expected contributions and their variances over all bins. See Kaastra (2017)
for more details.
The expected value Ce for C in a bin i and its variance Cv are given by:
Ce = 2
∞
k=0
Pk(µ)(µ − k + k ln(k/µ)), (3.3)
Sv = 4
∞
k=0
Pk(µ)(µ − k + k ln(k/µ))2
, (3.4)
Cv = Sv − C2
e , (3.5)
with Pk(µ) the Poisson distribution:
Pk(µ) = e−µµk
/k! (3.6)
and µ the expected number of counts. We show both quantities in Fig. 3.1.
40 Syntax overview
10−7
10−6
10−5
10−4
10−3
0.01 0.1 1 10 100
00.511.5
ContributionperbintoCstat
µ
Mean
R.M.S.
Figure 3.1: Expected value of the contribution per bin to C, and its r.m.s. uncertainty, as a
function of the mean expected number of counts µ.
Syntax
The following syntax rules apply:
fit - Execute a spectral fit to the data.
fit print #i - Printing the intermediate results during the fitting to the screen for every n-th step,
with n=#i (most useful for n = 1). Default value: 0 which implies no printing of intermediate steps.
fit iter #i - Stop the fitting process after #i iterations, regardless convergence or not. This is useful
to get a first impression for very cpu-intensive models. To return to the default stop criterion, type fit
iter 0.
fit weight model - Use the current spectral model as a basis for the statistical weight in all subsequent
spectral fitting.
fit weight data - Use the errors in the spectral data file as a basis for the statistical weight in all
subsequent spectral fitting. This is the default at the start of SPEX.
fit method classical - Use the classical Levenberg-Marquardt minimisation of χ2
as the fitting method.
fit method cstat - Use the C-statistics instead of χ2
for the minimisation. This is the default at start-
up.
Examples
fit - Performs a spectral fit. At the end the list of best fit parameters is printed, and if there is a plot
this will be updated.
fit print 1 - If followed by the above fit command, the intermediate fit results are printed to the screen,
and the plot of spectrum, model or residuals is updated (provided a plot is selected).
fit iter 10 - Stop the after 10 iterations or earlier if convergence is reached before ten iterations are
completed.
fit iter 0 - Stop fitting only after full convergence (default).
fit weight model - Instead of using the data for the statistical weights in the fit, use the current model.
fit weight data - Use the data instead for the statistical weights in the fit.
fit method clas - Switch from χ2
to C-statistics.
3.14 Ibal: set type of ionisation balance 41
fit method cstat - Switch back to C-statistics.
3.14 Ibal: set type of ionisation balance
Overview
For the plasma models, different ionisation balance calculations are possible.
Currently, the default set is Arnaud & Rothenflug (1985) for H, He, C, N, O, Ne, Na, Mg, Al, Si, S, Ar,
Ca and Ni, with Arnaud & Raymond (1992)) for Fe. Table 3.5 lists the possible options.
Table 3.5: Ionisation balance modes
Abbrevation Reference
reset default (=u17)
ar85 Arnaud & Rothenflug (1985)
ar92 Arnaud & Raymond (1992) for Fe,
Arnaud & Rothenflug (1985) for the other elements
bryans09 Bryans et al. (2009)
u17 Urdampilleta et al. (2017) (default)
Syntax
The following syntax rules apply:
ibal #a - Set the ionisation balance to set #a with #a in the table above.
ibal show - Show the currently active ionisation balance.
Examples
ibal reset - Take the standard ionisation balance
ibal ar85 - Take the Arnaud & Rothenflug ionisation balance
3.15 Ignore: ignoring part of the spectrum
Overview
If one wants to ignore part of a data set in fitting the input model, as well as in plotting this command
should be used. The spectral range one wants to ignore can be specified as a range in data channels or a
range in wavelength or energy. Note that the first number in the range must always be smaller or equal
to the second number given. If multiple instruments are used, one must specify the instrument as well.
If the data set contains multiple regions, one must specify the region as well. So per instrument/region
one needs to specify which range to ignore. The standard unit chosen for the range of data to ignore is
data channels. To undo ignore, see the use command (see section 3.31).
The range to be ignored can be specified either as a channel range (no units required) or in either any
of the following units: keV, eV, Rydberg, Joule, Hertz, ˚A, nanometer, with the following abbrevations:
kev, ev, ryd, j, hz, ang, nm.
42 Syntax overview
Syntax
The following syntax rules apply:
ignore [instrument #i1] [region #i2] #r - Ignore a certain range #r given in data channels of instrument
#i1 and region #i2. The instrument and region need to be specified if there are more than 1
data sets in one instrument data set or if there are more than 1 data set from different instruments.
ignore [instrument #i1] [region #i2] #r unit #a - Same as the above, but now one also specifies
the unites #a in which the range #r of data points to be ignored are given. The units can be either
˚A(ang) or (k)eV.
Examples
ignore 1000:1500 - Ignores data channels 1000 till 1500.
ignore region 1 1000:1500 - Ignore data channels 1000 till 1500 for region 1.
ignore instrument 1 region 1 1000:1500 - Ignores the data channels 1000 till 1500 of region 1 from
the first instrument.
ignore instrument 1 region 1 1:8 unit ang - Same as the above example, but now the range is
specified in units of ˚A instead of in data channels.
ignore 1:8 unit ang - Ignores the data from 1 to 8 ˚A, only works if there is only one instrument and
one region included in the data sets.
3.16 Ion: select ions for the plasma models
Overview
For the plasma models, it is possible to include or exclude specific groups of ions from the line calulations.
This is helpful if a better physical understanding of the (atomic) physics behind the spectrum is requested.
Currently these settings only affect the line emission; in the calculation of the ionisation balance as well
as the continuum always all ions are taken into account (unless of course the abundance is put to zero).
A new quicklook mode is introduced in SPEX 3.0. This mode can greatly reduce computation time
by excluding the atomic levels of outer shells that barely affect the obtained spectrum. The maximum
quantum numbers n and l of Hydrogen-like ions are provided in Table 3.6.
Warning: This mode will not work for CX model, since electron captured by charge exchange usually
populate the outer shells.
Table 3.6: Preset maximum n and l for quicklook mode (H-like)
Ion max. n max. l Ion max. n max. l Ion max. n max. l
C VI 16 3 N VII 16 3 O VIII 16 5
F IX 2 1 Ne X 16 4 Na XI 9 2
Mg XII 16 4 Al XIII 9 2 Si XIV 16 4
P XV 5 1 S XVI 16 4 Cl XVII 4 1
Ar XVIII 13 2 K XIX 4 1 Ca XX 9 2
Sc XXI 2 1 Ti XXII 4 1 V XXIII 2 1
Cr XXIV 5 1 Mn XXV 4 1 Fe XXVI 16 4
Co XXVII 2 1 Ni XXVIII 8 2 Cu XXIX 2 1
Zn XXX 2 1
3.16 Ion: select ions for the plasma models 43
Syntax
The following syntax rules apply:
ions show - Display the list of ions currently taken into account
ions use all - Use all possible ions in the line spectrum
ions use iso #i: - Use ions of the isoelectronic sequences indicated by #i: in the line spectrum
ions use z #i: - Use ions with the atomic numbers indicated by #i: in the line spectrum
ions use ion #i1 #i2: - Use ions with the atomic number indicated by #i1 and ionisation stage indicated
by #i2: in the line spectrum
ions ignore all - Ignore all possible ions in the line spectrum
ions ignore iso #i: - Ignore ions of the isoelectronic sequences indicated by #i: in the line spectrum
ions ignore z #i: - Ignore ions with the atomic numbers indicated by #i: in the line spectrum
ions ignore ion #i1 #i2: - Ignore ions with the atomic number indicated by #i1 and ionisation stage
indicated by #i2: in the line spectrum
ions nmax all #i: - Set maximum n for all ions
ions nmax iso #i1: #i2 - Set maximum n to #i2 for isoelectronic sequence indicated by #i1
ions nmax z #i1: #i2 - Set maximum n to #i2 for atomic number indicated by #i1
ions nmax ion #i1 #i2: #i3 - Set maximum n to #i3 for atomic number indicated by #i1 and ionisation
stage indicated by #i2.
ions lmax all #i: - Set maximum l for all ions
ions lmax iso #i1: #i2 - Set maximum l to #i2 for isoelectronic sequence indicated by #i1
ions lmax z #i1: #i2 - Set maximum l to #i2 for atomic number indicated by #i1
ions lmax ion #i1 #i2: #i3 - Set maximum l to #i3 for atomic number indicated by #i1 and ionisation
stage indicated by #i2.
ions old all - Force the old calculation for all ions
ions old iso #i1: - Force the old calculation for the isoelectronic sequence indicated by #i1
ions old z #i1: - Force the old calculation for atomic number indicated by #i1
ions old ion #i1 #i2: - Force the old calculation for atomic number indicated by #i1 and ionisation
stage indicated by #i2.
ions new all - Force the new calculation for all ions
ions new iso #i1: - Force the new calculation for the isoelectronic sequence indicated by #i1
ions new z #i1: - Force the new calculation for atomic number indicated by #i1
ions new ion #i1 #i2: - Force the new calculation for atomic number indicated by #i1 and ionisation
stage indicated by #i2.
Examples
ions ignore all - Do not take any line calculation into account
ions use iso 3 - Use ions from the Z = 3 (Li) isoelectronic sequence
ions use iso 1:2 - Use ions from the H-like and He-like isoelectronic sequences
ions ignore z 26 - Ignore all iron (Z = 26) ions
ions use ion 6 5:6 - Use C V to C VI
ions show - Display the list of ions that are used
ions ql - Quicklook mode on
ions old ion 6 6 - Use old calculation for C VI
ions nmax ion 26 25 5 - Set maximum principal quantum number for Fe XXV to n = 5.
ions lmax ion 26 25 3 - Set maximum angular momentum quantum number for Fe XXV to ℓ = 3.
44 Syntax overview
3.17 Log: Making and using command files
Overview
In many circumstances a user of SPEX wants to repeat his analysis for a different set of parameters. For
example, after having analysed the spectrum of source A, a similar spectral model and analysis could be
tried on source B. In order to facilitate such analysis, SPEX offers the opportunity to save the commands
that were used in a session to an ascii-file. This ascii-file in turn can then be read by SPEX to execute
the same list of commands again, or the file may be edited by hand.
The command files can be nested. Thus, at any line of the command file the user can invoke the execution
of another command file, which is executed completely before execution with the current command file
is resumed. Using nested command files may help to keep complex analyses manageable, and allow the
user easy modification of the commands.
In order to facilitate the readability of the command files, the user can put comment lines in the command
files. Comment lines are recognized by the first character, that must be #. Also blank lines are allowed
in the command file, in order to enhance (human) readability.
Saving commands to file
After the command log save #a is given on the SPEX command line (#a is the file name), all the
following commands entered by the user (NOT the ones before) are stored on the command file until the
log close out command is given. Exceptions are the commands read from a nested command file (it
is not necessary to save these commands, since they are already in the nested command file). Also, help
calls and the command to open the file (”log save #a”) are not stored.
All commands are expanded to the full keywords before they are saved in the file. However, for execution
this is not important, since the interpreter can read both abbrevated and full keywords.
Saving the commands to the command file can be stopped by giving the command log close save.
The file with the saved commands is closed and remains at the specified path. SPEX will automatically
append the extension ”.com” to the filename.
Saving output to file
It is also possible to store all the output that is printed on the screen to a file. This is usefull for
long sessions or for computer systems with a limited screen buffer. The output saved this way could be
inspected later by (other programs of) the user. It is also useful if SPEX is run in a kind of batch-mode.
The command to save the output is log out #a, where #a should be the filename without extension.
SPEX will automatically append the extension ”.out” to the filename.
Executing commands from file
ASCII files with the .com extension containing SPEX commands can be executed in SPEX using the
command log execute #a, where #a stands for the file name without the ”.com” extension. When a
command file is read and the end of file is reached, the text ”Normal end of command file encountered”
is printed on the screen, and execution of the calling command file is resumed, or if the command file
was opened from the terminal, control is passed over to the terminal again.
For example, the user may have a command file named run which does his entire analysis. This command
file might start with the line ”log exe mydata” that will run the command file mydata that contains all
information regarding to the data sets read, further data selection or binning etc. This could be followed
by a second line in run like ”log exe mymodel” that runs the command file mymodel which could contain
the set-up for the spectral model and/or parameters. Also, often used plot settings (e.g. stacking of
different plot types) could easily placed in separate command files.
3.18 Menu: Menu settings 45
Syntax
The following syntax rules apply for command files:
log exe #a - Execute the commands from the file #a. The suffix ”.com” will be automatically appended
to this filename.
log save #a [overwrite] [append] - Store all subsequent commands on the file #a. The suffix ”.com”
will be automatically appended to this filename. The optional argument ”overwrite” will allow to overwrite
an already existing file with the same name. The argument ”append” indicates that if the file
already exists, the new commands will be appended at the end of this file.
log close save - Close the current command file where commands are stored. No further commands
will be written to this file.
log out #a [overwrite] [append] - Store all subsequent screen output on the file #a. The suffix
”.out” will be automatically appended to this filename. The optional argument ”overwrite” will allow to
overwrite an already existing file with the same name. The argument ”append” indicates that if the file
already exists, the new output will be appended at the end of this file.
log close output - Close the current ascii file where screen output is stored. No further output will be
written to this file.
Examples
log save myrun - writes all subsequent commands to a new file named ”myrun.com”. However, in case
the file already exists, nothing is written but the user gets a warning instead.
log save myrun append - as above, but appends it to an existing file
log save myrun overwrite - as above, but now overwrites without warning any already existing file
with the same name.
log close save - close the file where commands are stored.
log exe myrun - executes the commands in file myrun.com.
log output myrun - writes all subsequent output to file myrun.out.
log close output - closes the file above.
3.18 Menu: Menu settings
Overview
When command lines are typed, it frequently happens that often the first keywords are identical for
several subsequent lines. This may happen for example when a plot is edited. SPEX offers a shortcut to
this by using the menu command.
Syntax
The following syntax rules apply:
menu none - Quit the current menu text settings (i.e., return to the default spex prompt.
menu text #a - For all following commands, the text string #a will be appended automatically before
the following commands
Examples
menu text plot - All following commants will get the ”plot” keyword put in front of them. So if the
next commant would be ”plot dev xs” it is sufficient to type ”dev xs” instead.
46 Syntax overview
menu none - Return to the normal SPEX prompt.
menu text "par 1 2" - All following commands wil get the ”par 1 2” keywords put in front of them.
The next command could be ”t val 4.”, which will be expanded to the full ”par 1 2 t val 4.” to set the
temperature of sector 1, component 2 to 4 keV. Note that here the text has three keywords (par, 1, 2)
and hence it has to be put between ””, to indicate that it is a single text string. If there is only one
keyword, these ”” are not necessary.
3.19 Model: show the current spectral model
Overview
This commands prints the current spectral model, for each sector, to the screen. The model is the set of
spectral components that is used, including all additive and multiplicative components. For all additive
components, it shows in which order the multiplicative components are applied to the additive (emitted)
components. See Sect. 3.6 for more details.
Syntax
The following syntax rules apply:
model show - Prints the model for all sectors to the screen.
model show #i - Prints the model for sector #i to the screen.
Examples
model show 2 - Prints the model for the second sector
3.20 Multiply: scaling of the response matrix
Overview
This command multiplies (a component of) the response matrix by a constant.
Warning: If this command is repeated for the same component then the original response matrix is
changed by the multiplication of the constants. For example, after multiplying the response matrix by a
factor of 2, the original matrix is recovered by multiplying the intermediate result by 0.5.
Warning: The instrument number must be given in this command even if you use only a single
instrument.
Syntax
The following syntax rules apply:
multiply #i1 [component #i2] #r - Multiplies the response matrix of component #i2 of instrument
#i1 by a constant #r.
3.21 Obin: optimal rebinning of the data 47
Examples
multiply 1 3.5 - Multiplies the response matrix from instrument 1 by a factor of 3.5.
multiply 1 component 2 3.5 - Multiplies the second component of instrument 1 by the constant 3.5.
3.21 Obin: optimal rebinning of the data
Overview
This command rebins (a part of) the data (thus both the spectrum and the response) to the optimal
bin size given the statistics of the source as well as the instrumental resolution. This is recommended
to do in all cases, in order to avoid oversampling of the data. The theory and algorithms used for this
rebinning are described in detail in Chap. 8. A simple cartoon of this is: binning to 1/3 of the FWHM,
but the factor of 1/3 depends weakly upon the local count rate at the given energy and the number of
resolution elements. The better the statistics, the smaller the bin size.
Syntax
The following syntax rules apply:
obin #i1: - Simplest command allowed. #i1: is the range in data channels over which the binning needs
to take place.
obin #r1: #i: unit #a - The same command as above, except that now the ranges over which the
data is to be binned (#r1:) are specified in units (#a) different from data channels. These units can be
eV, keV, ˚A, as well as in units of Rydberg (ryd), Joules (j), Hertz (hz) and nanometers (nm).
obin [instrument #i1:] [region #i2:] #i3: - Here #i3: is the same as #i1: in the first command.
However, here one can specify the instrument range #i1: and the region range #i2: as well, so
that the binning is done only for one given data set.
obin [instrument #i1:] [region #i2:] #r1: [unit #a] - This command is the same as the
above, except that here one can specify the range over which the binning should occur in the units
specified by #a. These units can be eV, ˚A, keV, as well as in units of Rydberg (ryd), Joules (j), Hertz
(hz) and nanometers (nm).
Examples
obin 1:10000 - Optimally bins the data channels 1:10000.
obin 1:4000 unit ev - Does the same as the above, but now the data range to be binned is given in
eV, from 1−4000 eV, instead of in data channels.
obin instrument 1 region 1 1:19 unit a - Bins the data from instrument 1 and region 1 between 1
and 19 ˚A.
3.22 Par: Input and output of model parameters
Overview
This command is used as an interface to set or display the parameters of the spectral model. Each model
parameter (like temperature T , abundance, normalization etc.) has a set of attributes, namely its value,
status, range and coupling. This is illustrated by the following example. Assume we have a spectral
model consisting of a thermal plasma. Consider the silicon abundance (acronym in the model: 14). It
48 Syntax overview
can have a value (for example 2.0, meaning twice the solar abundance). Its status is a logical variable,
true (thawn) if the parameter can be adjusted during the spectral fitting proces or false (frozen) if it
should be kept fixed during the spectral fit. The range is the allowed range that the parameter can
have during the spectral fit, for example 0–1000 (minimum – maximum values). This is useful to set
to constrain a spectral search to a priori ”reasonable” values (e.g. abundances should be non-negative)
or ”safe” values (SPEX could crash for negative temperatures for example). Finally the coupling allows
you to couple parameters, for example if the Si abundance is coupled to the Fe abundance, a change in
the Fe abundance (either defined by the user or in a spectral fitting process) will result automatically
in an adjustment of the Si abundance. This is a useful property in practical cases where for example a
spectrum has strong Fe lines and weaker lines from other species, but definitely non-solar abundances.
In this case, one may fit the Fe abundance, but the statistics for the other elements may not be sufficient
to determine their abundance accurately; however a priori insight might lead you to think that it is the
global metallicity that is enhanced, and therefore you would expect the Si abundance to be enhanced in
the same way as Fe.
With the par command, you can set for each parameter individually or for a range of parameters in the
same command, their attributes (value, status, range and coupling). Also, you can display the parameters
on the screen or write them on a SPEX command file, which allows you to start another run with the
current set of parameters.
When setting parameters, you can also specify the sector (range) and component (range). For your first
call, it is assumed that you refer to sector 1, component 1, first parameter. In all subsequent calls of
the parameter command, it is assumed that you refer to the same sector(s) and component(s) as your
last call, unless specified differently. This is illustrated by the following example. Suppose you have the
following model: power law (component 1), blackbody (component 2) and RGS line broadening (lpro,
component 3). If you type in the commands in that order, this is what happens:
• par val 2 – sets the norm (= first parameter) of the power law to value 2
• par gam val 3 – sets the photon index of the power law to value 3
• par 2 t val 2.5 – sets the temperature of the blackbody to 2.5 keV
• par norm val 10 – sets the norm of the blackbody to 10
• par 1:2 norm v 5 – sets the norm of both the PL and BB to 5
• par val 4.2 – sets the norm of both the PL and BB to 4.2
• par 3 file avalue myprofile.dat – sets for the LPRO component the file name with the broadening
kernel to myprofile.dat. Note that the command ’value’ changes here to ’avalue’ to indicate that
the parameter is an ascii string.
Instrument normalisations can be thawned by entering the instrument number as a negative sector number.
For example, freeing the instrument normalisation of instrument 2 is done with the command
par -2 1 norm stat thawn. The second value in the command (1) is the region number. Therefore,
freeing the normalisation of the third region of the fourth instrument is done with the command:
par -4 3 norm stat thawn.
Syntax
The following syntax rules apply:
par [#i1:] [#i2:] [#a1:] avalue #a2 - Assign the value #a2 to the parameters specified by the
(range of) name(s) #a1 of component range #i2: of sectors #i1:. The sector (range), component (range)
and parameter name (range) are optional. If #a2 should be an empty text string, specify the value
”none” (without quotes, and all four characters in lowercase). If they are not specified, the sector(s),
component(s) and parameter(s) of the last call are used. This command containing the word ”avalue”
holds for input of text strings. For the input of real numbers ”avalue” is replaced by ”value” and #a2.
3.22 Par: Input and output of model parameters 49
par [#i1:] [#i2:] [#a:] value #r - Assign the value #r to the parameters specified by the (range
of) name(s) #a of component range #i2: of sectors #i1:. The sector (range), component (range) and
parameter name (range) are optional. If not specified, the sector(s), component(s) and parameter(s) of
the last call are used.
par [#i1:] [#i2:] [#a:] status #l - As above but for the status of a (range of) parameters; #l
= T (true, thawn) means a parameter that can be adjusted during a spectral fit, #l = F (false, froze,
fixed) means a parameter that will remain fixed during the spectral fitting.
par [#i1:] [#i2:] [#a:] range #r1:#r2 - As above but fore the allowed range of the parameter.
#r1 denotes the lower limit and #r2 denotes the upper limit. Both should be specified.
par [#i1:] [#i2:] [#a1:] couple [#i3:] [#i4:] #a2: - Here #i1:, #i2:, #a1: are the sector(s),
component(s) and parameter(s) that are to be coupled. The parameter (s) to which they are
coupled are specified by #a2: and the optional #i3:, #i4:. If ranges are used, take care that the number
of sectors, components and parameters on the right and left match.
par [#i1:] [#i2:] [#a1:] couple [#i3:] [#i4:] #a2: factor #r - As above, but couple
using a scaling factor #r.
par [#i1:] [#i2:] #a: decouple - Decouples the parameter(s) #a: of (optional) components #i2:
of of (optional) sector(s) #i1:. Inverse operation of the couple command.
par show [free] - Shows on the display screen all parameters of all components. If the optional keyword
free is given, shows only parameters with fit status ”T” (true, thawn), i.e., the free parameters in
a spectral fit.
par write #a [overwrite] - Writes all parameters to a SPEX command file #a. #a should be specified
without extension, SPEX automatically adds the .com extension. If the optional overwrite command is
given, then the file #a will be overwritten with the new values.
Examples
par val 10 - Sets the value of the current parameter to 10.
par t val 4 - Sets the parameter named ”t” to 4.
par 06:28 value 0.3 - Sets the parameters named 06:28 (for example the abundances of C (Z = 6), N
(Z = 7), . . . Ni (Z = 28)) to the value 0.3.
par 2 nh val 0.01 - Sets the parameter named ”nh” of component 2 to the value 0.01
par 1 1 norm value 1E8 - Sets parameter named ”norm” of component 1 of sector 1 to the value 108
.
par file avalue myfile.with.data - sets the ascii-type parameter named ”file” to the value ”myfile.with.data”
(without quotes).
par file avalue none - sets the ascii-type parameter named ”file” to the value ”” (i.e. an empty string)
par status frozen - Sets the fit status of the current parameter to ”frozen” (fixed).
par 1 3 t stat thawn - Specifies that parameter ”t” of the third component of the model for sector 1
should be left free (thawn) during spectral fitting.
par 2 3 gamm range 1.6:1.9 - Limit parameter ”gamm” of component 3 of sector 2 to the range 1.6 –
1.9.
par norm range -1E8 1E8 - Set the range for the parameter ”norm” between −108
and +108
. This
command is necessary if for example the model is a delta line used to mimick an absorption line, which
normally has a default minimum value of 0. (for an emission line).
par 1 1 norm couple 2 1 norm - Couples the norm of the first component for the first sector to the
norm of the first component of the model for the second sector.
par 1 1 norm couple 2 1 norm factor 3 - The same command as the above, but now the norm of
the first component in the model for sector 1 is 3 times the norm of the first component of the model for
sector 2. For example, if the norm of the 1st component of sector 2 gets the value 40, then the norm of
the 1st component of sector 1 will automatically be updated to a value of 3 × 40 = 120.
par 3:5 02:30 couple 1 02:30 - Couples the abundances of He–Zn of components 3, 4 and 5 to the
He–Zn abundances of component 1.
par norm decouple - Decouples the norm of the current component from whatever it was coupled to.
par -2 1 norm stat thawn - Free the instrument normalisation of instrument 2 and region 1.
50 Syntax overview
par show - Shows all the parameters of the current model for all sectors and how they are coupled (if
applicable). For each parameter it shows the value, status, range and coupling information, as well as
info on its units etc. It also shows the fluxes and restframe luminosities of the additive components,
photon flux (phot/m**2/s) and energy flux (W/m**2) are the values observed at Earth (including any
transmission effects like Galactic absorption or intrinsic absoprtion that have been taken into account),
and the nr. of photons (photons/s) and luminosity (W) are all as emitted by the source, without any
attenuation.
par show free - As above, but only displays the parameters that have the status thawn.
par write mypar overwrite - SPEX writes all parameters for the model to a file named mypar.com.
Any previously existing file mypar.com is overwritten.
par write mypar - Same command as above, but now a new file is created. If there already exists a file
with the same filename SPEX will give an error message.
3.23 Plot: Plotting data and models
Overview
The plot command cause the plot to be (re)drawn on the graphics device. Multiple graphics devices can
be defined in one SPEX session. For example, a plot can be sent to both a postscript and a xs device.
A user can also set the number of plot frames in the currently active device(s), e.g. the data and model
can be displayed in one frame while the residuals can be displayed in a frame below. The user has to
specify what is to be plotted in in each frame.
In each plot frame, there can be different sets that can be specified by the ”set” keyword in the plot
command. For example, for the plot type data, each set corresponds to the spectrum of an instrument
or region; with this option it is therefore possible to give different instruments different colours or plot
symbols, etc., or just to omit one of the instruments from the plot.
The plot command is also used to select the axis plot units and scales as well as character commands like
font style, line weights, plot colours, etc. Finally, the plot command can also be used to dump the data
to an ascii file.
Warning: To make a plot, always start with a ”plot device” command to open any plot device you
wish. Next select a plot type using ”plot type”. After this you can give any plot commands to modify or
display the plot.
Warning: Some of the more fancy plotting options, like adding labels to a plot, are broken. To make
more sophisticated plots, it is advisable to save the plot to a QDP file with ‘plot adum’ and adapt them
through QDP (Ftools). We intent to update the plotting system in a future version of SPEX.
Syntax
The following syntax rules apply for plot:
plot - (Re)draws the plot on the graphics device. Take care to open at least one device first (with a
”plot dev” command)
plot frame new - Creates a new additional plot frame, where an other plot type can be displayed (or the
same plot type but with different units). Take care to position the viewport of the new and old frames
to the desired locations.
plot frame #i - Sets frame number #i to be the currently active frame. After this command has been
issued, all plot commands will only affect the currently active frame.
plot frame delete #i - Deletes frame number #i.
plot type #a - Specifies what is to be plotted in the selected frame. #a can be any of the plot types
specified in Sect. 6.2.
plot device #a1 [#a2] - Selects a graphics device #a1 and optional file name #a2 (in the case of a
3.23 Plot: Plotting data and models 51
postscript or gif device). File extensions (for example .ps) should be specified. For valid devices, see
Sect. 6.1.
plot close #i - Close graphics device number #i. Note, always close a postscript device before quiting
/spex, otherwise the contents may be corrupted.
plot hlan - Make a hardcopy in landscape orientation and send it to the standard printer. Use is made
of the unix command ”lp -c filename”.
plot hpor - As above, but for portrait orientation
plot x lin - Plot the x-axis on a linear scale
plot x log - Plot the x-axis on a log scale
plot y lin - Plot the y-axis on a linear scale
plot y log - Plot the y-axis on a log scale
plot y mix #r1 #r2 - Plot the y-axis on a mixed linear/logarithmic scale; for y-values below #r1 the
data will be plotted linear, and for y-values above #r1 the data will be plotted logarithmically; the linear
part occupies the fraction of the total frame height given by #r2. See also Sect. 6.8.2.
plot z lin - Plot the z-axis on a linear scale. The z-axis is defined for two-dimensional plots like contour
plots.
plot z log - As above, but using a log scale.
plot ux #a - Set the plot units on the x-axis, #a can be ˚A, keV, eV, or whatever unit that is allowed.
The allowed values depend upon the plot type. See Sect. 6.8.1 for allowed units for each plot type.
plot ux vel #r #a - Plot the x-axis in velocity units (km s−1
), with reference energy provided as #r if
#a is ”keV” or reference wavelength provided as #r if #a is ”Ang”. Note that the same zero scale will
be set for all plot windows.
plot uy #a - Same as above, but for the y-axis
plot uz #a - Same as above, but for the z-axis
plot rx #r1:#r2 - set the plot range on the x-axis from #r1 to #r2
plot ry #r1:#r2 - Same as above, but for the y-axis
plot rz #r1:#r2 - Same as above, but for the z-axis
plot view default #l - For #l is true, the default viewport is used. For #l is false, the default viewport
is overruled and you can specify your own viewport limits with the ”set view x” and ”set view y”
commands. Useful for stacking different plot frames.
plot view x #r1:#r2 - Set the x viewport range from #r1 to #r2, where #r1 and #r2 must be in the
range 0–1.
plot view y #r1:#r2 - Same as above, but for the y-range.
plot view back #i - Set the viewport background colour to value #i. See Sect. 6.3 for the allowed plot
colours.
plot view transp #l - If true, set the viewport background to to transparent, the plot frame will be
shown with the background colour selected by the ”plot view back” command. Default is false.
plot box disp #l - Display a box around the viewport, true/false
plot box edge #a #l - If true (default), display the edges of the plot box, #a should be one of the
following keywords: top, bottom, left, right. Note that whether you see the edges or not also depends on
the settings defined by the ”plot box disp” command.
plot box axis x #l - Plots an x-axis with tickmarks at the line y = 0. You only see this of course if
your y-range includes the value 0.
plot box axis y #l - As above, but for the y-axis
plot box grid x #l - Plot a grid for the x-axis
plot box grid y #l - Plot a grid for the y-axis
plot box numlab bottom #l - Show the tick number labels at the bottom of the plot, true/false
plot box numlab top #l - Same as above, but for the top
plot box numlab left #l - Same as above, but for the left
plot box numlab right #l - Same as above, but for the right
plot box numlab vert #l - Plot the tick number labels on the y-axis vertically or horizontally, set #l
to true for vertical tnumbers and false for horizontal numbers.
plot box numlab xscal #i - Way to denote the numerical numbers along the x-axis. Three values are
allowed: 0=automatic, 1=forced decimal labeling, 2=forced exponential labeling. Default is 0.
52 Syntax overview
plot box numlab yscal #i - As above, but for the y-axis
plot box tick invert x #l - Draw the tick marks on the x-axis on the inside or outside the box, set
#l to true for outside and false for inside (default).
plot box tick invert y #l - Same as above, but for the y-axis.
plot box tick minor x #l - Draw minor tick marks on the x-axis, true/false
plot box tick minor y #l - Same as above, but for the y-axis
plot box tick major x #l - Draw major tick marks on the x-axis, true/false
plot box tick major y #l - Same as above, but for the y-axis
plot box tick distance x #r - Set the distance between the major/labelled tick marks on the x-axis
to #r
plot box tick distance y #r - Same as above, but for the y-axis
plot box tick subdiv x #i - Draw #i minor tick marks between each major tick mark on the x-axis
plot box tick subdiv y #i - Same as above, but for the y-axis
plot box col #i - Set the box colour to colour number #i. See Sect. 6.3 for the allowed plot colours.
plot box lt #i - Set the box line type to #i. See Sect. 6.4 for allowed line types.
plot box lw #i - Set the box line weight to number #i. See Sect. 6.4 for more about line weights.
plot box fh #r - Set the box font height to number #i.
plot box font #i - Set the box font to number #i. See Sect. 6.5 for more details about text fonts.
plot cap #a disp #l - If #l is true, display the caption (default). For more about captions see Sect. 6.6.
Here and below, #a can be x, y, z, id, lt or ut.
plot cap #a col #i - Plot caption #a in colour number #i. See Sect. 6.3 for valid colour indices.
plot cap #a back #i - Set the background colour for caption #a to #i.
plot cap #a lw #i - Set the font line weight for caption #a to #i.
plot cap #a fh #r - Set the font height for caption #a to value #r.
plot cap #a font #i - Set the font type for caption #a to #i.
plot cap #a1 text #a2 - Set the text for caption #a1 to #a2. Note that the caption text should be
put between quotion marks, like ”best fit results” if you want to see the text: best fit results.
plot cap #a1 side #a2 - Plot caption #a1 (which can be x, y, z, id, lt, ut) at the side of the frame
specified by #a2, which may stand for t (top), b (bottom), lh (left, horizontal), rh (right, horizontal), lv
(left, vertical) and rv (right, vertical).
plot cap #a off #r - Offset caption #a by #r from the edge of the viewport, where #r is in units of
the character height. Enter negative values to write inside the viewport.
plot cap #a coord #r - Plot caption #a along the specified edge of the viewport, in units of the viewport
length, where 0.0 ≤ #r ≤ 1.0.
plot cap #a fjust #r - Controls justification of the caption #a parallel to the specified edge of the
viewport. If #r = 0.0, the left hand of #a will be placed at the position specified by ”coord” above; if
#r = 0.5, the center of the string will be placed at ”coord”, if #r = 1.0 the right hand of #a will be
placed at ”coord”. Other values can be used but are less useful.
plot string new #r1 #r2 #a - Plot a new string with text as specified in #a at x=#r1 and y = #r2.
See Sect. 6.5 for more deatils about text strings. Also do not forget to put #a between ”” if it consists
of more than one word (i.e., if it contains spaces).
plot string del #i: - Delete string numbers specified by the range #i from the plot.
plot string #i: disp #l - If true (default), display the strings specified by the range #i:.
plot string #i: text #a - Change the text of strings #i: to #a
plot string #i1: col #i2 - Set the colours of strings #i1: to #i2
plot string #i1: back #i2 - Set the background colour for the strings #i1: to the value #i2.
plot string #i1: lw #i2 - Set the line weight of strings #i1: to #i2.
plot string #i: fh #r - Set the font height of strings #i to #r.
plot string #i1: font #i2 - Set the font style of strings #i1 to #i2.
plot string #i: x #r - Set the x position of strings #i: to #r.
plot string #i: y #r - Set the y position of string #i: to #r.
plot string #i: angle #r - Set the angle of strings #i: to #r.
plot string #i: fjust #r - Controls justification of the strings #i: parallel to the specified edge of
the viewport. If #r = 0.0, the left hand of the strings will be placed at the position specified by ”x y”
3.23 Plot: Plotting data and models 53
above; if #r = 0.5, the center of the strings will be placed at ”x y”, if #r = 1.0 the right hand of #i:
will be placed at ”x y”. Other values can be used but are less useful.
plot string #i: box #l - If #l is true, plot a box around the text strings #i:. The default value is
false (no box).
plot string #i1: box lt #i2 - Set the line style of the box around the strings #i1: to the value #i2.
plot string #i1: box lw #i2 - As above, but for the line weight specified by #i2.
plot string #i1: box col #i2 - As above, but for the colour index for the box specified by #i2.
plot set #i: - Selects data set numbers as specified by #i:. Afterwards most plot commands will only
affect data sets #i:
plot set all - Selects all data sets that are present. All subsequent plot commands will be executed
for all data sets.
plot line disp #l - If #l is true, plots a connecting line through the data points, (default is false).
plot line col #i - Set the colour of the connecting line to #i.
plot line lt #i - Set the line style of the connecting line to #i.
plot line lw #i - Set the line weight of the connecting line to #i.
plot line his #l - If #l is true, plot the connecting line in histogram format (default is true).
plot elin disp #l - If #l is true, plots a connecting line through the end points of the error bars,
(default depends upon the plot type).
plot elin col #i - Set the colour of the connecting line through the end points of the error bars to #i.
plot elin lt #i - Set the line style of the connecting line through the end points of the error bars to
#i.
plot elin lw #i - Set the line weight of the connecting line through the end points of the error bars to
#i.
plot elin his #l - If #l is true, plot the connecting line through the end points of the error bars in
histogram format (default is true).
plot model disp #l - If #l is true, plot the current model corresponding to the relevant data set (default
is true).
plot model col #i - Set the colour of the model to number #i.
plot model lt #i - Set the line style of the model to number #i.
plot model lw #i - Set the line weight of the model to number #i.
plot model his #l - If #l is true, plot the model in histogram format (default is true).
plot back disp #l - If #l is true, plot the subtracted background (default is true).
plot back col #i - Set the colour of the subtracted background to number #i.
plot back lt #i - Set the line style of the subtracted background to number #i.
plot back lw #i - Set the line weight of the subtracted background to number #i.
plot back his #l - If true, plot the subtracted background in histogram format (default is true).
plot fill disp #l - If #l is true, fill the curve below the model with the colour specified by the next
command or the default colour.
plot fill col #i - Change the filling colour to #i.
plot fill lt #i - Change the line type of the filling lines to #i.
plot fill lw #i - Change the line weight of the filling lines to #i.
plot fill style #i - Change the style of the filling lines to the value #i. Here #i has values between
1–4, with the following meaning: 1 = solid filling (default), 2 = outline, 3 = hatched, 4 = cross-hatched.
plot fill angle #r - Set the angle for the filling lines for hatched filling. Default is 45 degrees.
plot fill sep #r - Set the distance between the filling lines for hatched filling. The unit spacing is 1 %
of the smaller of the height or width of the viewing surface. This should not be zero.
plot fill phase #r - The phase between the hatch lines that fill the area.
plot data disp #l - If #l is true, display the data.
plot data errx #l - If #l is true, display the error bars in the x-direction.
plot data erry #l - If #l is true, display the error bars in the y-direction.
plot data col #i - Give the data colour index #i.
plot data lt #i - Give the data line style #i.
plot data lw #i - Give the data line weight #i.
plot data fh #r - Give the symbols for the data font height #r.
54 Syntax overview
plot data symbol #i - Plot the data with symbol number #i. For symbol numbers, see Sect. 6.7.
plot adum #a [overwrite] [append] - Dump the data and model in the plot in an ascii file with filename
#a. The extension ”.qdp” will automatically be appended. Note that the data will be written as
they are, i.e. if you have a logarithmic x-axis or y-axis, the logs of the plotted quantities will be written.
If you want to replot your data later with for example the qdp package, take care that you plot the data
in SPEX on a lin-lin frame before you execute the ”plot adum” command. Also note that the data will be
written in the units that were specified in the plot (energy, wavelength or whatever is applicable. If the
optional ”append” keyword is present, the data will be appended to any existing file with the name #a;
if the optional ”overwrite” keyword is present, any pre-existing file with the name #a will be overwritten
by the new data.
Examples
plot device xs - Open the graphic device xs (xserver)
plot device ps myplot.ps - Select a postscript device connected to the file name myplot.ps
plot type data - Plot the data on the selected graphics device(s)
plot ux angstrom - Set the x-axis plot units to ˚A
plot uy angstrom - Set the y-axis plot units to Counts/s/˚A
plot frame new - Open a new frame in the selected graphics device(s)
plot frame 2 - Go to the 2nd frame, all plot commands will now only affect frame 2
plot type chi - Plot the residuals in frame 2
plot uy rel - Set the y-axis plot units in frame 2 to (Observed - Model)/Model
plot view default f - Set the default viewport keyword to false so that new user viewport values can
be specified for frame 2
plot view y 0.2:0.8 - Set the y viewport limits of frame 2 from 0.2 to 0.8 of the full device window
plot cap id disp f - Do not display the id caption of frame 2
plot cap ut disp f - Do not display the upper top caption of frame 2
plot cap lt disp f - Do not display the lower top caption of frame 2
plot ux a - Set the x-axis plot units of frame 2 to ˚A
plot ux 21.602 ang - Plot the x-axis as velocity in km −1
relative to a wavelength of 21.602 ˚A.
plot ry -1:1 - Set the y-axis plot range of frame 2 to between a lower limit of -1 and an upper limit of
1
plot frame 1 - Go to frame 1
plot view default f - Set the default viewport keyword to false so that new user viewport values can
be specified for frame 1
plot view x 0.25:0.75 - Set the x viewport limits of frame 1 from 0.25 to 0.75 of the full device window
plot de cps filename.ps - Open a colour postscript graphics device and write the output file to file-
name.ps
plot - Redraw the plot on all frames and devices
plot close 2 - Close device number 2, which is the postscript device in this case
3.24 Quit: finish the program
The quit option exits the execution of SPEX, closes the open plot-devices and scratch files (if any) and,
if requested outputs the cpu-time statistics.
Syntax
The following syntax rule applies:
3.25 Sector: creating, copying and deleting of a sector 55
quit - quit the program as described above.
3.25 Sector: creating, copying and deleting of a sector
Overview
This allows one to create, delete, copy and show the number of sectors, used for the analysis of the data.
A sector is a region on the sky with its own spectral model, or a part of the lightcurve of a variable source
with its time dependent spectrum, etc. See for more details about sectors and regions section 2.2. For
doing spectral fitting of data sets, the sectors need to be specified in the response matrix of the data: the
response file should tell which sector number corresponds to a given part of the matrix.
Syntax
The following syntax rules apply:
sector new - Creates a new sector, which can have its own model.
sector show - Gives the number of sectors that are currently used.
sector copy #i - Copies the model for sector #i to a new sector.
sector delete #i - Deletes sector #i.
Examples
sector new - Creates a new sector.
sector copy 2 - Creates a new sector, with the same spectral model as used in sector 2. This can be
useful if the spectra of the different sectors are very similar in composition.
sector delete 3 - Deletes sector number 3.
3.26 Shiftplot: shift the plotted spectrum for display purposes
Overview
This command shifts the observed spectrum as well as the model spectrum by adding a constant or by
multiplying a constant, as far as plots are concerned. The true data files do not change, so the shift is
only for representational purposes.
There are basically two options, indicated by the mode variable plotshift: For plotshift=1, a constant
shift is added to the plotted spectrum of a given part of the data, for plotshift=2 the plotted spectrum is
multiplied by the constant shift.
The multiplicative constant shift (plotshift=2) is generally preferred for log-log plots, while for linear
plots a constant additive shift (plotshift=1) is preferred.
Warning: In the case of addition (plotshift=1), the addition constant is given in counts/s. This thus
leads to a different (energy-dependent) constant being added to the plotted spectrum if the units are not
in counts/s. For the multiplicative case this is of course not the case.
Syntax
The following syntax rules apply:
56 Syntax overview
shiftplot #i #r - #i indicates whether a constant should be added (#i=1) or multiplied (#i=2) to
the spectrum and model. #r is then the constant to be added or multiplied by.
shiftplot [instrument #i1:] [region #i2:] #i3 #r - Shift the plot using a factor #r. Here #i3
(= plotshift) determines whether the constant is added (plotshift=1) or multiplied (plotshift=2). The
optional instrument range #i1: can be used to select a single instrument or range of instruments for
which the shift needs to be applied, and the optional region range #i2: the region for these instruments.
Examples
shiftplot 1 2.0 - Adds 2 counts/s to the plotted spectrum. Since no instrument or region is specified,
this applies for all spectra.
shiftplot 2 10.0 - Multiplies the plotted spectrum by a factor of 10.0
shiftplot instrument 1 region 2 1 2 - Adds 2 counts/s to the plotted spectrum for the data from
instrument 1 and region 2.
shiftplot region 2:3 1 2 - Adds 2 counts/s to the plotted spectrum for the data for all instruments
and regions 2−3.
3.27 Simulate: Simulation of data
Overview
This command is used for spectral simulations. The user should start with a spectral model and a spectral
data set (both matrix and spectrum). After giving the ”simulate” command, the observed spectrum will
be replaced by the simulated spectrum in SPEX. Note that the original spectrum file (with the .spo
extension) is not overwritten by this command, so no fear to destroy your input data! Different options
exist and several parameters can be set:
• Instrument, region: the instrument(s) and region(s) for which the simulation should be done (i.e.,
if you have more instruments you can do the simulation only for one or a few instruments)
• time: set the exposure time t (s) of the source spectrum as well as the background error scale factor
fb. This last option allows you to see what happens if for example the background would have a
ten times higher accuracy (for fb = 0.1).
• syserr: add a systematic error to both the source and background spectrum. An alternative way
to introduce systematic errors is of course to use the syserr command (Sect. 3.29). Take care not
to set the systematic errors twice, and remember that rebinning your spectrum later will reduce
the systematic errors, as these will be added in quadrature to the statistical errors. So first rebin
and then add systematics!
• noise: either randomize your data or just calculate the expected values
• back: do the background subtraction or keep it in the data
Warning: A response matrix and spectrum of the region and the instrument you want to simulate
are necessary, as SPEX needs the response matrix as well as the background to be subtracted for the
simulations.
Warning: If your background is taken from the same observation as your source, and you multiply the
original exposure time with a factor of S, you should put fb to S−0.5
, reflecting the fact that with increasing
source statistics the background statistics also improves. This is the case for an imaging observation where
a part of the image is used to determine the background. If instead you use a deep field to subtract the
3.28 Step: Grid search for spectral fits 57
background, then the exposure time of your background will probably not change and you can safely put
fb = 1 for any exposure time t.
Warning: If your subtracted background (one of the columns in the .spo file) is derived from a low
statistics Poissonian variable (for example a measured count rate with few counts per channel), then scaling
the background is slightly inaccurate as it takes the observed instead of expected number of background
counts as the starting point for the simulation.
Syntax
The following syntax rules apply:
simulate [instrument #i1:] [region #i2:] [time #r1 #r2] [syserr #r3 #r4] [noise #l1] [back
#l2] - #i1: and #i2: specify the instrument and region (range) to be used in the simulation. #r1 is the
exposure time t, #r2 the background error scale factor fb. If omitted, t will be taken as the exposure
time of the current data set, and fb = 1. #r2 must always be specified if t is specified. In case of doubt,
put fb = 1. #r3 and #r4 are the systematic errors as a fraction of the source and background spectrum,
respectively; again both should be specified or omitted together. Default values are 0. If #l1 is true,
Poissonian noise will be added (this is the default). If #l2 is true, the background will be subtracted
(this is the default).
Examples
simulate - This simulates a new spectrum/dataset with Poissonian noise and background subtraction
with the same exposure time and background as the original data set.
simulate noise f - As above, but without Poissonian noise. The nominal error bars are still plotted.
simulate back f - As first example, but now no background is subtracted.
simulate time 10000 1. - Simulate for 104
s exposure time and the same background as the template
spectrum.
simulate time 10000 0.2 - Simulate for 104
s exposure time but with a 5 times more accurate subtracted
background (the background errors are 5 times smaller).
simulate syserr 0.1 0.2 - As before but with a systematic error of 10 % of the source spectrum and
20 % of the subtracted background spectrum added in quadrature.
simulate instrument 2:4 region 3 time 5000 1 syserr 0.05 0.01 noise f back f - Simulate a
spectrum for region 3 of instruments 2–4, with 5000 s exposure time t, the nominal background error
scaleng fb = 1, a systematic error of 5 % of the source and 1 % of the background, no Poissonian noise
and no background subtraction.
3.28 Step: Grid search for spectral fits
Overview
A grid search can be performed of χ2
versus 1, 2, 3 or 4 parameters. The minimum, maximum and
number of steps for each parameter may be adjusted. Steps may be linear or logarithmic. For each set of
parameters, a spectral fit is made, using the last spectral fit executed before this command as the starting
point. For each step, the parameters and χ2
are displayed. This option is useful in case of doubt about
the position of the best fit in the parameter space, or in cases where the usual error search is complicated.
Further it can be useful incases of complicated correlations between parameters.
Warning: Take care to do a spectral fit first!
Warning: Beware of the cpu-time if you have a fine grid or many dimensions!
58 Syntax overview
Syntax
The following syntax rules apply:
step dimension #i - Define the number of axes for the search (between 1–4).
step axis #i1 parameter [[#i2] #i3] #a range #r1:#r2 n #i4 - Set for axis #i1, optional sector
#i2, optional component #i3 and parameter with name #a the range to the number specified by #r1
and #r2, with a number of steps n given by #i4. If n > 0, a linear mesh between #r1 and #r2 will be
taken, for n < 0, a logarithmic grid will be taken.
step - Do the step search. Take care to do first the ”step dimension” command, followed by as many
”step axis” commands as you entered the number of dimensions.
step file example - Do the step search and also write the results to an .stp file used by the stepcontour
program (see 7.7).
Warning: The step file command will overwrite existing .stp files with the same name by default.
Examples
Below we give a worked out example for a CIE model where we took as free parameters the normalization
”norm”, temperature ”t”, Si abundance ”14” and Fe abundance ”26”. To do a 3-dimensional grid search
on the temperature (logarithmic between 0.1 and 10 keV with 21 steps), Fe abundace (linear between 0.0
and 1.0 with 11 steps) and Si abundance (linear between 0.0 and 2.0 with 5 steps, i.e. values 0.0, 0.4,
0.8, 1.2, 1.6 and 2.0) the following commands should be issued:
fit - Do not forget to do first a fit
step dimension 3 - We will do a three-dimensional grid search
step axis 1 parameter 1 1 t range 0.1:10.0 n -21 - The logarithmic grid for the first axis, temperature;
note the − before the 21!
step axis 2 par 26 range 0:1 n 11 - The grid for axis 2, Fe abundance
step axis 3 par 14 range 0:2 n 5 - Idem for the 3rd axis, Silicon
step - Now do the grid search. Output is in the form of ascii data on your screen (and/or output file if
you opened one).
step file example - Grid search with output to your screen and .stp output file for use with the stepcontour
task.
3.29 Syserr: systematic errors
Overview
This command calculates a new error, adding the systematic error of the source and the background to
the Poissonian error in quadrature. One must specify both the systematic error as a fraction of the source
spectrum as well as of the subtracted background spectrum. The total of these fractions can either be
less or greater than 1.
Warning: This command mixes two fundamentally different types of errors: statistical (random fluctuations)
and systematic (offset). The resulting uncertainties are unjustly treated as being statistical, which
can lead to wrong results when the systematic offsets are substantial. Syserr should therefore be used with
extreme caution.
Warning: One should first rebin the data, before running syserr. Run syserr however before fitting the
data or finding errors on the fit.
Warning: Running syserr multiple times will increase the error every time. If the input to syserr
is wrong one should restart SPEX and rerun syserr with the correct values to calculate the total error
3.30 System: call system executables 59
correctly.
Syntax
The following syntax rules apply:
syserr #i: #r1 #r2 - The shortest version of this command. #i: is the range in data channels for
which the systematic error is to be calculated and added (in quadrature) to the Poissonian error. #r1 is
then the the relative systematic error due to the source and #r2 the relative systematic error due to the
background.
syserr [instrument #i1:] [region #i2:] #i3: #r1 #r2 - In this syntax one can also specify the
instrument and the region one wants to calculate the combined error for. Both can be ranges as well.
#i3: has the same role as #i: in the above command, and #r1 and #r2 are the same as above.
syserr [instrument #i1:] [region #i2:] #i3: #r1 #r2 [unit #a] - Exact same command as
above, except that now the data range (#i3:) for which the errors are to be calculated are given in units
different than data channels. These units can be ˚A (ang), eV (ev), keV (kev), Rydbergs (ryd), Joules (j),
Hertz (hz) and nanometers (nm). This is the most general command.
Examples
syserr 1:100000 0.3 0.5 - Calculates the combined Poissonian and systematic error for data channels
1:100000, where the fraction of the systematic error of the source is 0.3 and the background is 0.5.
syserr 0:2000 0.3 0.5 unit ev - The same as the above command, expect that now the error calculation
is performed between 0 and 2000 eV instead of data channels.
syserr instrument 2 region 1 0:2000 0.3 0.5 unit ev - The same as the above command, but
now the error calculation is only performed for the data set from the second instrument and the first
region thereof.
3.30 System: call system executables
Overview
Sometimes it can be handy if SPEX interacts with the computer system, for example if you run it in
command mode. You might want to check the existence of certain file, or run other programs to produce
output for you, and depending on that output you want to continue SPEX.
Therefore there is an option to execute any shell type commands on your machine, using the fortran ”call
system” subroutine.
Another useful goody is the possibility to stop SPEX automatically if you find some condition to occur;
this might be useful for example if you have a program running that calls SPEX, and depending on the
outcome of SPEX you might want to terminate the execution. This is achieved in SPEX by testing for
the existence of a file with a given filename; if the file exists, SPEX stops immediately execution and
terminates; if the file does not exist, SPEX continues normally.
Syntax
The following syntax rules apply:
system exe #a - execute the command #a on your UNIX/linux shell
system stop #a - stop SPEX if the file #a exists
60 Syntax overview
Examples
system exe "ls -l" - give a listing of all file names with length in the current directory
system exe "myfortranprogram" - execute the fortran program with name ”myfortranprogram”
system stop testfile - stop SPEX if the file with name testfile exists; if this file does not exist, continue
with SPEX
3.31 Use: reuse part of the spectrum
Overview
This command can only be used after the ignore command was used to block out part of the data set in
the fitting. The command re-includes thus (part of) the data set for fitting. As it undoes what the ignore
command did (see section 3.15) the syntax and use of both are very similar. Again one can/must specify
the instrument and region for one wants the data to be re-included. Further can one specify the units
chosen to give the range of data points to be included. The standard unit is that of data channels and
does not need to be specified. The data points re-included with use will automatically also be plotted
again.
The range to be reused can be specified either as a channel range (no units required) or in eiter any
of the following units: keV, eV, Rydberg, Joule, Hertz, ˚A, nanometer, with the following abbrevations:
kev, ev, ryd, j, hz, ang, nm. Note that spectra that were binned before using the bin command are not
binned anymore after the spectrum is ignored and reused again. In this case, the bin command should
be applied again to restore the desired spectral binning.
Syntax
The following syntax rules apply:
use [instrument #i1] [region #i2] #r - Use the range #r in fitting the data. The instrument #i1
and the region #i2 must be specified if either there are more than 1 instrument or more than 1 region
used in the data sets.
use [instrument #i1] [region #i2] #r unit #a - Same as the above, but now the units #a in which
the range #r of data points to be used is specified in any of the units mentioned above.
Examples
use 1000:1500 - Re-include the data channels 1000:1500 for fitting the data.
use instrument 1 region 1 1000:1500 - Re-include the data channels 1000:1500 of the first instrument
and the first region in the data set for fitting the data and plotting.
use instrument 1 region 1 1:1.5 unit kev - Same as the above, but now the unites are specified as
keV instead of in data channels.
use 1000:1500 unit ev - Re-iclude the data points between 1000 and 1500 eV for fitting and plotting.
Note that in this case the input data should come from only one instrument and should contain no regions.
3.32 Var: various settings for the plasma models 61
3.32 Var: various settings for the plasma models
3.32.1 Overview
For the plasma models, there are several quantities that have useful default values but can be adjusted
manually for specific purposes. We list them below.
Free-bound emission
Usually the freebound emission takes most of the computing time for the plasma models. This is because
it needs to be evaluated for all energies, ions and atomic sublevels that are relevant. In rder to reduce the
computational burden, there is a parameter gfbacc in SPEX that is approximately the accuracy level for
the free-bound calculation. The default value is 10−3
. If this quantity is higher, less shells are taken into
account and the computation proceeds faster (but less accurate). The users are advised not to change
this parameter unless they are knowing what they do!
Line emission contributions
By default, all possible line emission processes are taken into account in the plasma models. For testing
purposes, it is possible to include or exclude specific contributions. These are listed below in Table 3.7.
Table 3.7: Possible line emission processes
Abbrevation Process
ex electron excitation
rr radiative recombination
dr dielectronic recombination
ds dielectronic recombination satellites
ii inner shell ionisation
Doppler broadening
By default, thermal Doppler broadening is taken into account. However, the user can put this off for
testing purposes. The options for the broadening are:
1. No broadening at all
2. Only Doppler broadening (default)
3. Only natural broadening (works only for var calc new)
4. Doppler and natural broadening, Voigt profiles (best physical representation, works only for var
calc new)
Atomic data
The user can choose between the ”old” Mekal code (the current default) and updated calculations for
the ions for which this is possible.
Warning: The updated atomic database that can be used through the command ”var calc new” is still
being developed and incomplete. Using this database is therefore not yet recommended.
62 Syntax overview
Mekal code
We have made several minor improvements to the original Mekal plasma model. These improvements
are included by default. However, it is possible to discard some of these improvements by going back to
the old code. The improvements are classified as follows (with the appropriate syntax word added here).
Wav: wavelength corrections according to the work of Phillips et al. (1999), based upon Solar flare
spectra; in addition, the 1s-np wavelengths of Ni XXVII and Ni XXVIII have been improved.
Fe17: The strongest Fe XVII lines are corrected in order to agree with the rates as calculated by Doron
& Behar (2002).
Update: several minor corrections: the Si IX C7 line has been deleted; the Si VIII N6 line now only
has the 319.83 ˚A line strength instead of the total triplet strength; the Ni XVIII and Fe XVI Na1A and
NA1B lines plus their satellites have been deleted.
3.32.2 Syntax
The following syntax rules apply:
var gacc #r - Set the accuracy gfbacc for free-bound emission. Default is 10−3
, maximum value 1 and
minimum value 0. Do not change if you do not know what it does.
var gacc reset - Reset gfbacc to its default value.
var line #a #l - For process #a (where #a is one of the abbreviations in Table 3.7) the process is
allowed (if #l is true) or disabled (if #l is false). By default, all processes are allowed.
var line reset - Enable all line emission processes
var line show - Show the status of the line emission processses
var doppler #i - Line broadening, see the four allowed values in the above description
var calc old - Use the old Mekal code
var calc new - Use the new updated atomic data (for SPEX version 3.0 and higher)
var newmekal wav #l - if true (the default), use the updated wavelengths for the Mekal code
var newmekal fe17 #l - if true (the default), use the updated Fe XVII calculations for the Mekal code
var newmekal update #l - if true (the default), use the updates for some lines for the Mekal code
var newmekal all #l - if true (default), use all the above three corrections for the Mekal code
var ibalmaxw #l - if true use multi-Maxwellians (if relevant) for both the ionisation balance and the
spectrum (default); if false, only use it for the spectrum.
3.32.3 Examples
var gacc 0.01 - Set the accuracy gfbacc for free-bound emission.to 0.01
var gacc reset - Reset the accuracy gfbacc for free-bound emission.to its default value of 0.001
var line ex f - Exclude electron excitation
var line ds t - Include dielectronic satellites
var line reset - Include all line emission processes
var line show - Show status of all line emission proceses
var doppler f - Do not use thermal Doppler bvroadening
var calc new - Use the new atomic data (EXPERIMENTAL)
var newmekal wav f - Use the original Mekal wavelengths instead
var newmekal fe17 t - Use the updated Fe XVII calculations
var newmekal all f - Go back to the full old Mekal code
var newmekal all t - Take the full updated Mekal code
var ibalmaxw f - Do not use Multi-Maxwellians for the ionisation balance
3.33 Vbin: variable rebinning of the data 63
3.33 Vbin: variable rebinning of the data
Overview
This command rebins (a part of) the data (thus both the spectrum and the response) such that the signal
to noise ratio in that part of the spectrum is at least a given constant. Thus instead of taking a fixed
number of data channels for binning, the number of data channels binned is here variable as is the bin
width. On top of specifying the S/N ratio, you also specify the minimal bin width. This is useful for
rebinning low count data, which have no strong or sharp features or lines in it.
Warning: For high resolution spectra with sharp and strong lines, this binning can lead to very wrong
results. In this case either the emission lines or the continuum (in case of absorption lines) have a much
higher signal to noise ratio than the other component. As a result this function will try to bin the line
and continuum together, resulting in a smoothing out of the lines.
Warning: It is not always guaranteed that the minimum signal-to-noise ratio is obtained in all channels.
This is an effect of the applied algorithm. Channels with the highest S/N ratio and neighboring bins are
merged until sufficient S/N ratio is obtained. This process is continued for the remaining number of bins.
At the end of the process a few bins with a low S/N ratio will remain. These are merged with their
neighbors, resulting in a possibly lower S/N ratio for that bin.
Syntax
The following syntax rules apply:
vbin #i1: #i2 #r - Simplest command allowed. #i1: is the range in data channels over which the
binning needs to take place. #i2 in the minimum amount of data channels that need to be binned, and
#r is the minimal S/N ratio one wants the complete data set to have.
vbin #r1: #i #r2 unit #a - The same command as above, except that now the ranges over which the
data is to be binned (#r1:) are specified in units (#a) different from data channels. These units can be
eV, keV, ˚A, as well as in units of Rydberg (ryd), Joules (j), Hertz (hz) and nanometers (nm).
vbin [instrument #i1:] [region #i2:] #i3: #i4 #r - Here #i3: and #i4 are the same as #i1:
and #i2 in the first command, also #r is the minimal S/N ratio required. However, here one can specify
the instrument range #i1: and the region range #i2: as well, so that the binning only is performed for
a certain data set.
vbin [instrument #i1:] [region #i2:] #r1: #i2 #r2 [unit #a] - This command is the same
as the above, except that here one can specify the range over which the binning should occur in the units
specified by #a. These units can be eV, ˚A, keV, as well as in units of Rydberg (ryd), Joules (j), Hertz
(hz) and nanometers (nm).
Examples
vbin 1:10000 3 10 - Bins the data channels 1:10000 with a minimal bin width of 3 data channels, and
a minimum S/N ratio of 10.
vbin 1:4000 3 10 unit ev - Does the same as the above, but now the data range to be binned is given
in eV, from 1−4000 eV, instead of in data channels.
vbin instrument 1 region 1 1:19 3 10 unit a - Bins the data from instrument 1 and region 1 between
1 and 19 ˚A with the same minimum bin width and S/N as above.
64 Syntax overview
3.34 Watch
Overview
If you have any problems with the execution of SPEX, you may set the watch-options. For example, if
the computation time needed for your model is very large, it could be wise to check which parts of the
program consume most of the cpu-time. You might then hope to improve the performance by assuming
other parameters or by re-structuring a part of the code. In this case, you set the ”time” flag to true
(see below), and at the end of the program you will see how much time was spent in the most important
subroutines.
Another case occurs in the unlikely case that SPEX crashes. In that case it is recommended to re-execute
the program, saving all commands onto a log-file and use the ”sub” flag to report the entering and exiting
of all major subroutines. This makes it more easy to find the source of the error.
Timing is done by the use of the stopwatch package by William F. Mitchell of the NIST, which is free
available at the web. If the time flag is set to true, on exit SPEX will report for each subroutine the
following execution times (in s):
• The user time, i.e. the cpu-time spent in this subroutine
• The system time, i.e. the overhead system time for this subroutine
• The wall time, i.e. the total time spent while executing this subroutine.
Also the totals for SPEX as a whole are given (this may be more then the sum of the subroutine
components, since not all subroutines are listed separately; the wall tiem for SPEX as a whole also
includes the time that the program was idle, waiting for input from the user).
Syntax
The following syntax rules apply:
watch time #l - set the ”time” flag to true or false.
watch sub #l - set the flag that SPEX causes to report each major subroutine it enters or exits
Examples
watch time t - set the ”time” flag to true
watch sub f - set the subroutine report flag to false
Chapter 4
Spectral Models
4.1 Overview of spectral components
For more information on the definition of spectral components and the different types, see Sect. 2.3.
Currently the following models are implemented in SPEX, see Table 4.1.
66 Spectral Models
4.2 Absm: Morrison & McCammon absorption model
This model calculates the transmission of neutral gas with cosmic abundances as published first by
Morrison & McCammon (1983). It is a widely used model. The following is useful to know when this
model is applied:
1. The location of the absorption edges is not always fully correct; this can be seen with high resdolution
grating spectra
2. The model fails in the optical/UV band (i.e., it does not become transparent in the optical)
3. No absorption lines are taken into account
4. The abundances cannot be adjusted
If all the above is of no concern (as is the case in many situations), then the Morrison & McCammon
model is very useful. In case higher precision or more detail is needed, the user is advised to use the
”hot” model with low temperature in SPEX, which gives the transmission of a slab in collisional ionisation
equilibrium.
The parameters of the model are:
nh - Hydrogen column density in 1028
m−2
. Default value: 10−4
(corresponding to 1024
m−2
, a typical
value at low Galactic latitudes).
f - The covering factor of the absorber. Default value: 1 (full covering)
Recommended citation: Morrison & McCammon (1983).
4.3 Amol: oxygen edge molecules absorption model
This model calculates the transmission of various molecules.
The following compounds are presently taken into account (see Table 4.2).
Table 4.2: Molecules present in the amol model.
nr Name Chemical formula Atom & shell Reference
108 molecular oxygen O2 O 1s a
114 silicon crystal Si Si 1s h
126 metallic iron Fe Fe 1s,2p i,j
2001 water H2O O 1s c
2002 crystalline ice H2O O 1s d
2003 amorphous ice H2O O 1s d
2010 carbon monoxide CO O 1s a
2011 carbon dioxide CO2 O 1s a
2020 laughing gas N2O O 1s a,b
2100 silicon carbide SiC Si 1s h
2101 silicon nitrite Si3N4 Si 1s h
2102 silicon monoxide SiO Si 1s h
2103 quartz SiO2 Si 1s h
2104 silica SiO2 Si 1s h
2200 eskolaite Cr2O3 O 1s e
2300 iron monoxide FeO Fe 1s i
2301 iron oxide Fe1−xO O 1s e
Continued on next page
4.3 Amol: oxygen edge molecules absorption model 67
nr Name Chemical formula Atom & shell Reference
2302 magnetite Fe3O4 O, Fe 1s e,i
2303 hematite Fe2O3 O, Fe 1s; Fe 2p e,i,j
2304 iron sulfite FeS2 Fe 1s i
2400 nickel monoxide NiO O 1s e
2500 cupric oxide CuO O 1s e
3001 adenine C5H5N5 O 1s f
3100 enstatite MgSiO3 Si 1s h
3101 enstatite alfa MgSiO3 Si 1s h
3102 enstatite chondrite Mg2Si2O6 Si 1s h
3103 pyroxene MgSiO3 O 1s k
3200 calcite CaCO3 Ca 1s g
3201 aragonite CaCO3 Ca 1s g
3202 vaterite CaCO3 Ca 1s g
3203 perovskite CaTiO3 O 1s e
3300 hercynite FeAl2O4 O 1s e
3301 lepidocrocite FeO(OH) Fe 2p j
3302 fayalite Fe2SiO4 Fe 1s, 2p i,j
3303 iron sulfate FeSO4 Fe 2p j
3304 ilmenite FeTiO3 O 1s e
3305 chromite FeCr2O4 O 1s e
4001 guanine C5H5N5O O,N 1s f
4002 cytosine C4H5N3O O,N 1s f
4003 thymine C5H6N2O2 O,N 1s f
4004 uracil C4H4N2O2 O,N 1s f
4100 andradite Ca3Fe2Si3O12 O 1s e
4101 acmite NaFeSi2O6 O 1s e
4102 franklinite Zn0.6Mn0.8Fe1.6O4 O 1s e
4103 olivine Mg1.6Fe0.4SiO4 O 1s e
4104 almandine Fe3Al2(SiO4)3 O 1s e
4105 hedenbergite CaFeSi2O6 O 1s e
5001 dna (herring sperm) C39H61N15O36P4 O,N 1s f
6001 montmorillonite Na0.2Ca0.1Al2Si4O10(OH)2(H2O)10 Si 1s h
6002 nontronite Na0.3Fe3+
2 Si3AlO10(OH)2 • (H2O) Si 1s h
7001 enstatite paulite Ca2Mg4Al0.75Fe0.25(Si7AlO22)(OH)2 Si 1s h
References:
a
Barrus et al. (1979), 0.5-0.75 eV resolution
b
Wight & Brion (1974), 0.5 eV resolution
c
Hiraya et al. (2001), 0.055 eV resolution
d
Parent et al. (2002), 0.1 eV resolution
e
van Aken et al. (1998), 0.8 eV resolution
f
Fujii et al. (2003), unknown resolution
g
Hayakawa et al. (2008), unknown resolution
h
Lee (2010), unknown resolution
i
Lee & Ravel (2005), unknown resolution
j
Lee et al. (2009), 0.23 eV resolution
k
Lee et al. (2008), 0.7 eV resolution
The chemical composition of these minerals was mainly taken from the Mineralogy Database of David
Barthelmy1
. For DNA we assume equal contributions of adenine, cytosine, guanine and thymine, plus
1
http://webmineral.com/
68 Spectral Models
for each of these on average one phosphate and one 2-deoxyribose molecule. We take the cross-sections
from the references as listed in Table 4.2 in the energy interval where these are given, and use the cross
section for free atoms (Verner & Yakovlev 1995) outside this range.
van Aken et al. (1998) do not list the precise composition of iron oxide. We assume here that x = 0.5.
Some remarks about the data from Barrus et al. (1979): not all lines are given in their tables, because
they suffered from instrumental effects (finite thickness absorber combined with finite spectral resolution).
However, Barrus et al. (1979) have estimated the peak intensities of the lines based on measurements
with different column densities, and they also list the FWHM of these transitions. We have included
these lines in the table of cross sections and joined smoothly with the tabulated values.
For N2O, the fine structure lines are not well resolved by Barrus et al. (1979) Instead we take here the
relative peaks from Wight & Brion (1974), that have a relative ratio of 1.00 : 0.23 : 0.38 : 0.15 for peaks
1, 2, 3, and 4, respectively. We adopted equal FWHMs of 1.2 eV for these lines, as measured typically
for line 1 from the plot of Wight. We scale the intensities to the peak listed by Barrus et al. (1979).
Further, we subtract the C and N parts of the cross section as well as the oxygen 2s/2p part, using
the cross sections of Verner & Yakovlev (1995). At low energy, a very small residual remains, that we
corrected for by subtracting a constant fitted to the 510–520 eV range of the residuals. The remaining
cross section at 600 eV is about 10 % above the Verner cross section; it rapidly decreases; we approximate
the high-E behaviour by extrapolating linearly the average slope of the ratio between 580 and 600 eV
to the point where it becomes 1. The remaining cross section at 600 eV is about 10% above the Verner
& Yakovlev (1995) cross section; it rapidly decreases; we approximate the high-E behaviour therefore
by extrapolating linearly the average slope of the ratio between 580 and 600 eV to the point where it
becomes 1.
Warning: The normalisation is the total molecular column density. Thus, a value of 10−7
for CO2
means 1021
CO2 molecules m−2
, but of course 2×1021
O atoms m−2
, because each CO2 molecule contains
2 oxygen atoms.
Warning: The Table above shows for which edges and atoms the XAFS are taken into account. For
all other edges and atoms not listed there, we simply use the pure atomic cross-section (without absorption
lines). Note that for almost all constituents this may give completely wrong cross sections in the
optical/UV band, as at these low energies the effects of chemical binding, crystal structure etc. are very
important for the optical transmission constants. This is contrary to the SPEX models for pure atomic
or ionised gas, where our models can be used in the optical band.
Warning: It is possible to change the values of the output atomic column densities of H–Zn, that are
shown when you issue the ”show par” command of SPEX. However, SPEX completely ignores this and
when you issue the ”calc” or ”fit” commands, they will be reset to the proper values. Morale: just read
of those parameters, don’t touch them!
The parameters of the model are:
n1--n4 - Molecular column density in 1028
m−2
for molecules 1–4. Default value: 10−6
for molecule 1,
and zero for the others.
i1--i4 - the molecule numbers for molecules 1–4 in the list (Table 4.2). Default value: 108 (O2) for
molecule 1, zero for the others. A value of zero indicates that for that number no molecule will be taken
into account. Thus, for only 1 molecule, keep i2–i4 = 0.
The following parameters are common to all our absorption models:
f - The covering factor of the absorber. Default value: 1 (full covering)
zv - Average systematic velocity v of the absorber
The following parameters are only output parameters:
h--zn - The column densities in 1028
m−2
for all atoms added together for the all molecules that are
present in this component.
4.4 Bb: blackbody model 69
Recommended citation: Pinto et al. (2010).
4.4 Bb: blackbody model
The surface energy flux of a blackbody emitter is given by
Fν = πBν =
2πhν3
/c2
ehν/kT − 1
(4.1)
(cf. Rybicki & Lightman 1986, chapter 1). We transform this into a spectrum with energy units (conversion
from Hz to keV) and obtain for the total photon flux:
S(E)dE = 2πc[103
e/hc]3 E2
eE/T − 1
dE (4.2)
where now E is the photon energy in keV, T the temperature in keV and e is the elementary charge in
Coulomb. Inserting numerical values and multiplying by the emitting area A, we get
N(E) = 9.883280 × 107
E2
A/(eE/T
− 1) (4.3)
where N(E) is the photon spectrum in units of 1044
photons/s/keV and A the emitting area in 1016
m2
.
The parameters of the model are:
norm - Normalisation A (the emitting area, in units of 1016
m2
. Default value: 1.
t - The temperature T in keV. Default value: 1 keV.
Recommended citation: Kirchhoff (1860).
4.5 Cf: isobaric cooling flow differential emission measure model
This model calculates the spectrum of a standard isobaric cooling flow. The differential emission measure
distribution dY (T )/dT for the isobaric cooling flow model can be written as
D(T ) ≡ dY (T )/dT =
5 ˙Mk
2µmHΛ(T ),
(4.4)
where ˙M is the mass deposition rate, k is Boltzmann’s constant, µ the mean molecular weight (0.618
for a plasma with 0.5 times solar abundances), mH is the mass of a hydrogen atom, and Λ(T ) is the
cooling function. We have calculated the cooling function Λ using our own SPEX code for a grid of
temperatures and for 0.5 times solar abundances. The spectrum is evaluated by integrating the above
differential emission measure distribution between a lower temperature boundary T1 and a high temperature
boundary Tn. We do this by creating a temperature grid with n bins and calculating the spectrum
for each temperature.
Warning: Take care that n is not too small in case the relevant temperature is large; on the other hand
if n is large, the computational time increases. Usually a spacing with temperature differences between
adjacent bins of 0.1 (in log) is sufficient and optimal.
Warning: The physical relevance of this model is a matter of debate
The parameters of the model are:
norm - The mass deposition rate ˙M in M⊙ yr−1
t1 - Lower temperature cut-off temperature T1. Default: 0.1 keV.
tn - Upper temperature cut-off temperature Tn. Default: 1 keV.
nr - Number of temperature bins n used in the integration. Default value: 16
70 Spectral Models
p - Slope p = 1/α. Default: 0.25 (α = 4).
cut - Lower temperature cut-off, in units of Tmax. Default value: 0.1.
The following parameters are the same as for the cie-model:
ed - Electron density in 1020
m−3
it - Ion temperature in keV
vmic - Micro turbulent velocity in km/s
ref - Reference element
01. . .30 - Abundances of H to Zn
file - Filename for the nonthermal electron distribution
Recommended citation: Kaastra et al. (2004).
4.6 Cie: collisional ionisation equilibrium model
This model calculates the spectrum of a plasma in collisional ionisation equilibrium (CIE). It consists
essentially of two steps, first a calculation of the ionisation balance and then the calculation of the X-ray
spectrum. The basis for this model is formed by the mekal model, but several updates have been included.
4.6.1 Temperatures
Some remarks should be made about the temperatures. SPEX knows three temperatures that are used
for this model.
First there is the electron temperature Te. This is usually referrred to as ”the” temperature of the plasma.
It determines the continuum shape and line emissivities and the resulting spectrum is most sensitive to
this.
Secondly, there is the ion temperature Ti. This is only important for determining the line broadening,
since this depends upon the thermal velocity of the ions (which is determined both by Ti and the atomic
mass of the ion). Only in high resolution spectra the effects of the ion temperature can be seen.
Finally, we have introduced here the ionization balance temperature Tb that is used in the determination
of the ionization equilibrium. It is the temperature that goes into the calculation of ionization and recombination
coefficients. In equilibrium plasmas, the ratio Rb ≡ Tb/Te is 1 by definition. It is unphysical
to have Rb not equal to 1. Nevertheless we allow for the possibility of different values of Rb, in order to
mimick out of equilibrium plasmas. For Rb < 1, we have an ionizing plasma, for Rb > 1 a recombining
plasma. Note that for ionizing plasmas SPEX has also the nei model, which takes into account explicitly
the effects of transient (time dependent) ionization.
It is also possible to mimick the effects of non-isothermality in a simple way. SPEX allows for a Gaussian
emission measure distribution
Y (x) =
Y0
√
2πσT
e−(x − x0)2
/2σ2
T (4.5)
where Y0 is the total, integrated emission measure. By default x ≡ log T and x0 ≡ log T0 with T0 the
average temperature of the plasma (this is entered at the ”T” value in SPEX). However, this can be
changed to x ≡ T and x0 ≡ T0 by setting logt to 0. If the parameter sup is set > 10−5
, then the Gaussian
emission measure distribution model becomes asymmetric. The sig parameter determines the slope of the
low-temperature part of the Gaussian and sup determines the high-temperature side. Usually (default)
σT = 0 and in that case the normal isothermal spectrum is chosen. Note that for larger values of σT the
cpu time may become larger due to the fact that the code has to evaluate many isothermal spectra.
4.6 Cie: collisional ionisation equilibrium model 71
4.6.2 Line broadening
Apart from line broadening due to the thermal velocity of the ions (caused by Ti > 0) it is also possible
to get line broadening due to (micro)turbulence. In this case the line broadening is determined by vmicro,
which is given by vmicro ≡
√
2σv with σv the Gaussian velocity dispersion in the line of sight. Thus,
without thermal broadening the FWHM of the line would be 1.6651 times vmicro.
4.6.3 Density effects
It is also possible to vary the electron density ne of the plasma. This does not affect the overall shape
of the spectrum (i.e., by changing ne only SPEX still uses the previous value of the emission measure
Y ≡ nHneV ), but spectral lines that are sensitive to the electron density will get different intensities.
Usually this occurs for higher densities, for example under typical ISM conditions (ne = 1 cm−3
) this is
not an important effect.
4.6.4 Non-thermal electron distributions
The effects of non-thermal electron distribution on the spectrum can be included. See Sect. 5.5 for more
details.
4.6.5 Abundances
The abundances are given in Solar units. Which set of solar units is being used can be set using the ”abun”
command (see Sect. 3.2). For spectral fitting purposes it is important to distinguish two situations.
In the first case there is a strong thermal continuum. Since in most circumstances the continuum is
determined mainly by hydrogen and helium, and the X-ray lines are due to the other elements, the line to
continuum ratio is a direct measurement of the metal abundances compared to H/He. In this situation, it
is most natural to have the hydrogen abundance fixed and allow only for fitting of the other abundances
(as well as the emission measure).
In the other case the thermal continuum is weak, but there are strong spectral lines. Measuring for
example the Fe abundance will give large formal error bars, not because the iron lines are weak but
because the continuum is weak. Therefore, all abundances will get rather large error bars, and despite
the fact of strong O and Fe lines, the formal error bars on the O/Fe ratio becomes large. This can be
avoided by choosing another reference element, preferentially the one with the strongest lines (for example
Fe). Then the O/Fe ratio will be well constrained, and it is now only the H abundance relative to Fe
that is poorly constrained. In this case it is important to keep the nominal abundance of the reference
element to unity. Also keep in mind that in general we write for the normalisation nenXV in this case;
when the reference element is H, you mays substitute X=H; however when it is another element, like O,
the normalisation is still the product of nenXV where X stands for the fictitious hydrogen density derived
from the solar O/H ratio.
Example: suppose the Solar O abundance is 1E-3 (i.e. there is 0.001 oxygen atom per hydrogen atom
in the Sun). Take the reference atom oxygen (Z = 8). Fix the oxygen abundance to 1. Fit your
spectrum with a free hydrogen abundance. Suppose the outcome of this fit is a hydrogen abundance
of 0.2 and an emission measure 3 (in SPEX units). This means nenXV = 3 × 1064
m−3
. Then the
”true” emission measure nenHV = 0.2 × 3 × 1064
m−3
. The nominal oxygen emission measure is nenOV
= 0.001 × 3 × 1064
m−3
, and nominally oxygen would have 5 times overabundance as compared to
hydrogen, in terms of solar ratios.
4.6.6 Parameter description
Warning: When you make the temperature too low such that the plasma becomes completely neutral, the
model will crash. This is because in that case the electron density becomes zero, and the emission measure
72 Spectral Models
is undefined. The nominal temperature limits that are implemented in SPEX usually avoid that condition,
but the results may depend somewhat upon the metallicity because of the charge exchange processes in the
ionisation balance.
Warning: In high resolution spectra, do not forget to couple the ion temperature to the electron
temperature, as otherwise the ion temperature might keep its default value of 1 keV during spectral fitting
and the line widths may be wrong.
Warning: Some people use instead of the emission measure Y ≡ nHneV , the quantity Y ′
= n2
eV
as normalisation. This use should be avoided as the emission is proportional to the product of electron
and ion densities, and therefore use of Y ′
makes the spectrum to depend nonlinear on the elemental
abundances (since an increase in abundances also affects the ne/nH ratio).
Warning: The default line broadening is just Doppler broadening. This is fine and self-consistent for
the ‘old’ line calculation. To incorporate the natural line broadeing for the ‘new’ calculations, the user
must use the var dopp 4 option to get Voigt profiles. This is physically better but takes more computation
time.
The parameters of the model are:
norm - the normalisation, which is the emission measure Y ≡ nHneV in units of 1064
m−3
, where ne and
nH are the electron and Hydrogen densities and V the volume of the source. Default value: 1.
t - the electron temperature Te in keV. Default value: 1.
sig - the width σT of the gaussian emission measure profile. Default value: 0. (no temperature distribution
i.e. isothermal)
sup - the width σT of the high-temperature part of the gaussian emission measure profile. If larger than
10−5
keV, the sig parameter becomes the sigma value for the low-temperature end. Default value: 0
logt - Switch between linear and logarithmic temperature scale for the gaussian emission measure profile.
Default value: 1 (logarithmic)
ed - the electron density ne in units of 1020
m−3
(or 1014
cm−3
). Default value: 10−14
, i.e. typical ISM
conditions, or the low density limit.
it - the ion temperature Ti in keV. Default value: 1
rt - the ratio of ionization balance to electron temperature, Rb = Tb/Te in keV. Default value: 1.
vmic - the (micro)turbulent velocity vmicro, in km/s. Default value 0.
ref - reference element. Default value 1 (hydrogen). See above for more details. The value corresponds
to the atomic number of the reference element.
01 - Abundance of hydrogen (H, Z=1) in Solar units. Default 1.
02 - Abundance of helium (He, Z=2) in Solar units. Default 1.
. . .
30 - Abundance of zinc (Zn, Z=30) in Solar units. Default 1.
file - Filename for the nonthermal electron distribution. If not present, nonthermal effects are not taken
into account (default).
Recommended citation: Kaastra et al. (1996a).
4.7 Comt: comptonisation model
This is the model for Comptonisation of soft photons in a hot plasma, developed by Titarchuk (1994).
See the XSPEC manual for more details. The code was substantially improved and brought to the SPEX
standards.
4.7.1 Some modifications
Titarchuk (1994) gives an analytical approximation for β(τ) to the exact calculations as provided by
Sunyaev & Titarchuk (1985) for 0.1 < τ < 10. Their approximation has the proper asymptotic behaviour
4.8 CX: model for charge exchange plasmas 73
for small and large values of τ, but unfortunately has deviations up to 7 % over the 0.1 − 10 range for τ.
The approximation by Titarchuk is given in their equations (27) and (28) by
disk:β =
π2
12(τ + 2/3)2
(1 − e−1.35τ) + 0.45e−3.7τ ln
10
3τ
, (4.6)
sphere:β =
π2
3(τ + 2/3)2
(1 − e−0.7τ) + e−1.4τ ln
4
3τ
. (4.7)
We found an approximation that is better than 1 % using a slight modification of the above equations.
We use these new approximations in our calculations:
disk:β =
0.8351
(τ + 0.867)2
(1 − e−3.876τ) + 0.572e−3.75τ ln
1.06
τ
, (4.8)
sphere:β =
3.504
(τ + 1.2)2
(1 − e−2.09τ) + 1.013e−2.2τ ln
1.6
τ
. (4.9)
Warning: For the physically valid range of parameters, consult the XSPEC manual; see also Hua &
Titarchuk (1995), their Fig. 7.
The parameters of the model are:
norm - Normalisation A of the power law, in units of 1044
ph s−1
keV−1
. Due to the way the model is
calculated, this is not the flux at 1 keV! Default value: 1.
t0 - The temperature T of the seed photons in keV. Default value: 1 keV.
t1 - The plasma temperature T in keV. Default value: 100 keV.
tau - The optical depth. Default value: 3.
type - The type of geometry. Allowed values are 0 for a disk (default) or 1 for a sphere. This is a frozen
parameter (cannot be fitted).
Recommended citation: Titarchuk (1994)
4.8 CX: model for charge exchange plasmas
This model calculates the spectrum emitted from a hot plasma when it recombines with cold neutral
materials. This model is based on three key assumptions: (1) it considers only single electron capture in
ion-neutral collision; (2) all cross section data are obtained only with atomic hydrogen target, (3) electronic
collisional excitation and recombination are ignored in the spectral calculation. More informations
can be found in Gu et al. (2016).
4.8.1 Charge exchange cross sections
The CX cross section data used in the model are partly taken from literatures, including quantum
molecular-orbital close-coupling calculations for C5+
and O6+
by Wu et al. (2012) and Nolte et al. (2012),
multi-channel Laudau-Zener results for Fe25+
and Fe26+
by Mullen (2016), other data compilations for
C6+
and O8+
by Janev et al. (1993), and NIFS Charge Transfer Database (CHART) 2
for Be4+
, B5+
,
N7+
, and Ne10+
. For CHART database, we extracted all the data, from both theoretical calculations and
experiments (see a full list in Table 1 of Gu et al. (2016)), and fitted them with Eq.2 of Gu et al. (2016)
in the energy range of interests. In typical astrophysical velocity range (∼ 100 − 5000 km s−1
), the useful
CHART data are usually from molecular-orbital and atomic-orbital close-coupling methods, and a few
classical trajectory Monte Carlo calculations. All the above data are dependent on collision energy, and
resolved to levels described by quantum number n and l.
For ions not available in public sources, we developed a new method to interpolate by analyzing the known
ions. First we used a scaling law to determine total cross section for each ion, and applied another scaling
2
http://dbshino.nifs.ac.jp/
74 Spectral Models
law to represent the n− selectivity. The l− dependence is approximated by one of the five empirical
weighting functions presented in Eqs.4 − 8 of Gu et al. (2016).
Warning: CX model only works with the updated atomic database set through the command “ var calc
new”.
Warning: All Beryllium-like sequence ions are not included in the current version; will be available
later.
Warning: We will keep updating the CX model when new data (especially for molecular targets) from
theoretical calculations and experiments become available.
4.8.2 Parameter description
The parameters of the CX model are:
norm - the normalisation, which is the emission measure Y ≡ nHnnhV in units of 1064
m−3
, where nH and
nnh are the Hydrogen densities of the ionized and neutral materials, respectively, and V is the effective
interaction volume. Default value: 1.
hden - Hydrogen density of the neutral materials in units of 1020
m−3
(or 1014
cm−3
). Default value:
10−14
.
mode - Switch between a hot-cold interaction driven by thermal motion of hot plasma, and the one dominated
by flow velocity. Default value: 2 (kinematic).
t - the ionization temperature of hot matter in keV. It is also used to approximate the thermal motion
when mode is set to 1. Default value: 1.
sig - the width σT of the gaussian emission measure profile. Default value: 0. (no temperature distribution
i.e. isothermal)
sup - the width σT of the high-temperature part of the gaussian emission measure profile. If larger than
10−5
keV, the sig parameter becomes the sigma value for the low-temperature end. Default value: 0
logt - Switch between linear and logarithmic temperature scale for the gaussian emission measure profile.
Default value: 1 (logarithmic)
zv - Collision velocity in unit of km s−1
, used when mode is set to 2. Default value: 100
op - Switch between single and multiple collisions for each ion. In multiple collision case, one ion would
continuously undergo CX and produce various emission lines, until it becomes neutral. Default: 1 (single)
wt - Weighting functions for subshell l− population. When wt is set to 1, the l− population is approximated
by a series of empirical functions that switchs from one to another as a function of collision velocity.
See Gu et al. (2016) for details. These empirical functions are defined in Eqs.4 − 8 of Gu et al. (2016),
and will be selected when wt is set to 2 − 6, respectively. Default: 1
vmic - the (micro)turbulent velocity vmicro, in km/s. Default value 0.
ref - reference element. Default value 1 (hydrogen). See above for more details. The value corresponds
to the atomic number of the reference element.
01 - Abundance of hydrogen (H, Z=1) in Solar units. Default 1.
02 - Abundance of helium (He, Z=2) in Solar units. Default 1.
. . .
30 - Abundance of zinc (Zn, Z=30) in Solar units. Default 1.
file - Filename for the nonthermal distribution. If not present, nonthermal effects are not taken into
account (default).
Recommended citation: Gu et al. (2016).
4.9 Dabs: dust absorption model
This model allows the user to maake a zeroth order approximation to the effects of dust on an X-ray
absorption spectrum. basically, compared to absorption by atomic gas, the effects of dust are two-fold:
4.10 Dbb: disk blackbody model 75
• Modifications to the fine structure near the edge
• Reduced opacity due to self-shielding in grains
The dabs model only accounts for the second effect, reduced opacity due to self-shielding. The formalism
of Wilms et al. (2000) is followed, and we refer to that paper for a full explanation.
In the set of abundances, we use the depletion factors of Wilms et al. (2000).
H He Li Be B C N O F Ne Na Mg Al Si P
0 0 1 0 0 0.5 0 0.4 0 0 0.75 0.8 0.98 0.9 0.4
S Cl Ar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn
0.4 0.5 0 0 0.997 0 0.998 0 0.97 0.93 0.7 0.95 0.96 0 0
The numbers represent the fraction of the atoms that are bound in dust grains. Noble gases like Ne and
Ar are chemically inert hence are generally not bound in dust grains, but other elements like Ca exist
predominantly in dust grains.
Warning: For a realistic model, it is advised to combine the dabs model with a hot model, where (for
Solar abundances), the hot model should contain the elemnts not bound in the dust.
Finally, we note that the amol model can deal with the modified structure near the oxygen edge, but
that model does not take elf-shielding into account.
The parameters of the model are:
nh - Nominal hydrogen column density in 1028
m−2
. Default value: 1.
amin - Minimum grain size in µm. Default value: 0.025.
amax - Minimum grain size in µm. Default value: 0.25.
p - Power index grain size distribution. Default value: 3.5.
rho - Mean density of the grains in units of 1000 kg m−3
. Default value: 3.
ref - Reference atom. Default value: 3 (Lithium). because dust, according to the depletion factors used,
does not contain hydrogen, we substitute here formally Lithium. The user is advisednot to change this.
01. . .30 - Abundances of H to Zn. See the remark on depletion factors above.
The following parameters are common to all our absorption models:
fcov - The covering factor of the absorber. Default value: 1 (full covering)
zv - Average systematic velocity v of the absorber
Recommended citation: Wilms et al. (2000) and Kaastra et al. (2009).
4.10 Dbb: disk blackbody model
We take the model for a standard Shakura-Sunyaev accretion disk. The radiative losses from such a disk
are given by
Q =
3GM ˙M(1 − ri/r)
8πr3
, (4.10)
where Q is the loss term in W m−2
at radius r, M the mass of the central object, ˙M the accretion rate
through the disk and ri the inner radius. If this energy loss is radiated as a blackbody, we have
Q = σT 4
(4.11)
with σ the constant of Stefan-Boltzmann and T (r) the local temperature of the blackbody. The total
spectrum of such a disk is then obtained by integration over all radii. We do this integration numerically.
Note that for large r, T ∼ r−3/4
.
76 Spectral Models
Warning: A popular disk model (diskbb in XSPEC) assumes this temperature dependence over the
full disk. However, we correct it using the factor (1 − ri/r) in Q which corresponds to the torque-free
condition at the inner boundary of the disk.
The photon spectrum of the disk is now given by
N(E) =
8π2
E2
r2
i cos i
h3c2
fd(E/kTi, ro/ri), (4.12)
where i is the inclination of the disk (0 degrees for face-on disk, 90 degrees for an edge-on disk), E the
photon energy, ro the outer edge of the disk, and Ti is defined by
T 4
i = 3GM ˙M/8πr3
i σ (4.13)
and further the function fd(y, r) is defined by
fd(y, r) =
r
1
xdx
ey/τ − 1
(4.14)
where τ(x) is defined by τ4
(x) = (1 − 1/
√
x)/x3
.
In addition to calculating the spectrum, the model also allows to calculate the average radius of emission
Re at a specified energy Er. This is sometimes useful for time variability studies (softer photons emerging
from the outer parts of the disk).
Given the fit parameters Ti and ri, using (4.13) it is straightforward to calculate the product M ˙M.
Further note that if ri = 6GM/c2
, it is possible to find both M and ˙M, provided the inclination angle i
is known.
The parameters of the model are:
norm - Normalisation A (= r2
i cos i), in units of 1016
m2
. Default value: 1.
t - The nominal temperature Ti in keV. Default value: 1 keV.
ro - The ratio of outer to inner disk radius, ro/ri
ener - Energy Er at which the average radius of emission will be calculated
rav - Average radius Re of all emission at energy Er specified by the parameter above. Note that this is
not a free parameter, it is calculated each time the model is evaluated.
Recommended citation: Shakura & Sunyaev (1973).
4.11 Delt: delta line model
The delta line model is a simple model for an infinitely narrow emission line.
The spectrum is given by:
F(E) = Aδ(E − E0), (4.15)
where E is the photon energy in keV, F the photon flux in units of 1044
ph s−1
keV−1
, E0 is the line
energy of the spectral line (in keV) and A is the line normalisation (in units of 1044
ph s−1
). The total
line flux is simply given by A.
To ease the use for dispersive spectrometers (gratings) there is an option to define the wavelength instead
of the energy as the basic parameter. The parameter type determines which case applies: type=0 (default)
corresponding to energy, type=1 corresponding to wavelength units.
Warning: When changing from energy to wavelength units, take care about the frozen/thawn status of
the line centroid and FWHM
Warning: You need to do a ”calc” or ”fit” command to get an update of the wavelength (for type=0)
or energy (type=1).
4.12 Dem: differential emission measure model 77
The parameters of the model are:
norm - Normalisation A, in units of 1044
ph s−1
. Default value: 1.
e - The line energy E0 in keV. Default value: 6.4 keV.
type - The type: 0 for energy units, 1 for wavelength units.
w - The line wavelength λ in ˚A. Default value: 20 ˚A.
4.12 Dem: differential emission measure model
This model calculates a set of isothermal CIE spectra, that can be used later in one of the DEM analysis
tools (see the ”dem” commands of the syntax). The CIE spectra are evaluated for a logarithmic grid of
temperatures between T1 and T2, with n bins.
Warning: For the DEM methods to work, the dem model is the only allowed additive component
that can be present. No other additive components are allowed. But of course the spectrum of the dem
model may be modified by applying any combination of multiplicative models (redshifts, absorptions, line
broadening, etc.).
Warning: Because of the above, do not use the ”fit” commands when you have a dem model. If you
really need to fit, use the pdem model instead.
Warning: In general, the spacing between the different temperature components should not be smaller
than 0.10 in log T . Smaller step sizes will produce unstable solutions.
The parameters of the model are:
t1 - Lower temperature T1 in keV. Default value: 0.001 keV.
t2 - Upper temperature T2 in keV. Default value: 100 keV.
nr - Number of temperature bins. Default value: 64.
The following parameters are the same as for the cie-model:
ed - Electron density in 1020
m−3
it - Ion temperature in keV
vmic - Micro turbulent velocity in km/s
ref - Reference element
01. . .30 - Abundances of H to Zn
file - Filename for the nonthermal electron distribution
Recommended citation: Mewe et al. (1995).
4.13 Dust: dust scattering model
This model calculates the effective transmission of dust that scatters photons out of the line of sight.
No re-emission is taken into account, i.e. it is assumed that all scattered photons are lost from the line
of sight. This makes the model useful for instruments with a high spatial resolution (i.e, the spatial
resolution is much better than the typical size of the dust scattering halo).
Dust scattering is described for example by Draine (2003). In that paper, a link is given to the website
of Draine (http://www.astro.princeton.edu/ draine/dust/dustmix.html) This website contains slightly
updated cross sections for three cases as listed below. The scattering is computed for a Carbonaceous Silicate
Model for Interstellar Dust. The cases are:
1. set=1: for RV = 3.1;
2. set=2: for RV = 4.0;
3. set=3: for RV = 5.5.
78 Spectral Models
Warning: For any instrument where the extraction region has a size comparable to the size of the
dust scattering halo, this model should not be used, as the scattered X-rays will fall within the exctraction
region. Take care when fitting data from different instruments simultaneously.
Warning: This model only calculates the dust scattering, not the dust absorption
The parameters of the model are:
nh - Hydrogen column density in 1028
m−2
. Default value: 10−4
(corresponding to 1024
m−2
, a typical
value at low Galactic latitudes).
f - The covering factor of the absorber. Default value: 1 (full covering)
set - The set of cross sections being used. See table above.
Recommended citation: Draine (2003).
4.14 Ebv: Galactic interstellar extinction model
This model can be used to correct fluxes of optical/UV data for interstellar reddening in our Galaxy. The
reddening is caused by dust absorption and scattering (extinction) in the interstellar medium. The model
uses the extinction curve of Cardelli et al. (1989), including the update for near-UV given by O’Donnell
(1994).
The extinction law can be expressed as:
(Aλ/AV ) = aλ + (bλ/RV ) (4.16)
where, Aλ and AV are the total extinctions (measured in magnitude) at wavelength λ and the V -band,
respectively. The wavelength- dependent parameters aλ and bλ are provided by the aforementioned papers.
The scalar RV is defined as the ratio of total extinction AV to selective extinction AB − AV , where
AB is the total extinction at the B-band. So the selective extinction AB − AV represents a colour excess,
which is commonly denoted as E(B − V ). For Milky Way, the typical value for RV is reported to be
3.1. Thus, by specifying E(B − V ) and RV , the extinction Aλ can be derived, which in turn gives us the
unreddened flux (Fλ) from the observed reddened flux (F∗
λ ) using Fλ = (100.4Aλ
) F∗
λ .
Note that at energies above the Lyman limit, the transmission of the model is set to 1 in SPEX, thus it
can be used alongside the Galactic interstellar X-ray absorption models in SPEX.
The parameters of the model are:
ebv - The colour excess E(B − V ). The value is set by the user.
rv - The scalar RV . Default (recommended) value: 3.1
fcov - The covering factor of the absorber. Default value: 1 (full covering)
Recommended citation: Cardelli et al. (1989) and O’Donnell (1994).
4.15 Etau: simple transmission model
This model calculates the transmission T (E) between energies E1 and E2 for a simple (often unphysical!)
case:
T (E) = e−τ(E)
, (4.17)
with the optical depth τ(E) given by:
τ(E) = τ0Ea
. (4.18)
4.16 Euve: EUVE absorption model 79
In addition, we put here T ≡ 1 for E < E1 and E > E2, where E1 and E2 are adjustable parameters.
This allows the user for example to mimick an edge. Note however, that in most circumstances there are
more physical models present in SPEX that contain realistic transmissions of edges! If you do not want
or need edges, simply keep E1 and E2 at their default values.
Note that τ0 should be non-negative. For a > 0 the spectrum has a high-energy cut-off, for a < 0 it has
a low-energy cut-off, and for a = 0 the transmission is flat. The larger the value of a, the sharper the
cut-off is.
The model can be used as a basis for more complicated continuum absorption models. For example, if
the optical depth is given as a polynomial in the photon energy E, say for example τ = 2 + 3E + 4E2
,
one may define three etau components, with τ0 values of 2, 3, and 4, and indices a of 0, 1 and 2. This is
because of the mathematical identity e−(τ1+τ2)
= e−τ1
× e−τ2
.
The parameters of the model are:
tau0 - Optical depth τ0 at E = 1 keV. Default value: 1.
a - The index a defined above. Default value: 1.
e1 - Lower energy E1 (keV). Default value: 10−20
.
e2 - Upper energy E2 (keV). Default value: 1020
.
f - The covering factor of the absorber. Default value: 1 (full covering)
4.16 Euve: EUVE absorption model
This model calculates the transmission of gas with cosmic abundances as published first by Rumph et al.
(1994). It is a widely used model for the transimission at wavelenghts covered by the EUVE satellite
(λ > 70 ˚A). As it these wavelengths metals are relatively unimportant, it only takes into account hydrogen
and helium, but for these elements it takes into account resonances. However it is not recommended to
use the model for harder X-rays, due to the neglect of metals such as oxygen etc.
Otherwise the user is advised to use the ”absm” model or the ”hot” model with low temperature in
SPEX, which gives the transmission of a slab in collisional ionisation equilibrium.
The parameters of the model are:
nh - Hydrogen column density in 1028
m−2
. Default value: 10−4
(corresponding to 1024
m−2
, a typical
value at low Galactic latitudes).
he1 - The He i / H i ratio. Default value: 0.1.
he2 - The He ii / H i ratio. Default value: 0.01.
f - The covering factor of the absorber. Default value: 1 (full covering)
Recommended citation: Rumph et al. (1994).
4.17 File: model read from a file
This model reads a spectrum from a file. The user inputs a spectrum at n energy bins (n > 1). The file
containing the spectrum should have the follwing format:
• first line: n
• second line: E1, S1
• third line: E2, S2
• . . .
• last line: En, Sn
80 Spectral Models
Here Ei is the energy of a photon in keV, and Si is the spectrum in units of 1044
photons s−1
keV−1
. All
energies Ei must be positive, and the grid must be monotonically increasing (two subsequent energies
may not have the same value). Also, the spectrum Si must be strictly positive (i.e. Si = 0 is not allowed).
SPEX then calculates the spectrum by linear interpolation in the log E − log S plane (this is why fluxes
must be positive). For E < E1 and E > En however, the spectrum is put to zero. Finally, the spectrum
is multiplied by the scale factor N prescribed by the user.
The parameters of the model are:
norm - Normalisation factor N.Default value: 1.
file - The file name of the file containing the spectrum
4.18 Gaus: gaussian line model
The Gaussian line model is the simplest model for a broadened emission line.
The spectrum is given by:
F(E) = Ae(E − E0)2
/2σ2
, (4.19)
where E is the photon energy in keV, F the photon flux in units of 1044
ph s−1
keV−1
, E0 is the average
line energy of the spectral line (in keV) and A is the line normalisation (in units of 1044
ph s−1
). The
total line flux is simply given by A. Further σ is the Gaussian width, which is related to the full width
at half maximum FWHM by FWHM = σ
√
ln 256 or approximately FWHM = 2.3548σ.
To ease the use for dispersive spectrometers (gratings) there is an option to define the wavelength instead
of the energy as the basic parameter. The parameter type determines which case applies: type=0 (default)
corresponding to energy, type=1 corresponding to wavelength units.
Warning: Do not confuse σ with FWHM when interpreting your fit results with other data.
Warning: When changing from energy to wavelength units, take care about the frozen/thawn status of
the line centroid and FWHM
Warning: You need to do a ”calc” or ”fit” command to get an update of the wavelength (for type=0)
or energy (type=1).
The parameters of the model are:
norm - Normalisation A, in units of 1044
ph s−1
. Default value: 1.
e - The line energy E0 in keV. Default value: 6.4 keV.
fwhm - The line FWHM, in keV.
type - The type: 0 for energy units, 1 for wavelength units.
w - The line wavelength λ in ˚A. Default value: 20 ˚A.
awid - The line FWHM, in ˚A.
Recommended citation: Gauss (1809).
4.19 Hot: collisional ionisation equilibrium absorption model
This model calculates the transmission of a plasma in collisional ionisation equilibrium with cosmic
abundances.
For a given temperature and set of abundances, the model calculates the ionisation balance and then
determines all ionic column densities by scaling to the prescribed total hydrogen column density. Using
this set of column densities, the transmission of the plasma is calculated by multiplying the transmission
of the individual ions.
4.20 Hyd: model with user-own hydrodynamical simulation 81
The transmission includes both continuum and line opacity. For a description of what is currently in the
absorption line database, we refer to Sect. 5.2. You can mimick the transmission of a neutral plasma very
easy by putting the temperature to 0.5 eV (5 10−4
keV).
Warning: For solar abundances, do not take the temperature much lower than 0.0005 keV, because if
the plasma is completely neutral, the code will crash; a tiny fraction of ions such as Fe ii or Na ii will help
to keep a few free electrons in the gas without affecting the transmission too much. You can check the ion
concentrations by giving an ”asc ter . . . icon” command. Fill in the sector and component number of the
hot component for the . . . in the ”asc ter . . . icon” command to get the values for the right component.
The parameters of the model are:
nh - Hydrogen column density in 1028
m−2
. Default value: 10−4
(corresponding to 1024
m−2
, a typical
value at low Galactic latitudes).
t - the electron temperature Te in keV. Default value: 1.
rt - the ratio of ionization balance to electron temperature, Rb = Tb/Te in keV. Default value: 1.
The following parameters are common to all our absorption models:
f - The covering factor of the absorber. Default value: 1 (full covering)
v - Root mean square velocity σv
rms - Rms velocity σb of line blend components
dv - Velocity distance ∆v between different blend components
zv - Average systematic velocity v of the absorber
The following parameters are the same as for the cie-model (see there for a description):
ref - Reference element
01. . .30 - Abundances of H to Zn
file - Filename for the nonthermal electron distribution
Recommended citation: de Plaa et al. (2004) and Steenbrugge et al. (2005a).
4.20 Hyd: model with user-own hydrodynamical simulation
This model calculates the spectrum of a plasma with a given set of ion concentrations. It allows users
to calculate the X-ray spectrum corresponding to his own hydrodynamical simulation results. The basic
usage is that the user first runs own calculations to obtain the ion concentrations, and stores them in
an ascii file. The name should be either of “spexicon abs.dat” or “spexicon rel.dat”. Then the user runs
SPEX and loads the Hyd model to calculate the spectrum.
For users who are familiar with Fortran, we offer the supporting fortran90 subroutine, hydro driver, to
make the ion concentration file conveniently. The usage of the hydro driver is described in Section 7.5.
For more general cases users can directly load the Hyd model and just calculate the spectrum. The model
has two modes to specify the format for the ion concentrations: absolute (mode 1) or relative (mode 2).
For mode 1, the input file must have the name “spexicon abs.dat”, and the values are treated as absolute
ion concentrations (relative to hydrogen). In this mode the parameters of the elemental abundances do
not affect the ion concentration nor the spectrum at all (they are ignored). For the case that users wish to
treat elemental abundances as fitting parameters, mode=2 can be used. In this mode the input file must
have the name “spexicon rel.dat”, which contains the ion concentrations relative to the concentration of
the relevant chemical element.
The parameters of the model are:
hyd - Hydrogen density in 1020
m−3
mode - Mode of the model. Mode=1: read absolute ion concentration from “spexicon abs.dat”. mode=2:
read relative ion concentration from “spexicon rel.dat”
82 Spectral Models
The following parameters are the same as for the cie-model:
norm - the normalisation, which is the emission measure Y ≡ nenHV in units of 1064
m−3
, where ne and
nH are the electron and Hydrogen densities and V the volume of the source. Default value: 1.
t - the electron temperature Te in keV. Default value: 1.
it - Ion temperature in keV
vmic - Micro turbulent velocity in km/s
ref - Reference element
01. . .30 - Abundances of H to Zn
file - Filename for the nonthermal electron distribution
Warning: By default, SPEX starts with ”var calc old” (see the var menu for explanation). If you want
to use this model with the latest atomic database, you should set the ionisation balance to U16. Note that
this is only used to calculate inner-shell ionisation rates for the spectral evaluation, it will not affect the
ion concentrations that the user provides.
Recommended citation (first use): Kosenko et al. (2015).
4.21 Knak: segmented power law transmission model
The knak model is used to model the transmission of any spectrum using a set of contiguous segments
with a power-law transmission at each segment.
This component can be useful for new instruments, in order to test large scale calibration errors (effective
area errors for example), but other applications can also be made, of course. For example, if the spectrum
of the source has an unknown continuum shape with a superimposed absorption model, it is a good trick to
model the continuum by a power law, modify that by a knak model with adjustable or fixed transmission
at some relevant energies, and then apply the absorption. An example of this last application can be
found in Porquet et al. (2004).
The Transmission is given by:
T (E) = ciEai if Ei < E < Ei+1 (4.20)
for each value of i between 0 and n, the number of grid points. The transmission is 1 for E < E1 and
E > E2. Further, instead of using the constants ci and ai, we use instead the values of the transmission
at Ei, i.e. Ti ≡ T (Ei) = ciEai
i . This allows for a continuous connection between neighbouring segments.
Finally, for historical reasons we use here a wavelength grid instead of an energy grid; the corresponding
nodes λi should therefore be in strictly increasing order.
Warning: When applying this model, take care that at least one of the n transmission values is kept
fixed (otherwise you may run the risk that your model is unconstrained, for example if the normalisation
of the continuum is also a free parameter).
The parameters of the model are:
n - The number of grid points. Maximum value is 9.
w1 - Wavelength λ1 (˚A) of the first grid point
f1 - Transmission T (λ1) at λ1.
w2 - Wavelength λ2 (˚A) of the second grid point
f1 - Transmission T (λ2) at λ2.
- . . .
w9 - Wavelength λ9 (˚A) of the last grid point
f9 - Transmission T (λ9) at λ9.
Note that if n < 9, the values of Ti and λi will be ignored for i > n.
Recommended citation: Porquet et al. (2004).
4.22 Laor: relativistic line broadening model 83
4.22 Laor: relativistic line broadening model
This multiplicative model broadens an arbitrary additive component with a relativistic line profile. The
relativistic line profile is interpolated from tables produced by Laor (1991). In his model, the line
transfer function is determined for emission from the equatorial plane around a Kerr black hole, assuming
an emissivity law I(cos θ) ∼ 1. + 2.06 cosθ. The transfer function is calculated at a grid of 35 radii
(rn = 1600/(n + 1)2
for n = 1, . . . , 35, in units of GM/c2
), 31 inclinations uniformly spaced in cos i, and
300 frequencies, logarithmically spaced between 0.1 and 5 times the emission frequency, respectively.
Using these numbers, a radial integration is done using an emissivity law
I(r) ∼ 1/(r2
+ h2
)q/2
, (4.21)
where h is a characteristic scale height and q an asymptotic power law index (for large r, I(r) ∼ r−q
).
The integration is done between an inner radius r1 and an outer radius r2. Given the radial grid that is
provided in Laor’s data, the outer radius extends out to at most 400GM/c2
.
Warning: Of course, any line or continuum emission component can be convolved with the this broadening
model; for continuum components the computational time may be very large, however, due to the
convolution involved.
Warning: The outer radius cannot be larger than 400GM/c2
The parameters of the model are:
r1 - Inner radius of the disk, in units of GM/c2
. The minimum allowed value is 1.234 (for a maximally
rotating Kerr black hole). For a Schwarzschild black hole, one should take ri = 6. Default value: 1.234.
r2 - Outer radius of the disk, in units of GM/c2
. Keep this radius less than 400 (default value)
q - Emissivity slope q as described above. Default value: 2.
h - Emissivity scale height. Default value: 0.
i - Inclination angle (in degrees) of the disk (angle between line of sight and the rotation axis of the
disk). Default value: 45 degrees.
Recommended citation: Laor (1991).
4.23 Line: transmission model for a single spectral line
This model calculates the transmission T (E) for a single spectral emission or absorption model. It is
used as a multiplicative component, and can be used both for absorption and emission lines. The line
profile is a Voigt profile (the convolution between a Gaussian and a Lorentzian profile):
T (E) = e−τ(E)
, (4.22)
with the optical depth τ(E) given by:
τ(E) = τ0K(x, y), (4.23)
where K(x, y) is the Voigt profile given by
K(x, y) =
y
π
∞
−∞
e−t2
y2 + (x − t)2
dt, (4.24)
with
x =
2
√
ln 2
Fg
(E − E0) (4.25)
and
y =
√
ln 2
Fl
Fd
(4.26)
84 Spectral Models
where Fg and Fl are the Full Width at Half Maximum of the Gaussian and Lorentzian components,
respectively. Further, E0 is the line centroid.
The program also calculates the equivalent width of the line.
The model can be used both in energy (keV) mode or wavelength (˚A) mode. In each case, the quantities for
the other scaling (centroid, equivalent width, and FWHMs of the Gaussian and Lorentzian components)
are calculated. In addition, like all SPEX absorption models, also the covering factor can be varied.
Warning: The equivalent width is calculated at the energy grid in use for SPEX. Line flux outside this
range is not taken into account. That may be important in the case of strong Lorentzian wings.
Warning: The parameter τ0 only represents the optical depth at the line centre for a pure Gaussian
case. When the Lorentzian component becomes important, the ”true” depth at line center is smaller.
Warning: When changing from energy to wavelength units, take care about the frozen/thawn status of
the line centroid and FWHM.
Warning: You need to do a ”calc” or ”fit” command to get an update of the wavelength (for type=0)
or energy (type=1).
The parameters of the model are:
tau0 - Optical depth τ0 at line center. Default value: 1. Positive values correspond to absorption lines,
negative values to emission lines.
el - Line center energy E0 (keV). Default value: 6.4 keV.
fwhg - FWHM of the Gaussian component Fg in keV. Default value: 0.1 keV.
fwhl - FWHM of the Lorentzian component Fl in keV. Default value: 0.1 keV.
type - Type of calculation. Type=0: energy units; type=1: wavelength units.
wl - Line center wavelength E0 (˚A). Default value: 20 ˚A.
awhg - FWHM of the Gaussian component Fg in ˚A. Default value: 0.1 ˚A.
awhl - FWHM of the Lorentzian component Fl in ˚A. Default value: 0.1 ˚A.
ewk - Equivalent width of the line in keV. Calculated by the program, not an input variable.
ewa - Equivalent width of the line in ˚A. Calculated by the program, not an input variable.
fcov - The covering factor of the absorption/emission line. Default value: 1 (full covering).
4.24 Lpro: spatial broadening model
This multiplicative model broadens an arbitrary additive component with an arbitrarily shaped spatial
profile, in the case of dispersive spectrometers such as the RGS of XMM-Newton. In many instances,
the effects of a spatially extended source can be approximated by making use of the fact that for small
off-axis angles θ the expression dλ/dθ is almost independent of wavelength λ. This holds for example for
the RGS of XMM-Newton (for which dλ/dθ = 0.138/m ˚A/arcmin, with m the spectral order).
We can utilize this for a grating spectrum as follows. Make an image I(∆θ) of your source projected onto
the dispersion axis, as a function of the off-axis angle ∆θ. From the properties of your instrument, this
can be transformed into an intensity I(∆λ) as function of wavelength using ∆λ = ∆θdλ/dθ. Assume
that the spatial profile I(θ) is only non-zero within a given angular range (i.e. the source has a finite
extent). Then we can transform I(∆λ) into a probability distribution f(x) with f = 0 for very small or
large values of x (here and further we put x = ∆λ). The auxilliary task rgsvprof (see Section 7.6) is able
to create an input file for the lpro component from a MOS1 image.
The resulting spatially convolved spectrum Sc(λ) is calculated from the original spectrum S(λ) as
Sc(λ) = f(λ − λ0)S(λ0)dλ0. (4.27)
The function f(x) must correspond to a probability function, i.e. for all values of x we have
f(x) ≥ 0 (4.28)
4.25 Mbb: modified blackbody model 85
and furthermore
∞
−∞
f(x)dx = 1. (4.29)
In our implementation, we do not use f(x) but instead the cumulative probability density function F(x),
which is related to f(x) by
F(x) ≡
x
−∞
f(y)dy, (4.30)
where obviously F(−∞) = 0 and F(∞) = 1. The reason for using the cumulative distribution is that
this allows easier interpolation and conservation of photons in the numerical integrations.
If this component is used, you must have a file available which we call here ”vprof.dat” (but any name
is allowed). This is a simple ascii file, with n lines, and at each line two numbers: a value for x and
the corresponding F(x). The lines must be sorted in ascending order in x, and for F(x) to be a proper
probability distribution, it must be a non-decreasing function i.e. if F(xi) ≤ F(xi+1) for all values of i
between 1 and n − 1. Furthermore, we demand that F(x1) ≡ 0 and F(xn) ≡ 1.
Note that F(x) is dimensionless. In addition, we allow for two other parameters: a scale factor s and
an offset λo. Usually, s = 1, but if s is varied the resulting broadening scales proportional to s. This is
useful if for example one has an idea of the shape of the spatial profile, but wants to measure its width
directly from the observed grating spectrum. In addition, the parameter λo can be varied if the absolute
position of the source is unknown and a small linear shift in wavelength is necessary.
Warning: This model can be applied to grating spectra (like RGS), but if you include in your fit also
other data (for example EPIC), the same broadening will also be applied to that other data SET. This
can be avoided by using a separate sector for each detector type.
Warning: The above approximation of spatially extended sources assumes that there are no intrinsic
spectral variations over the surface area of the X-ray source. Only total intensity variations over the
surface area are taken into account. Whenever there are spatial variations in spectral shape (not in
intensity) our method is strictly speaking not valid, but still gives more accurate results than a pointsource
approximation. In principle in those cases a more complicated analysis is needed.
The parameters of the model are:
s - Scale parameter s, dimensionless. Default value: 1.
dlam - Offset parameter λo, in ˚A. Default value: 0 ˚A.
file - Ascii character string, containing the actual name of the vprof.dat file
Recommended citation: Tamura et al. (2004).
4.25 Mbb: modified blackbody model
This model describes the spectrum of a blackbody mdified by coherent Compton scattering. This is in
several instances a much better description than a simple blackbody (for example accretion disk spectra of
AGN). The physical background is described for example by Rybicki & Lightman (1986), pages 218–219.
The formulae that we use here with a derivation are given by Kaastra & Barr (1989). From that work
we derive the spectrum (1044
photons/s/keV):
N(E) = 1358.
AE0.25
eE/T (eE/T − 1)
(4.31)
where E is the photon energy in keV, T the temperature in keV and A the normalisation in units of
1026
m0.5
, defined by
A = n0.5
e O (4.32)
86 Spectral Models
with ne the electron density (units: 1020
m−3
) and O the emitting source area (units: 1016
m).
The parameters of the model are:
norm - Normalisation A (in units of 1026
m0.5
). Default value: 1.
t - The temperature T in keV. Default value: 1 keV.
Recommended citation: Kaastra & Barr (1989) and Rybicki & Lightman (1986).
4.26 Musr: User defined multiplicative model
The user model provides an interface to create an multiplicative model component calculated by a user
program. The interface is rather simple and therefore very flexible. The interface uses a set of two ASCII
files: input-?-?.prm and output-?-?.spc, where the ’?’ stands for the sector and component number of
the musr model component.
The input-?-?.prm is generated by the musr model and contains the parameter values and the energy
grid that SPEX uses to calculate the model. The file has a fixed structure:
• The first line contains one integer number containing the number of parameters that the model
needs to calculate (current maximum is 40).
• On the second line the array of parameter values is listed (with the length indicated on the previous
line.
• On the third line, an integer value is shown which indicates the number of model bins SPEX has
in its model grid.
• On the following lines, the model grid points are shown in three columns. The first column contains
the bin upper boundary (egb), the second column is the bin center (eg) and the third column is
the full bin width (deg). The energy values are in keV.
The user program is supposed to read the input file and calculate the multiplicative factors for each
energy bin on the grid. The spectrum array is called ’sener’ and has the same length as the energy grid.
In addition, it is also possible to calculate the model for the emission weighted center of the bin. In that
case the spectrum calculation is a bit more complicated, but it leads to better results. The user has the
option of also calculating the weighted spectrum, which is the average photon energy Eaver minus the bin
centroid Ecentroid times the flux (F):
W = (Eaver − Ecentroid) ∗ F (4.33)
The W values end up in the ’wener’ array. If you do not use weighing by average photon energy, ’wener’
values can be 0.
The user program should create an output ASCII file named output-?-?.spc with the following structure:
• On the first row, put the number of model bins. This should be the same number as written in the
input-?-?.prm file.
• Write the ’sener’ and ’wener’ values in two columns. The first column is the ’sener’ value that
represents the multiplication factor and the second column is the ’wener’ value.
In the directory ’user’ in the main SPEXdirectory some example user model programs can be found. The
source code can be adapted to accommodate the user’s wishes.
The parameters of the model are:
exec - User executable, for example ’./model.py’ for a python script in the same directory where you run
SPEX
npar - Number of free parameters in the model. Current maximum is 40.
p01...p40 - Model parameters of the user model.
4.27 Neij: non-equilibrium ionisation jump model 87
4.27 Neij: non-equilibrium ionisation jump model
This model calculates the spectrum of a plasma in non-equilibrium ionisation (NEI). For more details
about NEI calculations, see Sect. 5.4.
The present model calculates the spectrum of a collisional ionisation equilibrium (CIE) plasma with
uniform electron density ne and temperature T1, that is instantaneously heated or cooled to a temperature
T2. It then calculates the ionisation state and spectrum after a time t. Obviously, if t becomes large the
plasma tends to an equilibrium plasma again at temperature T2.
The ionisation history can be traced by defining an ionisation parameter,
u ≡ nedt (4.34)
with u = 0 defined at the start of the shock.
By default the model describes a classical NEI condition with a flat temperature profile:
u < 0 : T = T1, (4.35)
u > 0 : T = T2. (4.36)
For the case the user wands to calculate more complex situations, SPEX offers two modes to treat a
temperature profile T (u): analytic expression (mode 1) or ascii-file input (mode 2).
The temperature profile in mode=1 (analytic case) is given by
u < 0 : T = T1, (4.37)
0 < u < U : T = T2, (4.38)
U < u < U + dU : T = T (u). (4.39)
By setting a non-zero value for dU, this model offers the opportunity to calculate more complex evolution
in the last epoch (U < u < U+dU); e.g. with secondary heating/cooling process and/or change in density.
We introduce parameters α and β, which describe a power-law like evolution respectively for temperature
and density of the plasma after the “break” of constancy at time tbr:
T (t) = T2 (t/tbr)α
(4.40)
ne(t) = ne (t/tbr)β
, (4.41)
An immediate application of this break feature would be a recombining plasma due to rarefaction (adiabatic
expansion). Such a condition can be realised with α = −2 and β = −3. Note that we include the
effect of the density change here in the NEI calculation for the ion concentration, but of course the line
emission is calculated at the density prescribed by the parameter ed of the model, which represents the
true density at the epoch of emission of the spectrum.
To get the expression for T (u), we first calculate the increase of the ionisation parameter after t = tbr as
follows:
u − U =
tbr
n(t)dt =
tbr
ne(t/tbr)β
dt (4.42)
= netbr
1
(t/tbr)β
d(t/tbr) (4.43)
= U/(β + 1) · [(t/tbr)β+1
− 1], (4.44)
Then, by combining equations 4.40 and 4.44, we obtain:
T (u) = T2 · [1 + (β + 1) · (u − U)/U]α/(β+1)
, (4.45)
88 Spectral Models
T1
T2
T3
u
T(u)
U U+dU0
“jump” “break”
Figure 4.1: The temperature profile with mode=1.
and we get the final temperature at u = U + dU to be
T3 = T2 · [1 + (β + 1) · dU/U]α/(β+1)
. (4.46)
It should be noted that, for fixed values of α and β, the temperature change after the break is determined
by the ratio dU/U rather than dU itself. The user can check T3 with the ascdump plas command (see
§ 3.3) and also the histories of u and T (u) with the ascdump nei command (see § 3.3).
In some rare cases with a large negative β, T3 can get an unphysical value (T3 < 0). In such a case the
calculation will automatically be stopped at a lower-limit of T (u) = 10−4
keV.
For mode 2, the user may enter an ascii-file with u- and T -values. The format of this file is as follows: the
first line contains the number of data pairs (u, T ). The next lines contain the values of u (in the SPEX
units of 1020
s m−3
) and T (in keV). Note that u1 = 0 is a requirement, all Ti should be positive, and the
array of u-values should be in ascending order. The pairs (u, T ) determine the ionisation history, starting
from T = T1 (the pre-shock temperature), and the final (radiation) temperature is the temperature of
the last bin.
The parameters of the model are:
t1 - Temperature T1 before the sudden change in temperature, in keV. Default: 0.002 keV.
t2 - Temperature T2 after the sudden change in temperature, in keV. Default: 1 keV.
u - Ionization parameter U = net before the “break”, in 1020
m−3
s. Default: 10−4
.
du - Ionization parameter dU after the “break” in 1020
m−3
s. Default value is 0 (no break).
alfa - Slope α of the T (t) curve after the “break”. Default value is 0 (constant T ).
beta - Slope β of the n(t) curve after the “break”. Default value is 0 (constant n).
mode - Mode of the model. Mode=1: analytical case; mode=2: T (u) read from a file. In the latter case,
also the parameter hisu needs to be specified.
hisu - Filename with the T (u) values. Only used when mode=2.
The following parameters are the same as for the cie-model:
ed - Electron density in 1020
m−3
it - Ion temperature in keV
vmic - Micro turbulent velocity in km/s
ref - Reference element
01. . .30 - Abundances of H to Zn
file - Filename for the nonthermal electron distribution
Recommended citation: Kaastra & Jansen (1993).
4.28 Pdem: DEM models 89
4.28 Pdem: DEM models
The pdem model is intended to be used for differential emission measure analysis, simultaneous with
fitting of abundances etc. of an optically thin plasma.
It works as follows. The user gives a a number of temperature grid points n, a minimum temperature
T1, a maximum temperature Tn, a total emission measure Y and relative contributions y1 . . . yn. SPEX
assumes that the grid points between T1 and Tn are distributed logarithmically.
The relative contributions y1 . . . yn represents the values of dY/d ln T (note the logarithm!) at the grid
points. SPEX then interpolates in the log Ti −log yi space on a finer grid using splines. That temperature
grid on which the data are being evaluated has a fine mesh: step size is about 0.10 in log T (finer is not
usefull because uniqueness is no longer guaranteed), with the additional constraint that the number of
mesh points is at least n and not larger than 64 (practical limit in order to avoid excessive cpu-time).
The emission measure distribution is then simply scaled in such a way that its sum over the fine mesh
equals the total emission measure Y that went into the model.
Warning: At least one of the yi values should be kept frozen during fitting, when Y is a free parameter,
otherwise no well defined solution can be obtained! If Y is fixed, then all yi can be free.
The parameters of the model are:
norm - Normalisation, i.e. total integrated emission measure Y in units of 1064
m−3
t1 - Lower temperature T1 in keV
tn - Upper temperature Tn in keV
npol - Number of temperature grid points n; minimum value 2, maximum value 8
y1 - Relative contribution y1 at T1
y2 - Relative contribution y2 at T2
. . .
y8 - Relative contribution y8 at T8; note that the higher contributions yi are neglected if i > n
The following parameters are the same as for the cie-model:
ed - Electron density in 1020
m−3
it - Ion temperature in keV
vmic - Micro turbulent velocity in km/s
ref - Reference element
01. . .30 - Abundances of H to Zn
file - Filename for the nonthermal electron distribution
Note that the true emission measure on the finer mesh can be displayed by using the ”ascdump term #
# dem” command; you will get a list of temperature (keV) versus emission measure.
4.29 Pion: SPEX photoionised plasma model
The pion model calculates the transmission and emission of a slab of photo-ionized plasma, where all ionic
column densities are linked through a photoionisation model. The relevant parameter is the ionization
parameter ξ = L/nr2
, with L the source luminosity, n the hydrogen density and r the distance from the
ionizing source. The major difference is that while for the xabs model the photoionisation equilibrium
is pre-calculated for a grid of ξ-values by an external code, for instances Cloudy or XSTAR (or even
with the present pion model . . .), in the present pion model the photoionisation equilibrium is calculated
self-consistently using the available plasma routines of SPEX.
Warning: The default energy grid in SPEX has 8192 bins between 0.001 and 100 keV. This may not
be sufficient for the pion model when you use it without data. Recommended is a logarithmic grid between
10−6
− −106
keV with a step size of 0.005. You can get this by issuing the following command: ”Egrid
log 1E-6 : 1E6 step 0.005 keV”. Note that if you have read in data, SPEX automatically expands the
energy grid to this range and resolution, plus including all energy boundaries from the response matrix.
90 Spectral Models
Warning: This model is still under development and not all atomic data is fully updated. For instance,
no cooling by collisional excitation for ions of the K- to Zn-isolelectronic sequences is taken into account
yet. So use with care!
Warning: When setting up the model, be aware that the pion model is both additive and multiplicative
(even if you put the emission to zero). Therefore, the pion model needs the same com rel sequence as you
use for your absorption component. Example: ’com pow — com reds — com pion — com rel 1 3,2’ (a
powerlaw that powers a pion model and is then redshifted) needs as next command ’com rel 3 2’, telling
SPEX that the pion emission model is also redshifted.
Warning: Please note that all PION components must be multiplied by at least one continuum component
(using the usual comp rel command). Otherwise, photoionisation cannot be calculated and SPEX
may crash. A typical AGN SED spanning optical to X-ray energies can be set up with three continuum
components in SPEX: pow (primary hard X-ray power-law emission), refl (reflected power-law emission),
comt (thermal optical/UV disk continuum + the soft X-ray excess). See the SED of NGC 5548 derived
in Mehdipour et al. (2015).
The main advantage, however, is that the user can define his own ionising continuum by combining any
additive components of SPEX, and that ionising spectrum is fed through the pion component to get the
transmitted spectrum. In addition, multiple pion components can be used, with the light leaking from
one layer to the next. And it allows for spectral fitting, where the parameters of the ionising continuum
are determined simultaneously with the parameters of the absorbing layer. The number of parameters is
therefore unlimited (well, the memory and cpu speed of the computer will be the true limiting factors).
Prior to fitting a PION component, it is best to first calculate the model spectrum with your initial
parameter values (see calculate command). This helps to see if the initial values are reasonable numbers
and the model is not too far off the data.
4.29.1 Emission from the pion model
Latest news: we have now incorporated a first version of emission from the same layer. We cannot
give you any guarantee at the moment that it is bug-free. We know at the moment that the source has
probelms when the density gets too high; this is different for each ion; so unless you limit the density
in fitting, SPEX may encounter a situation where you surpass the critical density and you may get a
warning message. Here is an example. For a photoionised case, with log ξ = 3 (resulting kT = 0.64 keV)
the nominal occupation of the ground state of H i becomes negative for a density > 0.15 × 1020
m−3
.
This can be traced down to incomplete atomic data. For H i, we include collisional excitation and deexcitation
up to principal quantum number n = 5 but not above. As a result, in this example the 1s–5s
levels are mainly populated/depopulated by collisions, while 6s–16s are mainly populated by radiative
recombination and depopulated by radiative cascades downward or photon absorption. The nominal
occupation of 1s–5s then decreases from 0.035 (1s) to 0.0024 (5s), while for 6s–16s they increase slowly
from 0.020 to 0.027. This is of course physically unacceptable. It causes the lower levels to leak to the
higher levels, with eventually the catastrophe of negative occupation for the ground state. We mitigate
this by replacing the level populations by the LTE populations and issueing a warning. Without this
mitigation, SPEX would crash.
Warning: You can get the emission by putting the covering factor (omeg) to a non-zero value; it will
slow down the calculations compared to absorption-only calculations, so be aware
Normally, to calculate the emission from a full thin shell surrounding an ionising source, you should set
the parameter omeg to unity (a full shell of 4π steradians). Smaller factors could be associated e.g. to
ionisation cones; values larger than unity make physically no sense but you can formally play around with
it (for very large values, the emitted spectrum would start dominating the absorbed primary continuum,
but if you want to suppress the primary continuum in the observed spectrum, it is better to define your
model like the example below as:
com pow
com pion
4.29 Pion: SPEX photoionised plasma model 91
com etau
com rel 1 2,3
com rel 2 0
par 3 tau v 1e10
par 3 a v 0
In this example, the powerlaw goes through the pion component and is killed afterwards by the etau
component, while the emission from the pion component is not attenuated by etau.
You can vary the new parameter mix to get a different ratio of forwards to backwards emission. Putting
it to 1 (default) means you get the forward emission, putting it to 0 the backwards emission, and intermediate
values give you a mix.
Warning: The emission model uses currently only one layer. When the continuum optical depth of
the absorbed continuum, weighted with the incoming flux, becomes of order unity, the layer will become
inhomogeneous in terms of temperature structure, and our single-layer approximation will break down.
In order to make a PION component produce emission only, fix the covering fraction (cf) parameter to
zero so that no absorption is produced. Then fit the omega parameter. Note that any PION component
with a non-zero omega acts as an additive component in SPEX. Therefore, multiply these components
with your multiplicative components (like the Galactic absorption) using the comp rel command.
For more information on this model, the atomic data and parameters we refer to Sect. 5.2.3.
4.29.2 More options
No energy balance solution needed
The default option (tmod=0) for the pion model is to solve simultaneously for the ionisation balance and
the energy balance equations. This option is useful for e.g. photoionised winds of AGN or X-ray binaries.
However, there are situations where photo-ionisation or photo-excitation play a role but do not determine
the thermal structure. Examples are winds of hot stars, where shocks heat the wind but UV radiation
from the star can affect He-like triplet line emission ratios. Another example are the most teneous parts
of the WHIM, where photoionisation by the cosmic background can be important compared to collisional
ionisations.
For such cases, the user can set the parameter tmod=1; in that case, the user should also provide the
temperature tinp of the plasma. In this case, only the ionisation balance equation is solved, and there is
in general no energy balance (this can be checked by using the ascii-output option heat). Do not forget
to set the parameter omeg to a finite value (the default is zero), otherwise the emitted spectrum is zero.
External heat sources
In some cases there may be an other external heat or cooling source, like shock heating, magnetic
reconnection, adiabatic expansion etc. If one wishes to solve for the photoionisation equilibrium, then
this additional heat source can be used by putting the parameter exth to the proper value (units: W m−3
.
A negative value would mean a cooling contribution.
Multiple solutions
There are situations where there is not a unique solution to the energy balance equations. A simple
example can be obtained as follows: take a logarithmic energy grid between 10−6
− 106
keV, use a
powerlaw with photon index 1.5, apply the pion model to it and put exth to 5 × 10−25
W m−3
. In this
case there are 3 solutions. SPEX chooses by default the hottest solution. You can see all solutions by
putting the parameter fmod=1 and using the heat ascii output option. Or check the behaviour of the
hating balance by issuing the ebal ascii output option. You can select which solution you want to use in
SPEX by setting the soln parameter. Default is 0 (hottest solution), and for the above case of 3 solutions
92 Spectral Models
values of 1, 2 and 3 renders you the coldest, second ant hottest solution. Test this with the heat or plas
output options.
Warning: When you set soln to a non-zero value, use fmod=1, otherwise SPEX may crash.
No equilibrium solution
There are also situations where there is no equilibrium solution to the energy balance equations. This
may happen for instance if you put so much heat in the plasma that it cannot be balanced anymore by
cooling. Another example is a too hard powerlaw without high energy cut-off, where Compton-heating
might be very strong. In this case SPEX renders an error message, and you cannot trust the result of
the calculation anymore. The only remedie is to adjust your model parameters or the allowed range for
them in case of spectral fitting or error searches.
4.29.3 Model parameters
The parameters of the model are:
nh - Hydrogen column density in 1028
m−2
. Default value: 10−4
(corresponding to 1024
m−2
, a typical
value at low Galactic latitudes).
xi - the 10
log of the ionisation parameter log ξ in units of 10−9
W m. Default value: 1.
u - the Davidson (Cloudy) ionisation parameter U (dimensionless). This is calculated from the SED and
the value of ξ. Not fittable, just output.
The following parameters are common to all our absorption models:
fcov - The covering factor of the absorber. Default value: 1 (full covering)
v - Root mean square velocity σv
rms - Rms velocity σb of line blend components
dv - Velocity distance ∆v between different blend components
zv - Average systematic velocity v of the absorber
The following parameters are the same as for the cie-model (see there for a description):
ref - Reference element
01. . .28 - Abundances of H to Ni; only here we take H, He, C, N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Fe,
Ni.
file - File name for the electron distribution (in case of a sum of Maxwellians distribution)
The following parameters are unique for the pion model:
type - If type equals 0 (default value), it uses ξ as its main parameter; if type equals 1, it uses lixi (see
next parameter) as its main parameter
lixi - Optional alternative ionisation parameter, defines as Lion/ξ in units of 1039
m−1
. This is useful for
time-variable spectra where ξ has been determined from one spectrum and where one wants to calculated
the transmitted spectrum for fixed nr2
for a different ionising spectrum; in that case lixi can be kept
constant.
omeg - Covering factor Ω/4π, needed for emission. At this stage, keep it to zero, please.
mix - Fraction of emitted spectrum to the forward direction relative to the total. default value: 1 (all
emission forward). A value of 0 means SPEX gives all backwards emission.
exth - External heating in W m−3
. default value: 0.
fmod - Show all solutions in ascii output of the heating (fmod=1). Default is fmod=0. Set fmod=1 also
when you set soln> 0.
soln - The temperature solution to be used, from low to high values. Default value is 0 (hottest solution).
If this parameter is larger than the hootest solution, it adopts the hottest solution instead. Should be
used with fmod=1 in case soln> 0.
tmod - Temperature mode. Default value: 0 (solve for the temperature that provides energy balance). If
4.30 Pow: power law model 93
tmod=1, use tinp instead as temperature and do not solve for energy balance.
tinp - Temperature of the plasma in keV. Default: 1 keV. Only relevant if tmod=1.
Recommended citation: Miller et al. (2015) and Mehdipour et al. (2016).
4.30 Pow: power law model
The power law spectrum as given here is a generalization of a simple power law with the possibility of a
break, such that the resultant spectrum in the log F − log E plane is a hyperbola.
The spectrum is given by:
F(E) = AE−Γ
eη(E)
, (4.47)
where E is the photon energy in keV, F the photon flux in units of 1044
ph s−1
keV−1
, and the function
η(E) is given by
η(E) =
rξ + r2ξ2 + b2(1 − r2)
1 − r2
, (4.48)
with ξ ≡ ln(E/E0), and E0, r and b adjustable parameters. For high energies, ξ becomes large and then
η approaches 2rξ/(1 − r2
), while for low energies ξ approaches −∞ and as a consequence η goes to zero.
Therefore the break ∆Γ in the spectrum is ∆Γ = 2rξ/(1 − r2
). Inverting this we have
r =
1 + (∆Γ)2 − 1
|∆Γ|
. (4.49)
The parameter b gives the distance (in logarithmic units) from the interception point of the asymptotes
of the hyperbola to the hyperbola. A value of b = 0 therefore means a sharp break, while for larger values
of b the break gets smoother.
The simple power law model is obtained by having ∆Γ = 0, or the break energy E0 put to a very large
value.
Warning: By default, the allowed range for the photon index Γ is (-10,10). If you manually increase
the limits, you may run the risk that SPEX crashes due to overflow for very large photon indices.
Warning: Note the sign of Γ: positive values correspond to spectra decreasing with energy. A spectrum
with ∆Γ > 0 therefore steepens/softens at high energies, for ∆Γ < 0 it hardens.
As an extension, we allow for a different normalisation, namely the integrated luminosity L in a given
energy band E1–E2. If you choose this option, the parameter ”type” should be set to 1. The reason for
introducing this option is that in several cases you may have a spectrum that does not include energies
around 1 keV. In that case the energy at which the normalisation A is determined is outside your fit
range, and the nominal error bars on A can be much larger than the actual flux uncertainty over the
fitted range. Note that the parameters E1 and E2 act independently from whatever range you specify
using the ”elim” command. Also, the luminosity is purely the luminosity of the power law, not corrected
for any transmission effects that you may have specified in other spectral components.
Warning: When you do spectral fitting, you must keep either A or L a fixed parameter! The other
parameter will then be calculated automatically whenever you give the calculate or fit command. SPEX
does not check this for you! If you do not do this, you may get unexpected results / crashes.
Warning: The conversion factor between L and A is calculated numerically and not analytically
(because of the possible break). In the power law model, photon fluxes above the nominal limit (currently
e34
= 5.8 × 1014
in unscaled units) are put to the maximum value in order to prevent numerical overflow.
This implies that you get inaccurate results for low energies, for example for a simple power law with
Γ = 2 the results (including conversion factors) for E < 10−7
keV become inaccurate.
Warning: Note that when you include a break, the value of Γ is the photon index at energies below the
break. Also, the normalisation A is the nominal normalisation of this low-energy part. In such a case of
94 Spectral Models
a break, the true flux at 1 keV may be different from the value of A! Of course, you can always calculate
the flux in a given band separately.
The parameters of the model are:
norm - Normalisation A of the power law, in units of 1044
ph s−1
keV−1
at 1 keV. Default value: 1. When
∆Γ is not equal to 0, it is the asymptotic value at 1 keV of the low-energy branch.
gamm - The photon index Γ of the spectrum. Default value: 2. When ∆Γ is not equal to 0, it is the slope
of the low-energy branch.
dgam - The photon index break ∆Γ of the spectrum. Default value: 0. and frozen. If no break is desired,
keep this parameter 0 (and frozen!).
e0 - The break energy E0 (keV) of the spectrum. Default value: 1010
and frozen.
b - Smoothness of the break b. Default: 0.
type - Type of normalisation. Type= 0 (default): use A; type= 1: use L.
elow - E1 in keV, the lower limit for the luminosity calculation. Default value: 2 keV.
eupp - E2 in keV, the upper limit for the luminosity calculation. Default value: 10 keV. Take care that
E2 > E1.
lum - Luminosity L between E1 and E2, in units of 1030
W.
4.31 Reds: redshift model
This multiplicative model applies a redshift z to an arbitrary additive component. If a photon is emitted
at energy E, the redshift model will put it at energy (1 + z)E. In addition, a time dilatation correction
is applied such that the spectrum S(E) (expressed as photons/s per bin) is divided by 1 + z.
However, it is necessary to distinguish two different cases:
case 1 (flag=0): the redshift component can be used to calculate the effects of the cosmological redshift.
The cosmological redshift has the effect of the energy shift and the time dilatation as outlined above.
Therefore, the above procedure is essentially correct and this is what was used in older versions of SPEX
(before version 2.00.10). However, what was overlooked there is that in the determination of the finally
observed spectrum/flux as seen on Earth, a division by 4πd2
is necessary. For this distance d, we took
the luminosity distance. However, the factors (1 + z)2
are absorbed into the definition of the luminosity
distance. Therefore, in the older versions all fluxes were too small by a factor of (1 + z)2
. Since we
want to retain the luminosity distance as the natural distance measure for spectra, it appears necessary
to multiply the spectrum as calculated by the original subroutine by a factor of (1 + z)2
. But in the
other case (redshifts caused by the motion of a source at any distance), this re-correction should not be
done, reason why we introduce the other option. in summary, for redshift components corresponding to
cosmological redshifts, the option flag=0 (default) must be used.
case 2 (flag=1): this is the old case for a source with a redshift caused by motion away from us. It should
be used for any velocity fields other than the Hubble flow.
Warning: Note that this component should be used in tandem with the distance command (Section 3.9)
to take into account the cosmological redshift and its influence on the flux completely.
The parameters of the model are:
z - Redshift z. Default value: 0.
flag - Flag: 0 (cosmological redshift) or 1 (velocity redshift). Default value: 0.
4.32 Refl: reflection model
This model was kindly provided by Piotr Zycki. The related programs in XSPEC are felipl ans ferfschw.
The first one gives the reflected continuum (i.e. pexrav/pexriv) plus the line with correct energy
4.33 Rrc: radiative recombination continuum model 95
and intensity, the second one is the first one with the relativistic smearing added. Both are combined
into the single refl model in SPEX.
It is a model of reflection from a constant density X-ray illuminated atmosphere. It computes the
Compton-reflected continuum (cf. Magdziarz & Zdziarski 1995) and the iron K alpha line (cf. Zycki &
Czerny 1994), as described in Zycki et al. (1999). In addition it can be convolved with a relativistic
diskline model (for Schwarzschild geometry).
Chemical elements taken into account in this model are H, He, C, N, O, Ne, Mg, Si, S and Fe. The
standard abundances are taken from Morrison & McCammon (1983).
The incoming spectrum is characterized by:
Ni(E) = AE−Γ
exp [−E/Ec] , (4.50)
where E is the photon energy in keV, Ni(E) the number of photons per per second per keV, Γ is the
photon index and Ec a cut-off energy. The normalisation A is in units of 1044
photons s−1
keV−1
at
1 keV, just the same as in the standard power law model. The total spectrum N(E) is then given by
N(E) = Ni(E) + sR(E), (4.51)
where R(E) is the reflected spectrum and s is a scaling factor.
The parameters of the model are:
norm - Normalisation A of the power law
gamm - The photon index Γ of the ionising spectrum
ecut - The cut-off energy (keV) of the ionising spectrum. If no cut-off is desired, take this parameter
zero (and keep it frozen!).
pow - If pow=1, the incoming power law is added to the spectrum (default); if pow=0, only the reflected
spectrum is given
disk - If disk=1, the spectrum will be convolved with an accretion disk profile (default); if disk=0, this
is not done
fgr - Full general relativity used (default, for fgr=1)
t - Temperature of the reflector (disk) in keV
xi - Ionisation parameter ξ = L/nr2
in the usual (c.g.s. based) units of 10−9
W m
abun - The abundance of all metals excluding H and He, in solar units
feab - The iron abundance with respect to the other metals
cosi - The cosine of the inclination angle of the disk. cos i = 0 (i = π/2) corresponds to edge-on
scal - Scale s for reflection. For an isotropic source above the disk s = 1. This value corresponds to
seeing equal contributions from the reflected and direct spectra.
q - Emissivity index for the accretion disk; default value -3 (the emissivity scales with r+q
at large radii,
so q = −3 means r−
3. Note the sign difference with the Laor model.
r1 - Inner radius of the disk in units of GM/c2
. Default: 10.
r2 - Outer radius of the disk in units of GM/c2
. Default: 104
.
Recommended citation: Magdziarz & Zdziarski (1995) and Zycki et al. (1999).
4.33 Rrc: radiative recombination continuum model
This is a simplified model, aimed to calculate radiative recombination continua for photoionized plasmas.
It is a simple, limited shortcut to a more fully complete model for the emission from a recombining
plasma.
The user essentially prescribes the emission measure for each ion as well as the radiation temperature,
and then this model calculates the continuum emission corresponding to this temperature and set of
ionic emission measures. Line radiation is not taken into account. However, for physical self-consistency,
we take account of all three continuum emission components: Bremsstrahlung, two photon emission and
free-bound radiation (= the RRC).
96 Spectral Models
The reason for having no physical model to couple the ionic emission measures (contrary to for example
the CIE model), is that this allows the user to fit these emission measures without making a priori
assumptions about the ionization equilibrium. The user might then combine later the set of derived
emission measures with any of his relevant models.
Warning: Take care that for too high temperatures, two photon emission might be stronger than the
free-bound (RRC) emission!
Warning: Take care that the fit parameters are emission measures of a given ion, while the radiation
occurs in the next ion. For example radiative recombination of O ix to O viii is proportional to the
emission measure of O ix (nenO IXV ), but produces an emission edge in O viii at 14.22 ˚A.
Warning: No recombination is possible to neutrals, so therefore there is no H i, O i or Fe i in this
model.
The parameters of the model are:
t - The temperature T in keV. Default value: 1 keV.
h2 - The H ii emission measure nenH IIV in units of 1064
m−3
. Default value: 0.
he2 - The He ii emission measure nenHe IIV in units of 1064
m−3
. Default value: 0.
he3 - The He iii emission measure nenHe IIIV in units of 1064
m−3
. Default value: 0.
. . .
ni29 - The Ni xxix emission measure nenNi XXIXV in units of 1064
m−3
. Default value: 0.
4.34 Slab: thin slab absorption model
The slab model calculates the transmission of a slab of material, where all ionic column densities can be
chosen independently. This has the advantage that a spectrum can be fit without any knowledge of the
ionisation balance of the slab. After a spectral fit has been made, one may try to explain the observed
column densities by comparing the with predictions from any model (as calculated by SPEX, Cloudy,
XSTAR, ION or any other existing (photo)ionisation code).
For more information on this model, the atomic data and parameters we refer to Sect. 5.2.3. Below we
do not list all the parameters of the model, but for each ion of H, He, C, N, O, Ne, Na, Mg, Al, Si, S,
Ar, Ca, Fe and Ni there is a parameter, namely the logarithm (base 10) of the column density in SI units
(m−2
). So, a H 1 column of 1028
m−2
(1024
cm−2
should be entered as 28.0. The default values of 1
therefore correspond to an almost negligible column.
Warning: We do include here fully stripped ions, as their free electrons do produce Thomson scattering.
However, the user is advised not to take more than one column density of a bare nucleus as a free
parameter, as the shape of the Thomson scattering contribution is the same for all electrons, regardless
from which ion they came from. In the spectral fitting, there would be 100% correlations between the
column densities of these bare ions, which is undesirable.
The parameters of the model are:
h1 - log column density (m−2
) of H i. Default value: 1.
h2 - log column density (m−2
) of H ii. Default value: 1.
he1 - log column density (m−2
) of He i. Default value: 1.
he2 - log column density (m−2
) of He ii. Default value: 1.
he2 - log column density (m−2
) of He iii. Default value: 1.
c1 - log column density (m−2
) of H i. Default value: 1.
. . . ni27
- log column density (m−2
) of Ni xxvii. Default value: 1.
ni28 - log column density (m−2
) of Ni xxviii. Default value: 1.
The following parameters are common to all our absorption models:
4.35 Spln: spline continuum model 97
fcov - The covering factor of the absorber. Default value: 1 (full covering)
v - Root mean square velocity σv
rms - Rms velocity σb of line blend components
dv - Velocity distance ∆v between different blend components
zv - Average systematic velocity v of the absorber
Recommended citation: Kaastra et al. (2002).
4.35 Spln: spline continuum model
Sometimes the continuum of an X-ray source may be too complex to model with known physical components.
A situation like that may be found in AGN continua, which are a complex superposition of
hard power law, soft continuum excess, relativistically broadened and ”normal” broad lines with a priori
unknown line shape, etc., while in addition a superimposed warm absorber may have well defined narrow
absorption lines. In that case it might be useful to fit the continuum with an arbitrary profile in order
to get first an accurate description of the absorber, and then after having ”removed” the absorber try to
understand the underlying continuum spectrum.
For these situations the spln model introduced here is useful. It allows the user to model the continuum
within two boundaries b1 and b2 with a cubic spline.
The algorithm works as follows. The user selects the limits b1 and b2 as well as the number of grid
points n. SPEX then creates a grid x1, x2, . . . , xn with uniform spacing in b (see below for details). The
spectrum at these grid points is contained in the corresponding array y1, y2, . . . , yn. These have the usual
units of 1044
photons s−1
keV1
used throughout SPEX, and is the spectrum emitted at the source. The
parameters yi can be adjusted during the spectral fitting, but b1, b2 and n and thereby xi remain fixed.
At intermediate points between the xi, the photon spectrum is determined by cubic spline interpolation
on the (xi, yi) data pairs. We take a natural spline, i.e. at x1 and xn the second derivative of the spline
is zero.
Outside of the range b1–b2 however, the photon spectrum is put to zero, i.e. no extrapolation is made!
Finally note that we have chosen to define the spline in logarithmic space of y, i.e. the log of the photon
spectrum is fit by a spline. This is done in order to guarantee that the spectrum remains non-negative
everywhere. However, the y-values listed is the (linear) photon spectrum itself.
There are four different options for the energy grid xi, indicated by the parameter type:
• type=1: b1 is the lower energy in keV, b2 is the upper energy in keV, and the grid is linear in
energy in between.
• type=2: b1 is the lower energy in keV, b2 is the upper energy in keV, and the grid is logarithmic
in energy in between.
• type=3: b1 is the lower wavelength in ˚A, b2 is the upper wavelength in ˚A, and the grid is linear in
wavelength in between.
• type=4: b1 is the lower wavelength in ˚A, b2 is the upper wavelength in ˚A, and the grid is logarithmic
in wavelength in between.
Note that the logarithmic grids can also be used if one wants to keep a fixed velocity resolution (for
broadened line features for example). Further, each time that the model is being evaluated, the relevant
values of the xi grid points are evaluated.
Warning: Be aware that if you just set b1, b2 and n but do not issue the ”calc” command or the ”fit”
command, the xi values have not yet been calculated and any listed values that you get with the ”par
show” command will be wrong. After the first calculation, they are right.
Warning: If at any time you change one of the parameters type, b1, b2 or n, the yi values will not be
appropriate anymore as they correspond to the previous set of xi values.
98 Spectral Models
The maximum number n of grid points that is allowed is 999, for practical reasons. Should you wish to
have a larger number, then you must define multiple spln components, each spanning its own (disjunct)
b1–b2 range.
It should be noted, however, that if you take n very large, spectral fitting may become slow, in particular
if you take your initial guesses of the yi parameters not too close to the true values. The reason for the
slowness is two-fold; first, the computational time for each fitting step is proportional to the number of
free parameters (if the number of free parameters is large). The second reason is unavoidable due to our
spectral fitting algorithm: our splines are defined in log photon spectrum space; if you start for example
with the same value for each yi, the fitting algorithm will start to vary each parameter in turn; if it
changes for example parameter xj by 1, this means a factor of 10; since the neighbouring points (like
xj−1 and xj+1 however are not adjusted in thid step, the photon spectrum has to be drawn as a cubic
spline through this very sharp function, and it will show the well-known over-and undershooting at the
intermediate x-values between xj−1 and xj and between xj and xj+1; as the data do not show this strong
oscillation, χ2
will be poor and the fitting algorithm will decide to adjust the parameter yj only with a
tiny amount; the big improvement in χ2
would only come if all values of yi were adjusted simultaneously.
The parameters of the model are:
type - The parameter type defined above; allowed values are 1–4. Default value: 1.
n - The number of grid points n. Should be at least 2.
low - Lower x-value b1.
upp - Upper x-value b2. Take care to take b2 > b1.
x001 - First x-value, by definition equal to b1. x-values are not allowed to vary (i.e. you may not fit
them).
x002 - Second x-value
x003 - Third x-value
. . . - Other x-values
x999 - last x-value, by definition equal to bn. If n < 999, replace the 999 by the relevant value (for
example, if n = 237, then the last x-value is x237).
y001 - First y-value. This is a fittable parameter.
y002 - Second y-value
y003 - Third y-value
. . . - Other y-values
y999 - last y-value. If n < 999, replace the 999 by the relevant value (for example, if n = 237, then the
last y-value is y237).
4.36 User: User defined model
The user model provides an interface to create an additive model component calculated by a user program.
The interface is rather simple and therefore very flexible. The interface uses a set of two ASCII files:
input-?-?.prm and output-?-?.spc, where the ’?’ stands for the sector and component number of the user
model component.
The input-?-?.prm is generated by the user model and contains the parameter values and the energy grid
that SPEX uses to calculate the model. The file has a fixed structure:
• The first line contains one integer number containing the number of parameters that the model
needs to calculate (current maximum is 40).
• On the second line the array of parameter values is listed (with the length indicated on the previous
line.
• On the third line, an integer value is shown which indicates the number of model bins SPEX has
in its model grid.
4.37 Vblo: rectangular velocity broadening model 99
• On the following lines, the model grid points are shown in three columns. The first column contains
the bin upper boundary (egb), the second column is the bin center (eg) and the third column is
the full bin width (deg). The energy values are in keV.
The user program is supposed to read the input file and calculate the model spectrum for each energy
bin on the grid. The spectrum array is called ’sener’ and has the same length as the energy grid and unit
photons/s/bin. In addition, it is also possible to calculate the model for the emission weighted center of
the bin. In that case the spectrum calculation is a bit more complicated, but it leads to better results.
The user has the option of also calculating the weighted spectrum, which is the average photon energy
Eaver minus the bin centroid Ecentroid times the flux (F):
W = (Eaver − Ecentroid) ∗ F (4.52)
The W values end up in the ’wener’ array. If you do not use weighing by average photon energy, ’wener’
values can be 0.
The user program should create an output ASCII file named output-?-?.spc with the following structure:
• On the first row, put the number of model bins. This should be the same number as written in the
input-?-?.prm file.
• Write the ’sener’ and ’wener’ values in two columns. The first column is the ’sener’ value in
photons/s/bin and the second column is the ’wener’ value.
In the directory ’user’ in the main SPEXdirectory some example user model programs can be found. The
source code can be adapted to accommodate the user’s wishes.
The parameters of the model are:
exec - User executable, for example ’./model.py’ for a python script in the same directory where you run
SPEX
npar - Number of free parameters in the model. Current maximum is 40.
p01...p40 - Model parameters of the user model.
4.37 Vblo: rectangular velocity broadening model
This multiplicative model broadens an arbitrary additive component with a rectangular Doppler profile,
characterized by the half-width v. Therefore if a delta-line at energy E is convolved with this component,
its full energy width will be 2Ev/c, and line photons get a rectangular distribution between E − Ev/c
and E + Ev/c. Of course, any line or continuum emission component can be convolved with the this
broadening model.
The parameters of the model are:
vblo - Velocity broadening half-width v, in km/s. Default value: 3000 km/s.
4.38 Vgau: gaussian velocity broadening model
This multiplicative model broadens an arbitrary additive component with a Gaussian Doppler profile,
characterized by the Gaussian σ. The broadening kernel is therefore proportional to e−(c2
/2σ2
)(E − E0)2
/E2
0 .
The parameters of the model are:
sig - Gaussian velocity broadening σ, in km/s. Default value: 1 km/s
100 Spectral Models
4.39 Vpro: velocity profile broadening model
This multiplicative model broadens an arbitrary additive component with an arbitrarily shaped Doppler
profile, characterized by the half-width v and a profile shape f(x). The resulting spectrum Sc(E) is
calculated from the original spectrum S(E) as
Sc(E) = f
E − E0
E0
v
c
S(E0)dE0. (4.53)
The function f(x) must correspond to a probability function, i.e. for all values of x we have
f(x) ≥ 0 (4.54)
and furthermore
∞
−∞
f(x)dx = 1. (4.55)
In our implementation, we do not use f(x) but instead the cumulative probability density function F(x),
which is related to f(x) by
F(x) ≡
x
−∞
f(y)dy, (4.56)
where obviously F(−∞) = 0 and F(∞) = 1. The reason for using the cumulative distribution is that
this allows easier interpolation and conservation of photons in the numerical integrations.
If this component is used, you must have a file available which we call here ”vprof.dat” (but any name
is allowed). This is a simple ascii file, with n lines, and at each line two numbers: a value for x and
the corresponding F(x). The lines must be sorted in ascending order in x, and for F(x) to be a proper
probability distribution, it must be a non-decreasing function i.e. if F(xi) ≤ F(xi+1) for all values of i
between 1 and n − 1. Furthermore, we demand that F(x1) ≡ 0 and F(xn) ≡ 1.
Note that both x and F(x) are dimensionless. The parameter v serves as a scaling parameter for the total
amount of broadening. Of course for a given profile there is freedom for the choice of both the x-scale
as well as the value of v, as long as e.g. xnv remains constant. In practice it is better to make a logical
choice. For example, for a rectangular velocity broadening (equivalent to the vblo broadening model) one
would choose n = 2 with x1 = −1, x2 = 1, F(x1) = 0 and F(x2) = 1, and then let v do the scaling
(this also allows you to have v as a free parameter in spectral fits). If one would instead want to describe
a Gaussian profile (for which of course also the vgau model exists), one could for example approximate
the profile by taking the x-scale in units of the standard deviation; an example with a resolution of 0.1
standard deviation and a cut-off approximation at 5 standard deviations would be x =-5, -4.9, -4.8, . . .,
4.8, 4.9, 5.0 with corresponding values for F given by F = 0, 0.00000048, 0.00000079, . . ., 0.99999921,
0.99999952, 1.
The parameters of the model are:
v - Velocity broadening parameter v, in km/s. Default value: 1 km/s.
file - Ascii character string, containing the actual name of the vprof.dat file
4.40 Warm: continuous photoionised absorption model
The warm model is a multi-component version of the xabs model. In the warm model, we construct a
model for a continuous distribution of column density NH as a function of ξ. It is in some sense comparable
to the differential emission measure models used to model the emission from multi-temperature gas. Here
we have absorption from multi-ionization gas. Depending upon the physics of the source, this may be a
better approximation than just the sum of a few xabs components. A disadvantage of the model may be
4.41 Wdem: power law differential emission measure model 101
(but this also depends upon the physics of the source), that all dynamical parameters for each value of ξ
are the same, like the outflow velocity and turbulent broadening. If this appears to be the case in a given
source, one may of course avoid this problem by taking multiple, non-overlapping warm components.
The model assumes a logarithmic grid of n equidistant values of log ξ, between a lower limit ξ1 and
an upper limit ξ2. For each of the grid points ξi, a value of fi can be adjusted; here fi is given as
fi = dNH/d ln ξ evaluated at ξi, where the differential column density is assumed to be a continuous
function of ξ. At each intermediate point, the value of dNH/d ln ξ is then determined by doing cubic
spline interpolation in the ln f – ln ξ space. In order not to consume too much computer time, the step
size for numerical integration ∆ log ξ can be set. A typical, recommended value for this (the default) is
0.2.
For more information on this model, the atomic data and parameters we refer to Sect. 5.2.3.
The parameters of the model are:
xil1 - log ξ1 of the lower limit of the ionisation parameter range in units of 10−9
W m. Default value: -4.
xil2 - log ξ2 of the upper limit of the ionisation parameter range in units of 10−9
W m. Default value: 5.
npol - The number of grid points for the log ξ grid, including the end points for ξ1. Default value: 19;
lower values are generally recommended; minimum value is 2.
dxi - step size for numerical integration ∆ log ξ. Default value: 0.2.
f01. . .f19 - Values of fi = dNH/d ln ξ at the grid points. Default values 10−6
. When npol< 19, the
remaining values of fi are simply ignored.
The following parameters are common to all our absorption models:
fcov - The covering factor of the absorber. Default value: 1 (full covering)
v - Root mean square velocity σv
rms - Rms velocity σb of line blend components
dv - Velocity distance ∆v between different blend components
zv - Average systematic velocity v of the absorber
The following parameter is the same as for the xabs-model (see there for a description):
col - File name for the photoionisation balance parameters
Recommended citation: Steenbrugge et al. (2005b).
4.41 Wdem: power law differential emission measure model
This model calculates the spectrum of a power law distribution of the differential emission measure
distribution. It appears to be a good empirical approximation for the spectrum in cooling cores of
clusters of galaxies. It was first introduced by Kaastra et al. (2004) and is defined as follows:
dY
dT
=



0 if T ≤ βTmax;
cT α
if βTmax < T < Tmax;
0 if T ≥ Tmax.
(4.57)
Here Y is the emission measure Y ≡ nHneV in units of 1064
m−3
, where ne and nH are the electron and
Hydrogen densities and V the volume of the source.
For α → ∞, we obtain the isothermal model, for large α a steep temperature decline is recovered while
for α = 0 the emission measure distribution is flat. Note that Peterson et al. (2003) use a similar
parameterisation but then for the differential luminosity distribution). In practice, we have implemented
the model (4.57) by using the integrated emission measure Ytot instead of c for the normalisation, and
instead of α its inverse p = 1/α, so that we can test isothermality by taking p = 0. The emission measure
distribution for the model is binned to bins with logarithmic steps of 0.10 in log T , and for each bin the
spectrum is evaluated at the emission measure averaged temperature and with the integrated emission
102 Spectral Models
measure for the relevant bin (this is needed since for large α the emission measure weighted temperature
is very close to the upper temperature limit of the bin, and not to the bin centroid). Instead of using
Tmin directly as the lower temperature cut-off, we use a scaled cut-off β such that Tmin = βTmax.
From the parameters of the wdem model, the emission weighted mean temperature kTmean can be calculated
(de Plaa et al. 2006):
Tmean =
(1 + α)
(2 + α)
(1 − β2+α
)
(1 − β1+α)
Tmax (4.58)
Warning: Take care that β < 1. For β = 1, the model becomes isothermal, regardless the value of α.
The model also becomes isothermal for p=0, regardless of the value of β.
Warning: For low resolution spectra, the α and β parameters are not entirely independent, which could
lead to degeneracies in the fit.
The parameters of the model are:
norm - Integrated emission measure between Tmin and Tmax
t0 - Maximum temperature Tmax, in keV. Default: 1 keV.
p - Slope p = 1/α. Default: 0.25 (α = 4).
cut - Lower temperature cut-off β , in units of Tmax. Default value: 0.1.
The following parameters are the same as for the cie-model:
ed - Electron density in 1020
m−3
it - Ion temperature in keV
vmic - Micro turbulent velocity in km/s
ref - Reference element
01. . .30 - Abundances of H to Zn
file - Filename for the nonthermal electron distribution
Recommended citation: Kaastra et al. (2004).
4.42 Xabs: photoionised absorption model
The xabs model calculates the transmission of a slab of material, where all ionic column densities are
linked through a photoionisation model. The relevant parameter is the ionization parameter ξ = L/nr2
,
with L the source luminosity, n the hydrogen density and r the distance from the ionizing source. The
advantage of the xabs model over the slab model is that all relevant ions are taken into account, also those
which would be detected only with marginal significance using the slab model. In some circumstances,
the combined effect of many weak absorption features still can be significant. A disadvantage of the xabs
model happens of course when the ionization balance of the source is different from the ionization balance
that was used to produce the set of runs with the photo ionization code. In that case the xabs model
may fail to give an acceptable fit, while the slab model may perform better.
The xabs model needs an ascii-file as input. The user can provide such a file (see parameter ”col” in
the parameter list), but there is also a default file in SPEX that is read if the user does not provide
a separate file. The default is based on a run with Cloudy, using the spectral energy distribution of
NGC 5548 as used in Steenbrugge et al. (2005a). Such an ascii-files contains a pre-calculated list of
ionic column densities versus ionisation parameter, as well as electron temperatures versus ionisation
parameter (needed for the thermal line broadening). If you want to produce such a file, you can use the
auxiliary program xabsinput, that will run Cloudy for you and make the file to be used in SPEX. See
Sect. 7.2 for more details how to use that program.
For more information on this model, the atomic data and parameters we refer to Sect. 5.2.3.
The parameters of the model are:
nh - Hydrogen column density in 1028
m−2
. Default value: 10−4
(corresponding to 1024
m−2
, a typical
value at low Galactic latitudes).
4.42 Xabs: photoionised absorption model 103
xi - the 10
log of the ionisation parameter log ξ in units of 10−9
W m. Default value: 1.
The following parameters are common to all our absorption models:
fcov - The covering factor of the absorber. Default value: 1 (full covering)
v - Root mean square velocity σv
rms - Rms velocity σb of line blend components
dv - Velocity distance ∆v between different blend components
zv - Average systematic velocity v of the absorber
The following parameters are the same as for the cie-model (see there for a description):
ref - Reference element
01. . .28 - Abundances of H to Ni; only here we take H, He, C, N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Fe,
Ni.
The following parameter is unique for the xabs-model and the warm model:
col - File name for the photoionisation balance parameters
Recommended citation: Steenbrugge et al. (2003).
104 Spectral Models
Table 4.1: Available spectral components
acronym description
additive components:
pow Power law
delt Delta line
gaus Gaussian line
bb Blackbody
mbb Modified blackbody
dbb Accretion disk blackbody
cie Collisional ionisation equilibrium spectrum
comt Comptonisation model Titarchuk
cx Charge exchange model
neij Non-equilibrium ionisation spectrum
sed Sedov adiabatic SNR model
chev Chevalier adiabatic SNR model with reverse shock
soli Solinger isothermal SNR model
band Band isothermal SNR model with reverse shock
pdem Differential emission measure model, polynomials
cf Isobaric cooling flow model
wdem Power law differential emission measure with high T cut-off
dem Differential emission measure model, for DEM analysis
refl Reflection model of Zycki
file Table model from file
multiplicative components, shifts:
reds Redshift model
multiplicative components, convolutions:
vgau Gaussian velocity profile
vblo Square velocity profile
vpro Arbitrary velocity profile (needs input file)
lpro Spatial profile modeling for RGS (needs input file)
laor Laor relativistic line profile
multiplicative components, absorption/transmission:
absm Morrison & McCammon ISM absorption
euve EUVE absorption model Rumph et al. (1994) (H+He)
ebv Galactic interstellar extinction model
hot SPEX absorption by plasma in CIE
slab Absorption by a slab with adjustable ionic columns
xabs Absorption by a slab in photoionization equilibrium
pion Photoionised absorption model
warm Absorption by a slab with continuous distribution in ionization
knak Transmission piecewise power law
etau Transmission for optical depth τ(E) a power law
dust Dust scattering model
amol Absorption by molecular oxygen
Chapter 5
More about spectral models
5.1 Plasma model in SPEX 3.0
5.1.1 The core of the plasma model
The old plasma code used by SPEX in version 2.0 and below is essentially the same plasma code as
developed originally by Rolf Mewe and colleagues, with relatively minor updates to the atomic data (like
wavelength improvements, corrections of a few typo’s, improvements for Fe XVII).
Its basis were precalculated and parametrized line emissivities for each spectral line, as a function of
temperature, with for relevant lines empirical density corrections. For some transitiuons, like the He-like
triplets, the calculations were rather complex and required several correction factors to account for the
full density dependence.
In the new approach presented here, the basic plasma processes are evaluated for each individual level,
and then the occupation numbers of the excited states are calculated for the full ion, solving a matrix
equation. This has the great advantage that with the same effort a multitude of processes can be taken
into account, including effects of photo-excitation and photo-ionisation. From the occupation numbers
and the radiative transition probabilities it is then straightforward to calculate the emitted spectrum.
In order to keep the code fast and flexible, we have chosen for a procedure to parametrise all relevant
processes, and using simple analytical formulae with a limited number of parameters for each process.
This is beneficial both in terms of computation time and storage demands and formed the basis for the
succes of Mewe’s original work.
The production of the relevant files is not yet complete, but in the first release of version 3.0 we incorporate
the data for the H, He, and Li isoelectronic sequences, and some data for the other sequences, including
the Fe-L ions. For an overview of what is in the code see Section 5.1.2 below.
By default, the plasma code is the old version 2.0 code, but by giving the command ”var calc new”, for
the ions for which new data are available, the new code is used. This leads in principle to higher accuracy
and many more spectral lines. A disadvantage is of course that the computations become somewhat
slower. For spectral fitting, one could envision a procedure where in a first run the old code is used to
get close to the best parameters, and then to refine using the new plasma core.
If you want to use the new plasma model, it is important to change the ionisation balance from the
default (Bryans et al. 2009) to the new u16 balance. This new balance has improved collisional ionisation
rates and allows to calculate properly inner-shell transitions that are needed for the new calculations.
The paper describing this (Urdampilleta et al.) will be published soon.
Finally, it is advised that the users have a look to the various ascii-output options that are available for
the plasma models, allowing to get deeper insight into the physical process and parameters that are being
used.
106 More about spectral models
5.1.2 Ions for which updated calculations are available
Below we list for each iso-electronic sequence what data is available for the new plasma calculations.
Each line corresponds to one ion, with ii, iz and jz corresponding to the iso-electronic sequence, nuclear
charge and ionisation stage, respectively. Then for a number of process we list two quantities: N, the
number of entries we have (e.g., number of energy levels or transition rates), and nmax the maximum
principal quantum number for wich we use data for that ion and process. Note that nmax refers to the
highest level included for a transition between two levels.
The processes incorporated and shown in the table are:
1. levels – Energy levels
2. Arad – Radiative transition probabilities (Einstein coefficients)
3. Atwo – Two-photon processes
4. El col – Electron collisional excitation
5. Pr col – Proton collisional excitation
6. Aug – Auger rates (auto-ionisation, needed for dielectronic recombination)
7. CX – Charge exchange recombination
8. RR – Radiative recombination
9. II – Inner-shell processes (this is merely the number of quantum states after ionisation; the number
of fluorescent lines will be larger)
5.1 Plasma model in SPEX 3.0 107
Table 5.1: Hydrogen like.
ii iz jz levels Arad Atwo El Col Pr col Aug CX RR II
N nmax N nmax N nmax N nmax N nmax N nmax N nmax N nmax N nmax
1 1 1 256 16 3245 16 1 2 291 5 3 2 0 0 0 0 256 16 0 0
1 2 2 256 16 3244 16 1 2 355 10 3 2 0 0 0 0 256 16 0 0
1 3 3 256 16 3242 16 1 2 354 10 3 2 0 0 0 0 256 16 0 0
1 4 4 256 16 3253 16 1 2 354 10 3 2 0 0 72 6 256 16 0 0
1 5 5 256 16 3267 16 1 2 358 10 3 2 0 0 96 7 256 16 0 0
1 6 6 284 20 4305 20 1 2 428 20 3 2 0 0 380 7 256 16 0 0
1 7 7 284 20 4359 20 1 2 430 20 3 2 0 0 490 7 256 16 0 0
1 8 8 284 20 4378 20 1 2 430 20 3 2 0 0 568 7 256 16 0 0
1 9 9 256 16 3345 16 1 2 360 10 3 2 0 0 128 8 256 16 0 0
1 10 10 284 20 4431 20 1 2 430 20 3 2 0 0 812 9 256 16 0 0
1 11 11 256 16 3364 16 1 2 360 10 3 2 0 0 162 9 256 16 0 0
1 12 12 284 20 4456 20 1 2 428 20 3 2 0 0 1328 10 256 16 0 0
1 13 13 256 16 3388 16 1 2 360 10 3 2 0 0 242 11 256 16 0 0
1 14 14 284 20 4506 20 1 2 430 20 3 2 0 0 1798 12 256 16 0 0
1 15 15 256 16 3448 16 1 2 360 10 3 2 0 0 313 13 256 16 0 0
1 16 16 284 20 4557 20 1 2 430 20 3 2 0 0 338 13 256 16 0 0
1 17 17 256 16 3502 16 1 2 360 10 3 2 0 0 392 14 256 16 0 0
1 18 18 284 20 4608 20 1 2 430 20 3 2 0 0 450 15 256 16 0 0
1 19 19 256 16 3544 16 1 2 360 10 3 2 0 0 450 15 256 16 0 0
1 20 20 284 20 4664 20 1 2 430 20 3 2 0 0 450 15 256 16 0 0
1 21 21 256 16 3587 16 1 2 360 10 3 2 0 0 450 15 256 16 0 0
1 22 22 284 20 4691 20 1 2 430 20 3 2 0 0 450 15 256 16 0 0
1 23 23 256 16 3613 16 1 2 360 10 3 2 0 0 450 15 256 16 0 0
1 24 24 284 20 4725 20 1 2 430 20 3 2 0 0 450 15 256 16 0 0
1 25 25 256 16 3640 16 1 2 360 10 3 2 0 0 450 15 256 16 0 0
1 26 26 284 20 4757 20 1 2 434 20 3 2 0 0 450 15 256 16 0 0
1 27 27 256 16 3666 16 1 2 360 10 3 2 0 0 450 15 256 16 0 0
1 28 28 284 20 4790 20 1 2 430 20 3 2 0 0 450 15 256 16 0 0
1 29 29 256 16 3702 16 1 2 360 10 3 2 0 0 450 15 256 16 0 0
1 30 30 256 16 3783 16 1 2 358 10 3 2 0 0 450 15 256 16 0 0
Table 5.2: Helium like.
ii iz jz levels Arad Atwo El Col Pr col Aug CX RR II
N nmax N nmax N nmax N nmax N nmax N nmax N nmax N nmax N nmax
2 2 1 511 16 7935 16 1 2 72 7 3 2 0 0 0 0 127 8 2 2
2 3 2 511 16 8156 16 1 2 78 7 3 2 0 0 0 0 127 8 2 2
2 4 3 511 16 8349 16 1 2 448 7 3 2 0 0 0 0 127 8 2 2
2 5 4 511 16 8479 16 1 2 448 7 3 2 0 0 60 4 127 8 2 2
2 6 5 678 16 12345 16 1 2 1599 10 3 2 166 5 392 4 127 8 2 2
2 7 6 678 16 12500 16 1 2 1616 10 3 2 166 5 636 5 127 8 2 2
2 8 7 678 16 12648 16 1 2 1625 10 3 2 166 5 872 7 127 8 2 2
2 9 8 678 16 12289 16 1 2 1547 7 3 2 166 5 108 6 127 8 2 2
2 10 9 678 16 12799 16 1 2 1636 10 3 2 166 5 1478 8 127 8 2 2
2 11 10 678 16 12606 16 1 2 1559 7 3 2 166 5 254 8 127 8 2 2
2 12 11 678 16 13071 16 1 2 1640 10 3 2 166 5 2194 10 127 8 2 2
2 13 12 678 16 12997 16 1 2 1557 7 3 2 166 5 398 10 127 8 2 2
2 14 13 678 16 13344 16 1 2 1632 10 3 2 166 5 2976 11 127 8 2 2
2 15 14 678 16 13288 16 1 2 1565 7 3 2 166 5 0 0 127 8 2 2
2 16 15 678 16 13564 16 1 2 1637 10 3 2 166 5 204 10 127 8 2 2
2 17 16 678 16 13437 16 1 2 1542 7 3 2 166 5 204 10 127 8 2 2
2 18 17 678 16 13683 16 1 2 1623 10 3 2 166 5 228 11 127 8 2 2
2 19 18 678 16 13542 16 1 2 1540 7 3 2 166 5 228 11 127 8 2 2
2 20 19 678 16 13744 16 1 2 1642 10 3 2 166 5 252 12 127 8 2 2
2 21 20 678 16 13586 16 1 2 1525 7 3 2 166 5 252 12 127 8 2 2
2 22 21 678 16 13783 16 1 2 1582 10 3 2 166 5 302 13 127 8 2 2
2 23 22 678 16 13615 16 1 2 1502 7 3 2 166 5 276 13 127 8 2 2
2 24 23 678 16 13818 16 1 2 1634 10 3 2 166 5 330 14 127 8 2 2
2 25 24 678 16 13627 16 1 2 1495 7 3 2 166 5 330 14 127 8 2 2
2 26 25 678 16 13834 16 1 2 1619 10 3 2 166 5 898 15 127 8 2 2
2 27 26 678 16 13618 16 1 2 1549 7 3 2 166 5 358 15 127 8 2 2
2 28 27 678 16 13851 16 1 2 1614 10 3 2 166 5 324 15 127 8 2 2
2 29 28 678 16 13662 16 1 2 1540 7 3 2 166 5 386 16 127 8 2 2
2 30 29 678 16 13679 16 1 2 1558 7 3 2 166 5 348 16 127 8 2 2
108 More about spectral models
Table 5.3: Lithium like.
ii iz jz levels Arad Atwo El Col Pr col Aug CX RR II
N nmax N nmax N nmax N nmax N nmax N nmax N nmax N nmax N nmax
3 4 2 255 16 3119 16 0 0 0 0 0 0 0 0 0 0 63 8 0 0
3 5 3 255 16 3151 16 0 0 0 0 0 0 0 0 0 0 63 8 0 0
3 6 4 815 16 13609 16 0 0 912 6 0 0 1041 5 30 4 63 8 1 2
3 7 5 815 16 13495 16 0 0 911 6 0 0 1040 5 42 5 63 8 1 2
3 8 6 815 16 13657 16 0 0 899 5 0 0 1041 5 69 7 63 8 1 2
3 9 7 271 16 3483 16 0 0 66 5 0 0 0 0 54 6 63 8 1 2
3 10 8 815 16 13812 16 0 0 898 5 0 0 1041 5 54 6 63 8 1 2
3 11 9 271 16 3520 16 0 0 66 5 0 0 0 0 66 7 63 8 1 2
3 12 10 815 16 14061 16 0 0 912 5 0 0 1041 5 66 7 63 8 1 2
3 13 11 271 16 3564 16 0 0 66 5 0 0 0 0 78 8 63 8 1 2
3 14 12 815 16 14450 16 0 0 922 5 0 0 1041 5 78 8 63 8 1 2
3 15 13 271 16 3591 16 0 0 66 5 0 0 0 0 90 9 63 8 1 2
3 16 14 815 16 14543 16 0 0 914 5 0 0 1051 5 90 9 63 8 1 2
3 17 15 271 16 3646 16 0 0 66 5 0 0 0 0 102 10 63 8 1 2
3 18 16 815 16 14532 16 0 0 924 5 0 0 1051 5 102 10 63 8 1 2
3 19 17 271 16 3710 16 0 0 66 5 0 0 0 0 114 11 63 8 1 2
3 20 18 815 16 14502 16 0 0 928 5 0 0 1051 5 114 11 63 8 1 2
3 21 19 271 16 3748 16 0 0 66 5 0 0 0 0 126 12 63 8 1 2
3 22 20 815 16 14448 16 0 0 925 5 0 0 1051 5 126 12 63 8 1 2
3 23 21 271 16 3781 16 0 0 66 5 0 0 0 0 151 13 63 8 1 2
3 24 22 815 16 14281 16 0 0 928 5 0 0 1051 5 138 13 63 8 1 2
3 25 23 271 16 3812 16 0 0 66 5 0 0 0 0 165 14 63 8 1 2
3 26 24 815 16 14188 16 0 0 1153 7 0 0 1051 5 165 14 63 8 1 2
3 27 25 271 16 3843 16 0 0 66 5 0 0 0 0 150 14 63 8 1 2
3 28 26 815 16 14010 16 0 0 922 5 0 0 1051 5 179 15 63 8 1 2
3 29 27 271 16 3867 16 0 0 66 5 0 0 0 0 162 15 63 8 1 2
3 30 28 815 16 14027 16 0 0 920 5 0 0 1051 5 193 16 63 8 1 2
Table 5.4: Berilium like.
ii iz jz levels Arad Atwo El Col Pr col Aug CX RR II
N nmax N nmax N nmax N nmax N nmax N nmax N nmax N nmax N nmax
4 6 3 720 16 12924 16 0 0 1487 6 0 0 0 0 0 0 127 8 8 2
4 7 4 745 16 15977 16 0 0 2223 6 0 0 0 0 58 4 127 8 8 2
4 8 5 694 16 10103 16 0 0 1934 6 0 0 0 0 190 7 127 8 8 2
4 9 6 578 16 9524 16 0 0 402 3 0 0 0 0 84 5 127 8 4 2
4 10 7 720 16 12398 16 0 0 1850 5 0 0 0 0 108 6 127 8 8 2
4 11 8 578 16 9774 16 0 0 403 3 0 0 0 0 108 6 127 8 4 2
4 12 9 720 16 13352 16 0 0 1908 5 0 0 0 0 132 7 127 8 8 2
4 13 10 578 16 10112 16 0 0 404 3 0 0 0 0 132 7 127 8 4 2
4 14 11 720 16 13670 16 0 0 1914 5 0 0 0 0 156 8 127 8 8 2
4 15 12 578 16 10435 16 0 0 404 3 0 0 0 0 156 8 127 8 4 2
4 16 13 720 16 14106 16 0 0 1938 6 0 0 0 0 180 9 127 8 8 2
4 17 14 578 16 10727 16 0 0 403 3 0 0 0 0 180 9 127 8 4 2
4 18 15 720 16 14106 16 0 0 1919 5 0 0 0 0 204 10 127 8 8 2
4 19 16 577 16 11014 16 0 0 394 3 0 0 0 0 204 10 127 8 4 2
4 20 17 720 16 14294 16 0 0 1922 5 0 0 0 0 228 11 127 8 8 2
4 21 18 578 16 11299 16 0 0 404 3 0 0 0 0 228 11 127 8 4 2
4 22 19 720 16 14412 16 0 0 1909 5 0 0 0 0 252 12 127 8 8 2
4 23 20 578 16 11509 16 0 0 404 3 0 0 0 0 252 12 127 8 4 2
4 24 21 720 16 14471 16 0 0 1902 5 0 0 0 0 302 13 127 8 8 2
4 25 22 578 16 11632 16 0 0 404 3 0 0 0 0 276 13 127 8 4 2
4 26 23 770 16 21854 16 0 0 3093 7 3 2 0 0 330 14 127 8 8 2
4 27 24 578 16 11745 16 0 0 404 3 0 0 0 0 330 14 127 8 4 2
4 28 25 720 16 14574 16 0 0 1859 5 0 0 0 0 300 14 127 8 8 2
4 29 26 578 16 11849 16 0 0 404 3 0 0 0 0 358 15 127 8 4 2
4 30 27 720 16 14593 16 0 0 1733 5 0 0 0 0 324 15 127 8 8 2
5.1 Plasma model in SPEX 3.0 109
Table 5.5: Boron like.
ii iz jz levels Arad Atwo El Col Pr col Aug CX RR II
N nmax N nmax N nmax N nmax N nmax N nmax N nmax N nmax N nmax
5 6 2 714 16 16260 16 0 0 535 5 0 0 0 0 0 0 63 8 16 2
5 7 3 968 16 19713 16 0 0 1276 5 0 0 0 0 0 0 65 8 16 2
5 8 4 968 16 20225 16 0 0 1262 5 0 0 0 0 28 4 66 8 16 2
5 9 5 744 16 16610 16 0 0 955 5 0 0 0 0 42 5 66 8 8 2
5 10 6 968 16 20644 16 0 0 681 5 0 0 0 0 42 5 67 8 16 2
5 11 7 744 16 16965 16 0 0 974 5 0 0 0 0 54 6 67 8 8 2
5 12 8 968 16 20393 16 0 0 677 5 0 0 0 0 54 6 67 8 16 2
5 13 9 744 16 16100 16 0 0 970 5 0 0 0 0 66 7 67 8 8 2
5 14 10 967 16 20640 16 0 0 618 5 0 0 0 0 66 7 68 8 16 2
5 15 11 744 16 17123 16 0 0 984 5 0 0 0 0 78 8 68 8 8 2
5 16 12 968 16 21143 16 0 0 666 5 0 0 0 0 78 8 68 8 16 2
5 17 13 744 16 17161 16 0 0 985 5 0 0 0 0 90 9 69 8 8 2
5 18 14 968 16 21046 16 0 0 644 5 0 0 0 0 90 9 69 8 16 2
5 19 15 744 16 16583 16 0 0 991 5 0 0 0 0 102 10 69 8 8 2
5 20 16 968 16 20764 16 0 0 680 5 0 0 0 0 102 10 69 8 16 2
5 21 17 744 16 16705 16 0 0 996 5 0 0 0 0 114 11 69 8 8 2
5 22 18 968 16 20997 16 0 0 663 5 0 0 0 0 114 11 69 8 16 2
5 23 19 744 16 16719 16 0 0 999 5 0 0 0 0 126 12 69 8 8 2
5 24 20 968 16 20718 16 0 0 660 5 0 0 0 0 126 12 69 8 16 2
5 25 21 744 16 16508 16 0 0 994 5 0 0 0 0 151 13 69 8 8 2
5 26 22 803 16 25244 16 0 0 4636 6 0 0 0 0 138 13 69 8 16 2
5 27 23 744 16 16455 16 0 0 989 5 0 0 0 0 165 14 69 8 8 2
5 28 24 968 16 20435 16 0 0 631 5 0 0 0 0 165 14 69 8 16 2
5 29 25 744 16 16204 16 0 0 990 5 0 0 0 0 150 14 69 8 8 2
5 30 26 968 16 20132 16 0 0 991 5 0 0 0 0 179 15 69 8 16 2
Table 5.6: Carbon like.
ii iz jz levels Arad Atwo El Col Pr col Aug CX RR II
N nmax N nmax N nmax N nmax N nmax N nmax N nmax N nmax N nmax
6 6 1 1199 7 23942 5 0 0 4050 5 0 0 0 0 0 0 61 7 20 2
6 7 2 1192 6 24112 5 0 0 4855 5 0 0 0 0 0 0 55 6 20 2
6 8 3 1210 5 24175 5 0 0 5170 5 0 0 1104 5 0 0 55 5 20 2
6 10 5 1188 5 24174 5 0 0 5173 5 0 0 0 0 204 5 56 5 20 2
6 12 7 1188 5 24793 5 0 0 5360 5 0 0 0 0 0 0 57 5 20 2
6 14 9 1188 5 24206 5 0 0 5254 5 0 0 0 0 0 0 57 5 20 2
6 16 11 1188 5 24294 5 0 0 5406 5 0 0 0 0 0 0 57 5 20 2
6 18 13 1210 5 24028 5 0 0 5795 5 0 0 1104 5 0 0 57 5 20 2
6 20 15 1210 5 24588 5 0 0 5697 5 0 0 1104 5 0 0 57 5 20 2
6 22 17 1210 5 24108 5 0 0 5750 5 0 0 1104 5 0 0 57 5 20 2
6 24 19 1210 5 23129 5 0 0 5836 5 0 0 1104 5 0 0 57 5 20 2
6 26 21 848 5 15719 5 0 0 15614 5 0 0 0 0 0 0 57 5 10 2
6 28 23 1210 5 22519 5 0 0 5823 5 0 0 1104 5 0 0 57 5 20 2
6 30 25 1210 5 22247 5 0 0 5799 5 0 0 1104 5 0 0 57 5 20 2
Table 5.7: Nitrogen like.
ii iz jz levels Arad Atwo El Col Pr col Aug CX RR II
N nmax N nmax N nmax N nmax N nmax N nmax N nmax N nmax N nmax
7 26 20 1087 5 41963 5 0 0 15338 5 0 0 0 0 0 0 30 5 8 2
Table 5.8: Oxygen like.
ii iz jz levels Arad Atwo El Col Pr col Aug CX RR II
N nmax N nmax N nmax N nmax N nmax N nmax N nmax N nmax N nmax
8 26 19 994 5 36028 5 0 0 9205 5 0 0 0 0 0 0 81 5 0 0
Table 5.9: Fluor like.
ii iz jz levels Arad Atwo El Col Pr col Aug CX RR II
N nmax N nmax N nmax N nmax N nmax N nmax N nmax N nmax N nmax
9 26 18 501 5 13095 5 0 0 1436 5 0 0 0 0 0 0 83 5 0 0
110 More about spectral models
Table 5.10: Neon like.
ii iz jz levels Arad Atwo El Col Pr col Aug CX RR II
N nmax N nmax N nmax N nmax N nmax N nmax N nmax N nmax N nmax
10 14 5 894 10 19321 10 0 0 911 10 0 0 842 10 204 5 215 8 0 0
10 16 7 894 10 20629 10 0 0 1187 10 0 0 826 10 276 6 215 8 0 0
10 18 9 894 10 19871 10 0 0 657 10 0 0 814 10 348 7 215 8 0 0
10 20 11 894 10 21169 10 0 0 305 6 0 0 798 10 100 6 215 8 0 0
10 22 13 894 10 20802 10 0 0 761 10 0 0 790 10 492 9 215 8 0 0
10 24 15 894 10 19759 10 0 0 758 10 0 0 762 10 564 10 215 8 0 0
10 26 17 894 10 20434 10 0 0 1189 10 0 0 762 10 400 10 215 8 0 0
10 28 19 894 10 19878 10 0 0 759 10 0 0 740 10 212 10 215 8 0 0
10 30 21 894 10 20140 10 0 0 699 10 0 0 733 10 212 10 215 8 0 0
Table 5.11: Sodium like.
ii iz jz levels Arad Atwo El Col Pr col Aug CX RR II
N nmax N nmax N nmax N nmax N nmax N nmax N nmax N nmax N nmax
11 20 10 356 5 19534 5 0 0 352 5 0 0 0 0 0 0 21 5 0 0
11 22 12 356 5 19596 5 0 0 350 5 0 0 0 0 0 0 21 5 0 0
11 24 14 356 5 19553 5 0 0 349 5 0 0 0 0 0 0 21 5 0 0
11 26 16 356 5 19594 5 0 0 352 5 0 0 0 0 0 0 21 5 0 0
11 28 18 355 5 19507 5 0 0 349 5 0 0 0 0 0 0 21 5 0 0
5.2 Absorption models 111
5.2 Absorption models
5.2.1 Introduction
In most astrophysical sitiuations we have to take into account absorption of photons between the emitting
region and the observer. Apart from a few standard models like the ones by Morrison & McCammon
(1983, our ”absm” model) and Rumph et al. (1994, our ”euve” model) we have constructed our own
absorption models based upon the atomic database used by SPEX.
Essentially, we adopt a few steps, which will be described below. First, we produce a set of column
densities, in different ways for the diferent absorption models (see Sect. 5.2.3). Next, using a dynamical
model for the absorber we calculate its transmission (Sect. 5.2.4). For these calculations, we use our
atomic database as described in Sect. 5.3.
A basic assumption in all the absorption models is that there is no re-emission, i.e. we look through
an absorbing nmedium that has a very small solid angle as seen from the X-ray source. This allows
essentially to calculate the transmission simply as e−τ(E)
with τ(E) the optical depth.
5.2.2 Thomson scattering
The above approach also allows us to include Thomson-scattering in the transmission. Any source photon
aimed at the observer but that suffers from Thomson scattering is scattered out of the line of sight and
hanec in this approximation is not seen by the observer. We have included not simply the Thomson
cross-section σT but have taken the Klein-Nishina correction into account (see Rybicki & Lightman
1986), eqn. 7.5 (exact expression) and 7.6 (approximations)). The evaluation of the exact formula for the
cross section is non-trivial, as terms up to the third power in x = E/mec2
cancel; we have extended the
low-energy polynomial approximation (7.6.a) of Rybicki & Lightman by comparing to quadruple precision
calculations using the exact formula, and made the following approximation that has a relative accuracy
of better than 3 × 10−4
for all energies, when evaluated using single precision arithmetics:
σ =



σT (1 − 2x + 5.2x2
− 13.3x3
+ 32.685x4
) x < 0.05;
0.75σT
1+x
x3
2x(1+x)
1+2x − ln(1 + 2x) + ln(1+2x)
2x − 1+3x
(1+2x)2 0.05 < x < 5000;
0.375σT (ln(2x) + 0.5)/x x > 5000.
(5.1)
5.2.3 Different types of absorption models
We have a set of spectral models available with different levels of sophistication and applicability, that
we list below.
Slab model
The slab model calculates the transmission of a slab of material, where all ionic column densities can be
chosen independently. This has the advantage that a spectrum can be fit without any knowledge of the
ionisation balance of the slab. After a spectral fit has been made, one may try to explain the observed
column densities by comparing the with predictions from any model (as calculated by SPEX, Cloudy,
XSTAR, ION or any other existing (photo)ionization code).
Xabs model
In the xabs model, the ionic column densities are not independent quantities, but are linked through a
set of runs using a photo ionization code. See the description of the xabs model for more details about
this. The relevant parameter is the ionization parameter ξ = L/nr2
, with L the source luminosity, n the
hydrogen density and r the distance from the ionizing source. The advantage of the xabs model over the
slab model is that all relevant ions are taken into account, also those which would be detected only with
112 More about spectral models
marginal significance using the slab model. In some circumstances, the combined effect of many weak
absorption features still can be significant. A disadvantage of the xabs model happens of course when
the ionization balance of the source is different from the ionization balance that was used to produce the
set of runs with the photo ionization code. In that case the xabs model may fail to give an acceptable
fit, while the slab model may perform better.
Warm model
In the warm model, we construct a model for a continuous distribution of column density NH as a
function of ξ. It is in some sense comparable to the differential emission measure models used to model
the emission from multi-temperature gas. Here we have absorption from multi-ionization gas. Depending
upon the physics of the source, this may be a better approximation than just the sum of a few xabs
components. A disadvantage of the model may be (but this also depends upon the physics of the source),
that all dynamical parameters for each value of ξ are the same, like the outflow velocity and turbulent
broadening. If this appears to be the case in a given source, one may of course avoid this problem by
taking multiple, non-overlapping warm components.
Hot model
In the hot model, we link the different ionic column densities simply by using a collisional ionsation (CIE)
plasma. It may be useful in situations where photoionisation is relatively unimportant but the source has
a non-negligible optical depth. A special application is of course the case for a low temperature, where
it can be used to mimick the absorption of (almost) neutral gas.
Pion model
Finally we have in SPEX the pion model, which does a self-consistent photo ionization calculation of the
slab of material.
5.2.4 Dynamical model for the absorbers
For each of the absorption models described in the previous section, we have the freedom to prescribe
the dynamics of the source. The way we have implemented this in SPEX is described below.
The transmission T (λ) of the slab is simply calculated as
T (λ) = exp[−τc(λ) − τl(λ)] (5.2)
with τc and τl the total continuum and line optical depth, respectively. As long as the thickness of the
slab is not too large, this most simple approximation allows a fast computation of the spectrum, which
is desirable for spectral fitting.
In particular UV observations of AGN show that the absorption lines can often be decomposed into
multiple velocity components. In the X-ray band these are not always fully resolvable, which led us to
the following approach. Each absorption line is split into different velocity components, using
τl(v) =
i
τi exp −(v − vi)2
/2σ2
v (5.3)
(or the equivalent generalisation to the Voigt profile). Further, we take
vi = v0 + i ∆v, (5.4)
τi = K exp −v2
i /2σ2
b , (5.5)
where v0 is the average velocity of the blend (a negative value corresponds to a blue-shift or outflow),
∆v is the separation between the velocity components, and the r.m.s. width of the blend σb is in general
5.3 Atomic database for the absorbers 113
larger than the intrinsic width σv of the components (do never confuse both σ’s!). The normalization K
is defined in such a way that τi = τ0. Finally, the total optical depth τ0 is given by
τ0 = 0.106fN20λ/σv,100. (5.6)
Here f is the oscillator strength, λ the wavelength in ˚A, σv,100 the velocity dispersion in units of 100 km/s
and N20 the total column density of the ion in units of 1020
m−2
.
This dynamical structure offers the user a broad range of applicability. However, we advise the user to
use the extension with σb with caution! Always start with the most simple case. The default values for
SPEX are defined in such a way that σb = 0. This will produce the ”normal” case of single absorption
lines. In that case, the velocity separation ∆v is an irrelevant parameter.
Finally, we make a remark on the r.m.s. line width of individual lines, σv. In our code, this only includes
the turbulent broadening of the lines. The thermal broadening due to motion of the ions is included by
adding it in quadrature to the tutbulent broadening. The only exception is the slab model, where of
course due to the lack of underlying physics the thermal broadening is unknown, and therefore in using
the slab model one should be aware that σv also includes a thermal contribution.
5.3 Atomic database for the absorbers
The continuum opacities are taken from Verner & Yakovlev (1995). Line opacities and wavelengths for
most ions are from Verner et al. (1996), with the following additions and exceptions.
5.3.1 K-shell transitions
For some hydrogenic ions (C, N, O, Ne, Mg, Si, S and Ar) we added the transitions from principal
quantum numbers 11–20 to the ground using our own SPEX database.
C-K transitions
Three inner-shell K-shell transitions for C i were calculated by Raassen using the Cowan code, but here
only the oscillator strengths were calculated, and therefore calculated equivalent widths for large optical
depths will be too weak. We added two C iv lines from the work of Nahar et al. (2001).
N-K transitions
For N i the K-shell transitions were calculated by Raassen using the Cowan code. We adjusted the
wavelength of the strongest 1s–2p line acording to measurements. However, for the 1s–2p lines towards
1s2s2
2p4 4
P, we used oscilator strengths and Auger widths from Garc´ıa et al. (2009).
Inner-shell K-shell transitions for N ii were also calculated by Raassen using the Cowan code, but here
only the oscillator strengths were calculated, and therefore calculated equivalent widths for large optical
depths will be too weak. The exception to this are the 1s–2p absorption lines to the 1s2s2
2p3 3
S1, 3
P1
and 3
D1 levels, for which we use Garc´ıa et al. (2009).
For N iii we added the 1s–2p absorption lines towards the 1s2s2
2p2 2
S, 2
P and 2
D3/2 levels from the
paper by Garc´ıa et al. (2009). Wavelengths are theoretical, so may be somewhat off.
For N iv we added the 1s–2p absorption lines towards the 1s2s2
2p 1
P1 and 1s2p3 1
P1 levels from the
paper by Garc´ıa et al. (2009). Wavelengths are theoretical, so may be somewhat off.
For N v we added the 1s–2p absorption lines towards the 1s(2S)2s2p(3P) 2
P doublet and 1s(2S)2s2p(1P) 2
P
doublet from the paper by Garc´ıa et al. (2009). Wavelengths were corrected according to the measurements
of Beiersdorfer et al. (1999).
For N vi we added the 1s–np lines for n = 5 − 7 from our SPEX database.
114 More about spectral models
O-K transitions
We included the inner shell K-shell transitions of oxygen ions (O i – O vi) from earlier work of Behar
(HULLAC calculations, private commumication).
We adjusted the wavelength of the strongest O v line to 22.370 ± 0.010 ˚A, taken from Gu et al. (2005).
The two 1s–2p 2
P1/2,3/2 lines of O iv were adjusted to 22.741 and 22.739 ˚A, respectively following Gu
et al. (2005). The lines to the 2
D3/2 and 2
S1/2 terms were not adjusted as no values are given by Gu
et al. (2005).
For O iii, Gu et al. (2005) give only a single line instead of the three dominant lines to 3
D1, 3
S1, 3
P1. The
oscillator-strength weighted average wavelength for these three lines using Behar’s HULLAC calculations
is 23.058 ˚A, compared to 23.065 ˚Aas given by Gu et al. (2005). Other sets of calculation differ much from
this, up to 0.05–0.10 ˚A (Olalla et al. 2002; Pradhan et al. 2003; Juett et al. 2004); so we keep the Behar
values lacking more reliable calculations.
For O ii, Juett et al. (2004) identified a feature in observed Chandra HETGS spectra towards several
sources with the 1s–2p line from this ion; their measured wavelength is 23.351±0.003 ˚A. This identification
seems to be justified given the Auger electron measurements of Krause (1994) and Caldwell et al. (1994)
as cited by Garc´ıa et al. (2005). The relevant transitions are from the ground 4
S3/2to the 4
P5/2, 4
P3/2,
and 4
P1/2 levels; the oscillator strength weighted wavelength from Behar is 23.3012 ˚A. Therefore we shift
the wavelengths of these transitions by +0.0498 ˚A in order to match the Juett et al. (2004) value.
Finally, in a similar way we shift the strong 1s–2p doublet from O i to match the weighted average of the
value found by Juett et al. (2004) with the Chandra HETGS (23.508±0.003 ˚A) and in Mrk 421 with RGS
(23.5130±0.0022 ˚A) to (23.5113±0.0018 ˚A). For all O i lines, we have updated the oscillator strengths
and transition rates to values obtained by Ton Raassen using Cowan’s code, and benchmarked to an
adjusted wavelength scale.
Lines from O vii up to n = 100 were calculated by extrapolation of the data for n ≤ 10.
Ne-K to Ca-K transitions
The strongest K-shell transitions from Li-like to F-like ions of Ne, Mg, Al, Si, S, Ar, and Ca were taken
from Behar & Netzer (2002).
Fe-K transitions
K-shell transitions in Fe ii–Fe xxiv were included from the series of papers by Palmeri et al. (2003b),
Mendoza et al. (2004) and Bautista et al. (2004).
In addition, the strongest 1s–3p transitions in Fe xxiii were added from Behar & Netzer (2002).
5.3.2 L-shell transitions
Fe-L transitions
For the L-shell ions of iron (Fe xvii − Fe xxiv) we used HULLAC calculations. The wavelengths of these
L-shell transitions were adjusted according to Phillips et al. (1999). Also the L-shell ions of Si viii–Si xii,
S x–S xiv and Ar xv were calculated using the HULLAC code. In addition, we added the 2p–3d inner
shell resonance lines of Fe i−Fe xvi from Behar et al. (2001). These inner shell resonance lines occur
mainly in the 16−17 ˚A band and appear to be extremely important diagnostic tools, since the normal
resonance lines of these lowly ionized iron ions have their wavelengths mainly in the inaccessible EUV
band.
5.4 Non-equilibrium ionisation (NEI) calculations 115
Ni-L transitions
L-shell transitions of Ni i–Ni xviii were calculated by Raassen using Cowan’s code, with the neglect of
line broadening due to auto-ionizations.
5.3.3 M-shell transitions
For M-shell transitions of Fe ions, we have used data calculated by Ehud Behar using HULLAC (Fe i –
Fe xvi). The calculations for (Fe vi – Fe xvi) were replaced on November 21, 2008 by updated calculations
by Ming Feng Gu using FAC and compared with the NGC 3783 spectrum in Gu et al. (2006). They
represent slight ( 0.03 Angstrom) shifts from Behar’s initial calculations. Also, they exhibit typically
2–3 times higher total transition rates (Auger rates).
5.4 Non-equilibrium ionisation (NEI) calculations
Our current implementation of time-dependent, non-equilibrium ionisation spectra is based upon the
work of Kaastra & Jansen (1993), KJ hereafter. The method consists essentially upon calculating the
transition matrix (containing ionisation and recombination rates) for a grid of temperatures, calculating
the eigenvalues and eigenvectors of these matrices and also the inverse eigenvector matrix, and storing
those on disk. The ionisation balance is calculated then by dividing the temperature history in several
steps, with the steps defined in such a way that the temperature over each time interval is close to one
temperature grid point. Then for each step the time evolution of the plasma is calculated using eigenvalue
decomposition and using the pre-calculated coefficients for the relevant temperature. For more details
see KJ.
Here we make a few changes with respect to KJ. First, KJ adopted a prescribed history of the Hydrogen
density, and calculate the corresponding electron density at each time from the ion concentrations at
that time. This was motivated by the argument that for a fixed plasma element the number of Hydrogen
atoms remains constant over time, while the number of electrons depends upon the degree of ionisation
and may be time-dependent, thus not known before the ionisation balance has beeen solved completely.
But the situation is slightly more complicated. If the plasma is not (nearly) completely ionised, then for
normal abundances there must be a considerable population of neutral Hydrogen or Helium. But in that
case charge exchange reactions become important, and should be taken into account in the transition
matrix. This however is impossible to incorporate in the KJ method, since in this case there are 3 free
parameters (ne/nH, ne/nHe and T ) instead of 1 (T ), and storage of matrices etc. becomes physically
impossible. Knowing that the method of KJ becomes inaccurate for low ionisation rates we decided to
leave the prescribed nH concept and return to the prescribed ne concept. This has the advantage that
the equations for the ionisation balance of each chemical element can be calculated independently from
the other elements; KJ need to calculate the concentrations of all elements for each time step in order to
determine the conversion from Hydrogen to electron density.
Another rationale behind the above-mentioned modification is the following. For self-similar supernova
remnants, a class of problems where non-equilibrium ionisation applies, the hydrodynamics is inconsistent
with a time- or place varying electron/Hydrogen ratio: that would introduce another scale length and
destroy the assumptions behind self-similarity. Thus, for SNR models it is necessary to assume that the
plasma is (almost) completely ionised in order to assure self-consistency. We will neglect small changes
in the electron/Hydrogen ratio of SNRs therefore.
The second modification concerns the temperature grid. Contrary to KJ, we use a keV grid instead of
a K grid. Further, since we now include 30 chemical elements instead of 15, we had to reduce the step
size h of the grid from 0.05 in log T to 0.10, in order not to get disk storage problems. This change
however is compensated by a better interpolation technique used here. KJ just rounded all temperatures
to the nearest grid point. Here we interpolate the calculated concentrations between two temperature
grid points linearly, which is one order of magnitude (h) better. A rough estimate learns that the error
in the method of KJ per decade is nh2
which gives for n = 1/h an error of order 0.05, while the current
116 More about spectral models
implementation has typical errors per decade of nh3
which gives a typical error of 0.01 per decade.
5.5 Non-thermal electron distributions
In the current version of SPEX it is possible to include the effects of non-thermal (NT) electron distributions.
Such NT distributions affect the spectrum in two ways: by changing the ionization balance and
the emitted spectrum. Currently we take both effects into account for all our plasma models. The only
exception is the NEI model, for non-equilibrium ionisation. The way we calculate the ionisation balance
does not allow us to include the NT effects in the ionisation balance, but we do take it into account in
the spectrum.
The way we implemented it is as follows. Our atomic data (like collision strengths) are all parameterized
in a way that allow for analytical integration over simple electron distributions like delta-functions,
Maxwellians or power laws. But there are other processes like radiative recombination where such an
analytical approach fails. However, one way or the other, we use expressions for Maxwellian-averaged
rates in all our calculations. In principle, it is possible to decompose any electron distribution as a linear
combination of Maxwellians. The total rate, for example a recombination rate, is then the sum of the
rates caused by the individual Maxwellian components.
Therefore, in all our rate calcualtions we build the total rate based upon such a linear combination of
Maxwellians. This is done for all relevant processes (ionization, recombination, excitation, etc.)
In all our thermal models, there is an ascii-parameter called ”file”; if this value is defined (i.e. when a file
name of an existing file is entered), it will read the parameters of the Maxwellians from an ascii-file with
that filename. If there is not such a file, or if the filename is reset by entering the ”par file aval none”
command, no file will be taken into account (i.e., we have a simple, single Maxwellian again).
The (ascii) file should have the following format. On the first line, the number of Maxwellians is given.
Then for each Maxwellian there is a separate line containing two numbers: the first number is the
temperature of the Maxwellian, in units of the main temperature of the plasma; the second number is
the total number of electrons in this Maxwellian, relative to the main component. It is wise to have the
parameters of the main component as the first line of this list.
Let us give an example. Suppose we have a plasma with three components: 2, 20 and 200 keV
Maxwellians, with electron densities of 3000, 300 and 30 m−3
, respectively. In this case the parameters
of the cie model should be: temperature 2 keV, electron density 3000 m−3
, and the corresponding
file should be as follows:
3
1 1
10 0.1
100 0.01
The first line tells us that there are three Maxwellians. The second line contains the parameters of the
first Maxwellian, that we scale here to 1 1 (it is the one with temperature 2 keV and electron density
3000 m−3
). The third lines contain the second Maxwellian, which has a 10 times higher temperature
but also a 10 times lower electron density as the first component. Finally, the fourth line contains the
parameters of the third Maxwellian, which has a 100 times higher temperature and a 100 times lower
electron density as the first component.
Warning: Note that you can give your ascii-file any name, except of course the name ”none”, which
is reserved for resetting the file name.
Warning: Note that both numbers for each Maxwellian must be positive, i.e. positive temperatures and
electron densities.
5.6 Supernova remnant (SNR) models 117
5.6 Supernova remnant (SNR) models
For the calculation of SNR models we follow Kaastra & Jansen (1993). But also here we make some
modifications in the implementation.
The X-ray spectrum of a SNR is characterised in lowest order by its average temperature T , ionisation
parameter U and emission measure Y . If one calculates a specific model however, these average values
are not known a priori. A relevant set of input parameters could be the interstellar density, the shock
radius and the explosion energy. These are the parameters used by KJ. A disadvantage is that this
choice is not suitable for spectral fitting: changing one of the parameters gives correlated changes in T ,
U and Y , which is an undesirable feature in spectral fitting. KJ solved this by inputting a guess of T ,
U, and Y and using these guess parameters as the fitting parameters. After fitting, the model had to
be calculated another time in order to find the relation between guessed and true parameters. here we
take another choice. We will select input parameters which scale with T , U and Y respectively but are
connected to the SNR parameters independent of the hydrodynamical model. The first parameter is the
shock temperature
Ts, (5.7)
the second the shock ionisation parameter defined by
Us ≡ net (5.8)
where ne is the electron density before the shock (for a completely ionised gas), and t the age of the
remnant. Further we define the shock reduced emission measure by
Ys ≡ nenHr3
s/d2
(5.9)
where rs is the main shock radius, and d the distance to the source. We have introduced here also the
electron density ne instead of the more natural Hydrogen density, because this allows an efficient use of
the model for spectral fitting: if one fits a spectrum with variable chemical abundances, then using the
current scaling we need to calculate (for a given Ts, Us and Ys) the relative ion concentrations only once;
for other abundances, the relative concentrations may be simply scaled without a need to redo completely
the ionisation balance calculations. Finally we introduced the distance in the definition of Ys in order to
allow an easy comparison with spectra observed at earth. These 3 input parameters Ts, Us and Ys will
serve as input parameters for all hydrodynamical models. They are linked to other parameters as follows:
fpkTs = fTǫρmpr2
s/t2
(5.10)
where ǫρ is a dimensionless factor representing the average mass in units of a proton mass per Hydrogen
atom (ρ = ǫρmpnH with mp the proton mass), and fp is another dimensionless factor, representing
the ratio of electron plus ion density over the Hydrogen density. Further, fT is a model-dependent
dimensionless scaling factor which is given by
fT =
f2
v
η − 1
(5.11)
with fv the velocity scaling discussed below and η the density jump at the main shock front, which
depends upon the Hydrodynamical model. Another scaling law links the gas velocity to the temperature:
v2 = fvrs/t (5.12)
with v2 the post-shock gas velocity (not to be confused with the shock velocity!). The velocity scaling
factor is given by
118 More about spectral models
fv ≡
(n − 3)(η − 1)
(n − s)η
(5.13)
with the understatement that for the Sedov and Solinger model one should take formally the limit n = 5.
The explosion energy E0 is linked to the other parameters by
E0 =
αr5
s ρ
t2
, (5.14)
where α is the dimensionless energy integral introduced by Sedov. The value of α depends both upon
the hydrodynamical model and the value for s and n, the density gradient scale heights of the interstellar
medium and the stellar ejecta.
If we express Ts in keV, Us in 1020
m−3
s, Ys in 1020
m−5
, rs in units of 108
m, nH in 1020
m−3
, d in
units of 1022
m and t in s, we obtain from (5.10) the value for the proton mass of mp = 1.043969 ×
105
keVs2
(1016
m2
)−1
. Using this value and defining fm = fT ǫρmp/fp, the scaling laws for SNRs may be
written as
ne =
T 1.5
s U3
s
f1.5
m Ysd2
(5.15)
t =
f1.5
m Ysd2
ne
T 1.5
s U2
s nH
(5.16)
r =
fmYsd2
ne
U2
s TsnH
(5.17)
v =
fvT 0.5
s
f0.5
m
(5.18)
E0 = [1.6726231 × 1033
J]
αǫρf0.5
m Y 2
s d4
ne
U3
s T 0.5
s nH
(5.19)
M = [8.409 × 10−14
M⊙]
ǫρβηf1.5
m Y 2
s d4
ne
U3
s T 1.5
s nH
(5.20)
where M is the mass integral, and β is the dimensionless mass integral (defined by β = 4π ρ
ρs
r
rs
2
d r
rs
).
Chapter 6
More about plotting
6.1 Plot devices
The following devices are available (may depend somewhat on your local operating system, i.e. the
allowed devices in your local pgplot installation):
1. null : Null device (no output)
2. xwin : Workstations running X Window System
3. xser : Persistent window on X Window System
4. ps : PostScript printers, monochrome, landscape
5. vps : Postscript printers, monochrome, portrait
6. cps : PostScript printers, color, landscape
7. vcps : PostScript printers, color, portrait
8. gif : GIF-format file, landscape
9. vgif : GIF-format file, portrait
Warning: Note that when you enter the device name in SPEX you do not need to enter the leading
shlash; this is only required in other applications using the pgplot library.
6.2 Plot types
There are several plot types available in SPEX. below we list them together with the acronym that should
be used when defining this plot type (in a ”plot type” command).
• data – a spectrum observed with an instrument plus optionally the folded (predicted) model spectrum
and/or the subtracted background spectrum.
• model – the model spectrum, not convolved by any instrumental profile
• area – the effective area of the instrument. If the response matrix of the instrument contains more
components, also the contribution of each component is plotted separately.
• fwhm – the peak energy of the response matrix (as the model) as well as the FWHM limits (as
the data) are plotted. The FWHM limits are the energies at which the response reaches half of its
maximum value. If for the y-axis the option ”de/e” is chosen, all calculated energies are divided
by the energy of the incoming photon.
120 More about plotting
Table 6.1: Available plot colours.
Value Colour
00 Black (background)
01 White (default)
02 Red
03 Green
04 Blue
05 Cyan (Green + Blue)
06 Magenta (Red + Blue)
07 Yellow (Red + Green)
08 Orange (Red + Yellow)
09 Green + Yellow
10 Green + Cyan
11 Blue + Cyan
12 Blue + Magenta
13 Red + Magenta
14 Dark Gray
15 Light Gray
• chi – the fit residuals, either expressed in units such as counts/s or the same units as the spectrum,
or expressed in terms of numer of standard deviations, or as a relative error.
• dem – a differential emission measure distribution).
6.3 Plot colours
Table 6.1 lists the plot colours that are available. See also Fig. 6.3.
6.4 Plot line types
When drawing lines, the following line types are possible:
1. -------------
2. - - - - - - -
3. .-.-.-.-.-.-.
4. .............
5. -..-..-..-..The
first is the default value.
Further, the user can specify the thickness of the lines. Default value is 1, larger values give thicker lines.
Maximum value is 200. Recommended value for papers: use line weight 3. For an example of different
line weights, see also Fig. 6.4.
6.5 Plot text 121
Figure 6.1: Plot colours available with pgplot. Note that on a hardcopy colour 1 is black and
the background (colour 0) is white, while on most terminal screens colour 0 is balck and colour
1 is white.
6.5 Plot text
In SPEX it is possible to draw text strings on the plot surface or near the frame of the plot. Several
properties of the text can be adjusted, like the fontheight, font type, colour, orientation and location of
the text. See Fig. 6.5.1 for an example of possible fonts.
6.5.1 Font types (font)
The following fonts types are allowed (values between 1–4):
1. normal font (default)
2. roman font
3. italic font
4. script font
6.5.2 Font heights (fh)
The font height can be entered as a real number, the default value is 1. A useful value for getting results
that are still readable for publications is 1.3. Note that if you make the font height for the captions of
the figure too large, you may loose some text off the paper.
6.5.3 Special characters
The texts strings that are plotted may be modified using the pgplot escape sequences. These are
character–sequences that are not plotted, but are interpreted as instructions to change the font, draw
superscripts or subscripts, draw non-ASCII characters, Greek letters, etc. All escape sequences start with
122 More about plotting
Figure 6.2: Example of different line weights.
a backslash character (\). A list of the defined escape sequences is given in tab. 6.2. A lookup table for
Greek letters is presented in tab. 6.3. Some useful non-ASCII characters are listed in tab. 6.4. Fig. 6.4
shows some examples of the use of pgplot escape sequences in character strings.
6.6 Plot captions
Spex has a set of captions defined for each plot. The properties of these captions as well as the text can
be modified by the user. For the properties (font types etc.) see Sect. 6.5.
The following captions exist:
• x : the x-axis, plotted below the frame
• y : the y-axis, plotted left from the frame
• z : the z-axis (for contour plots and images), plotted at the upper left edge of the frame
• ut : the upper title text, plotted in the middle above the frame
6.6 Plot captions 123
Table 6.2: A list of available escape sequences.
Seq. description
\u start a superscript or end a subscript. A \u must be
ended by a \d!
\d start a subscript or end a superscript. A \d must be
ended by a \u!
\\ backspace (i.e. do not advance textpointer after plotting
the previous character)
\A ˚Angstrom symbol (˚A)
\gx greek letter corresponding to roman letter x
\fn switch to Normal font
\fr switch to Roman font
\fi switch to Italic font
\fs switch to Script font
\(n) character number n, see pgplot manual appendix B,
tab. 1
Table 6.3: List of upper- and lower case Greek letters (G) and their corresponding Roman letters
(R).
R : A B G D E Z Y H I K L M N C O P R S T U F X Q W
G : A B Γ ∆ E Z H Θ I K Λ M N Ξ O Π P Σ T Υ Φ X Ψ Ω
R : a b g d e z y h i k l m n c o p r s t u f x q w
G : α β γ δ ǫ ζ η θ ι κ λ µ ν ξ o π ρ σ τ v φ χ ψ ω
Table 6.4: Some useful non-ASCII character sequences.
∼ 2248 ± 2233 ∇ 0583
≈ 0248 ∓ 2234
√
2267
∼= 0250 × 2235 2268
∝ 2245 ÷ 2237 2269
= 2239 ≡ 2240 ∞ 2270
<
= 2243 † 2277 ∂ 2286
>
= 2244 ‡ 2278 ⊙ 2281
124 More about plotting
Figure 6.3: Example of different fonts.
• lt : the lower title text, plotted between the upper title text and the frame
• id : the plot identification, plotted to the upper right corner of the frame (usually contains the
SPEX version and time and date).
With the ”plot cap” series of commands, the text, appearance and position of all these captions can be
modified.
6.7 Plot symbols
When plotting data, the data can be labeled with different symbols as indicated in Fig. 6.7.
6.8 Plot axis units and scales
6.8.1 Plot axis units
Different units can be chosen for the quantities that are plotted. Which units are available depends upon
the plot type that is used, for example an observed spectrum (data), a Differential Emission Measure
6.8 Plot axis units and scales 125
Displayed pgplot escape sequence
f(x) = x2 cos(2πx) \fif(x) = x\u2\d \frcos\fi(\fr2\fi\gpx)
H0 = 75 ± 25 km s−1 Mpc−1 \fiH\d0\u\fr = 75 \(2233) 25 km s\u-1\d Mpc\u-1\d
L/L⊙ = 5.6 (λ1216˚A) \fsL/L\fr\d\(2281)\u = 5.6 (\gl1216\A)
Figure 6.4: Some examples of the use of pgplot escape sequences.
Figure 6.5: Plot symbols that are available.
distribution (DEM) etc. For the availabe plot types see Sect. 6.2.
Note also that depending upon the plot type, there are two or three axes available, the x-axis, y-axis and
z-axis. The last axis is only used for contour maps or images, and corresponds to the quantity that is
being plotted in the contours or image.
The units that are allowed for the x-axis are listed in Tables 6.5–6.6, and for the y-axis in Tables 6.7–6.12.
126 More about plotting
Note: when using the velocity scale, negative values correspond to a blueshift, positive values to a redshift.
Also note that in this case one needs to provide the reference energy or wavelength.
Warning: For the plot type data option, there are options (starting with ”f”) that are essentially
counts m−2
. In these cases, the observed count rates (counts/s/keV for instance) are divided by the
nominal effective area at the relevant energy. This nominal effective area is determined for a flat input
spectrum, and is defined as the ratio of predicted count rate and model spectrum flux. Response parts
below 0.75 times the original photon energy are ignored in the estimation of the predicted count rate,
in an attempt to remove higher order spectral lines. Note however that if your spectrum really contains
significant higher order lines, you cannot remove these from your plot. Also beware of end-effects. If you
want to see the underlying model, it is often better to select the plot type model!
6.8.2 Plot axis scales
The axes in a plot can be plot in different ways, either linear or logarithmic.
For the y-axis we also have made an option for a mixed linear and logarithmic scale. The lower part of
the plot will be on a linear scale, the upper part on a logarithmic scale. This option is useful for example
for plotting a background-subtracted spectrum. Often there are bins with a low count rate which scatter
around zero after background suntraction; for those channels a linear plot is most suited as a logarithmic
scaling cannot deal with negative numbers. On the other hand, other parts of the spectrum may have
a high count rate, on various intemsity scales, and in that case a logarithmic representation might be
optimal. The mixed scaling allows the user to choose below which y-value the plot will be linear, and
also which fraction of the plotting surface the linear part will occupy. For an example see Fig. 6.8.2.
Figure 6.6: Example of the mixed y-axis scale. Simulation of a Chandra LETGS spectrum for
a thermal plasma with a temperature of 1 keV.
6.8 Plot axis units and scales 127
Table 6.5: x-axis units for plot type model, data, chi, area, fwhm and spec:
bin Bin number
kev keV (kilo-electronvolt), default value
ev eV (electronvolt)
ryd Rydberg units
hz Hertz
ang ˚A (˚Angstrom)
nm nm (nanometer)
vel km s−1
Table 6.6: x-axis units for plot type dem:
bin Bin number
kev keV (kilo-electronvolt), default value
ev eV (electronvolt)
ryd Rydberg units
k K (Kelvin)
mk MK (Mega-Kelvin)
Table 6.7: y-axis units for plot type model, spec:
Photon numbers:
cou Photons m−2 s−1 bin−1
kev Photons m−2 s−1 keV−1 (default value)
ev Photons m−2 s−1 eV−1
ryd Photons m−2 s−1 Ryd−1
hz Photons m−2 s−1 Hz−1
ang Photons m−2 s−1 ˚A−1
nm Photons m−2 s−1 nm−1
Energy units:
wkev W m−2 keV−1
wev W m−2 eV−1
wryd W m−2 Ryd−1
whz W m−2 Hz−1
wang W m−2 ˚A−1
wnm W m−2 nm−1
jans Jansky (10−26 W m−2 Hz−1
νFν units:
iw W m−2
ij Jansky Hz (10−26 W m−2)
Various:
bin Bin number
128 More about plotting
Table 6.8: y-axis units for plot type data:
bin Bin number
cou Counts
cs Counts s−1
kev Counts s−1 keV−1 (default value)
ev Counts s−1 eV−1
ryd Counts s−1 Ryd−1
hz Counts s−1 Hz−1
ang Counts s−1 ˚A−1
nm Counts s−1 nm−1
fkev Counts m−2 s−1 keV−1
fev Counts m−2 s−1 eV−1
fryd Counts m−2 s−1 Ryd−1
fhz Counts m−2 s−1 Hz−1
fang Counts m−2 s−1 ˚A−1
fnm Counts m−2 s−1 nm−1
Table 6.9: y-axis units for plot type chi:
bin Bin number
cou Counts
cs Counts s−1
kev Counts s−1 keV−1 (default value)
ev Counts s−1 eV−1
ryd Counts s−1 Ryd−1
hz Counts s−1 Hz−1
ang Counts s−1 ˚A−1
nm Counts s−1 nm−1
fkev Counts m−2 s−1 keV−1
fev Counts m−2 s−1 eV−1
fryd Counts m−2 s−1 Ryd−1
fhz Counts m−2 s−1 Hz−1
fang Counts m−2 s−1 ˚A−1
fnm Counts m−2 s−1 nm−1
dchi (Observed - Model) / Error (default)
rel (Observed - Model) / Model
Table 6.10: y-axis units for plot type area:
bin Bin number
m2 m2 (default)
cm2 cm2
6.8 Plot axis units and scales 129
Table 6.11: y-axis units for plot type fwhm:
bin Bin number
kev keV (kilo-electronvolt), default value
ev eV (electronvolt)
ryd Rydberg units
hz Hertz
ang ˚A (˚Angstrom)
nm nm (nanometer)
de/e ∆E/E
Table 6.12: y-axis units for plot type dem: the emission measure Y is defined as Y ≡ nenHV
and is expressed in units of 1064 m−3. Here ne is the electron density, ne is the Hydrogen density
and V the emitting volume.
bin Bin number
em Y (default)
demk dY/dT, per keV
demd dY/dT, per K
130 More about plotting
Chapter 7
Auxilary programs
7.1 Trafo
Program trafo allows you to transform spectra and response matrices from standard OGIP format (or
from SPEX version 1 format) to the format used by SPEX. It also gives you some options to combine
data sets for simultaneous spectral fitting, and to optimses the spectral data set for speed, We discuss
here first the different file formats, and then explain the use of trafo.
Some theoretical background and technical details on the SPEX file format are given in Chapter 8 and
we refer the interested reader to that chapter for full details. Here we summarise some of the basics.
The basic philosophy behind the SPEX file format is:
keep things as simple as possible unless there is absolutely no alternative.
Therefore, SPEX uses one file containing all the information on the spectrum, including subtracted
background, that must have the extension .spo and has FITS format with well-defined extensions and
columns. Also, there is only a single file containing all the information on the response matrix, including
effective area information, that must have the extension .res and also has FITS format with well-defined
extensions and columns.
Trafo always produces the .spo and the .res files at the same time, as both are linked together tightly.
Examples of the usage of trafo can be found in the SPEX Cookbook, which is available on the SPEX
website: http://www.sron.nl/spex
7.1.1 File formats spectra
There are a number of differences between OGIP and SPEX spectral file formats. The OGIP format
has been documented at http://heasarc.gsfc.nasa.gov /docs /heasarc /ofwg /docs /spectra /ogip 92 007
/ogip 92 007.html.
In Table 7.1 we show the difference in structure between the OGIP spectral file format and the format
used by SPEX. In addition to that, we make the following remarks.
For the energy grids, only energy (keV) units are allowed (not wavelength units), as there is a one-toone
relation between both. This number should be in double precision: for high-resolution spectra the
difference between upper- and lower energy can be small, and close enough to the machine precision for
single precision to cause some annoying numerical problems.
In the error column, it is essential to give real Poissonian errors (in case the spectrum is based on counts),
and the use of e.g. Gehrels statistics must be avoided; in those cases, it is better to calculate the formal
errors just from the square root of the number of raw counts. Chandra grating spectra are sometimes
delivered with Gehrels errors, but this gives problems when the data need to be re-binned, and this is
132 Auxilary programs
Table 7.1: Differences between OGIP and SPEX in spectral file structure
Property OGIP SPEX
Spectrum:
Files Separate files for source & optionally
background and correction file
One file for all
Channel 2-byte or 4-byte column in spectral
file
Not used (should be by definition the
row number of the table, starting to
count at 1 without gaps)
Bin boundaries Real, but not in spectral file but in
ebounds extension matrix
Double precision (for high-res spectra),
and in spectral file
Data Counts (2-byte or 4-byte integer) or
count rate (real, in counts s−1)
Only count rate (real, in counts s−1)
Errors Either explicitly given, or calculated
using Poissonian statistics if poiserr
keyword is given
Always explicitly given
Exposure (s) One value for full spectrum Can differ for each bin
Background Unscaled value in separate file;
needs backscal keyword or column
in source & background file to determine
scaling for source region
Background subtracted value in
one column; subtracted background
(and its statistical error) in other
columns
Quality flag 2-byte integer with 4 different values
(0=good, 1=bad by s/w, 2=dubious
by s/w, 5=set bad by user
”no-nonsense” logical, bin is either
to be used (true) or not (false)
Grouping 2-byte integer, +1 for start channel,
−1 for continuation bin, 0 if no
grouping defined
Two logicals: true/false is bin is
first/last of a group (i.e., for no
grouping, both are true)
Area scaling Areascal keyword or column Not allowed (can be handled with
exposure time or response matrix)
Background
scaling
Backscal keyword or column Worked out through explicit background
subtraction in the spectrum
Systematic
error
Keyword or column sys err in both
source & background files
Two columns: one for fraction of
source, one for fraction of back-
ground
7.1 Trafo 133
usually the case as the Chandra-data are delivered over-sampled. Also, never use 90 % errors, but always
r.m.s. (”1σ”) errors.
For the same reasons, the use of systematic errors should be avoided in the spectral file, because after
rebinning they would become smaller. It is better to use no systematic errors in the spectral file, but in
case you really need them, within SPEX you can set them after you have done the proper binning.
Also the use of quality flags should be avoided. It is better to provide the user either with only ”good”
data, or to make the user aware of any systematic limitations of the dats. When needed (either for
instrumental or astrophysical reasons), within SPEX it is possible to ignore data ranges.
The usefulness of the areascal keywords is not very clear; the XMM-Newton RGS software uses the arescal
for some dead-time corrections, but SPEX solves this in a more elegant way by allowing the exposure
time to be different for each data bin. Whenever trafo encounters the arescal, it uses it to adjust the
exposure time per bin. If you give the ”show data” command in SPEX, you see for each data set some
statistics, including mean, minimum and maximum exposure time per bin.
Finally, OGIP uses three columns (the background count rate, and the backscal for the source and
background region) to determine the background that needs to be subtracted. In SPEX this reduces to
two columns containing essentially the same information, namely the scaled background count rate and
its statistical error. Actually, what is important in this is only the ratio of the backscal columns, not
their individual values.
In summary, whenever possible we recommend to use only the first seven columns (bin boundaries,
exposure time, source and background count rates with their errors), and leave the other columns empty
/ default (first/last channel flags, used, systematic errors).
7.1.2 File formats responses
The OGIP standard is described in https://heasarc.gsfc.nasa.gov /docs /heasarc /caldb /docs /memos
/cal gen 92 002 /cal gen 92 002.html.
In Table 7.2 we show the difference in structure between the OGIP response file format and the format
used by SPEX.
7.1.3 Multiple spectra
With trafo, you can combine different datasets into one combined spectrum and response file. There can
be various reasons to do so:
1. You may want to combine different, similar instruments from the same observation (e.g. RGS1 and
RGS2) or different spectral orders (e.g. RGS1 −1 and RGS1 −2 spectral order), or even combine
pn with RGS. However, in these cases you may prefer to have the spectra in separate files, as that
allows you easier to use only part of the data.
2. You may have time-resolved spectra of the same source taken with the same instrument
3. You may have multiple spatial regions of the same source, observed with the same instruments.
For more info, we refer to Sect. 2.2. Trafo allows you to achieve this.
7.1.4 How to use trafo
Trafo is an interactive program. It asks a few questions, which are usually self-explanatory. However,
here we give a brief overview.
1. The first question trafo asks if you want to transform data from OGIP format (option 1), the now
abandoned SPEX version 1 binary format (option 2) or the new SPEX format (option 3).
134 Auxilary programs
Table 7.2: Differences between OGIP and SPEX in response matrix structure
Property OGIP SPEX
Response:
Files Separate files for response (.rmf) &
ancillary response file (.arf)
One file for all
Rmf exten-
sion:
Components 1 component only Matrix may have multiple compo-
nents
Energy grid One grid for the matrix, single pre-
cision
Each component can have its own
grid, double precision
Response
groups (≡
contiguous row
of non-zero
matrix elements
for the same
energy)
Multiple groups per row; specify
number of groups (2-byte), first
channel & number of channels (2byte
or 4-byte) and the matrix elements
for each group
In extension ”spex resp group”
specify bin lower and upper energy,
first channel, last channel and
number of channels for the group; in
extension ”spex resp resp give the
matrix elements
Optimalisation No Matrix may also contain derivatives
of the matrix with respect to photon
energy
Ebounds ex-
tension:
Channel ener-
gies
Single precision Not here, but in spectral file and
double precision
Arf extension:
Columns Contains lower, upper energy and
area (in cm2)
N/A (included in matrix; but note
units are SI, i.e. m2)
7.1 Trafo 135
2. The next question is how many spectra you want to transform. Usually you will enter here the
number 1, but if you want to create concantinated spectra (see previous section) you should enter
here the number of spectra. In that case, the next questions will be repeated for each spectrum.
3. Now you are asked to enter the maximum number of response groups per energy per spectrum.
This is needed in order to allocate scratch memory; for almost any ”sane” spectrum that we have
seen sofar, a large number like 10000 is always sufficent here. Anyway, trafo will warn you and quit
whenever you will reach this limit.
4. Optional: for multiple spectra, you are asked how many sectors you want to create. See the
description in Sect. 2.2 for more info on sectors and regions.
5. Optional: if you have more than 1 spectrum, trafo asks you to enter the sector and region number
that you want to assign to the spectrum that you will enter next. If The sector or region number
are out of the allowed range as specified before, trafo will keep repeating this question until you
have entered valid numbers.
6. Next a question is asked about partitioning of the matrix. You have here basically three options.
Option 1: keep the structure of the matrix essentially as provided by the software package that
created the OGIP files. The SPEX matrix will have 1 component, with no re-arrangements. Option
2: rearrange the matrix into contiguous groups. Your matrix may have been splitted into multiple
regions, and for one photon energy you might have multiple regions (for instance, higher spectral
orders for grating spectrometers without energy-sensitive detectors like the LETG/HRC-S or EUVE
spectrometers); or a main diagonal and a fluorescence component, etc. Trafo will attempt to sort
your response matrix accrding to these physically distinct components, by checking if for a given
energy a response group has overlap in energy with an already existing group. Option 3: split
into N roughly equal-sized components. This option is recommended for large matrices of highresolution
instruments such as RGS. It allows for the optimal usage of multiple processors during
spectral fitting, provided your machine has of course more than one processor.
Note that if you combine spectra that are already in SPEX version 2.0 or higher format, you do
not have this option because we assume you have already optimised your matrix when creating the
original version 2.0 files.
7. Optional: if you have selected option 3 above, trafo ask you the number of components. This can
be any number, but experience has shown that a power of 2, typically between 8 and 32 works best
(even on dual core processors).
8. Now you must enter the file name of the OGIP-type spectrum. Alternatively, if you combine SPEX
version 2.0 files, you are prompted for the .spo file and you do not need to answer some of the
questions below.
9. If the OGIP spectral file does not provide you the name of a background spectrum, you are
prompted if you want to subtract a background spectrum. Be aware that sometimes background
subtraction has already been taken into account in OGIP-spectra. Check carefully. If you answer
”yes” to this question, then trafo will ask you for the filename of the background file.
10. In a few rare cases (e.g. Einstein SSS data), there is a second background file needed, the so-called
”correction file”. If such a file is to be used, tarfo will read it but it must be indicated then as the
corfil extension in the spectral file.
for each file
11. Trafo now makes a few sanity checks. If there is some problem, trafo will report it and stop. It
checks for the same number of data channels in source and background (or correction) file. Further,
and this is important to know, data bins that are being qualified as ”bad” in the background or
correction files, but ”good” in the source file, will end up as ”bad” bins in the final, background
subtracted spectrum.
136 Auxilary programs
12. Trafo reports the total number of bad channels. You now can decide if you want to ignore the bad
channels. Default is no (keep data; why would you otherwise have taken the burden to keep them
in your datasets), but if you answer ”yes”, the bad channels will be ignored by trafo (well, flaged
as not to be used in the .spo file).
13. Optional: if the OGIP-spectrum contains grouping information, trafo asks if that grouping should
be used or ignored in the final spectrum.
14. Optional: if there is no response matrix file specified in the spectral pha-file, trafo asks for the
name of the matrix.
15. Optional: while reading the response matrix, trafo makes some sanity checks. For instance, if the
lower bin boundary of an energy bin is not smaller than the upper bin boundary, the user can
correct this manually (some matrices are provided erroneously with zero width bins). But be sure
that you understand here whjat you are doing!
16. Optional: also, some instruments assign an energy 0 to the lower energy boundary of the first bin.
SPEX does not like this (as it gives trouble if you convert to a wavelength scale, for instance), so
you can change the lower boundary manually to a small, non-zero number here.
17. Optional: in a few rare cases, matrices/data are poorly designed, such that the spectrum starts
with a channel 0, but the matrix starts with channel 1. It is then not always clear which spectral
element corresponds to which response element. Trafo tests for occurrences where the ”flchan”
keyword in the matrix equals 1, but the first channel in the data is 0. In this case it is possible
to shift the response array by 1 channel, although this should be done as a last resort, and needs
careefull checking if no mistakes are made! Trafo also tests for occurrences where the ”flchan”
keyword in the matrix does not equal 1 (usually 0), but the first channel in the data is 0. In this
case it is advisable and possible to shift the response array by 1 channel, but again care should be
taken!
18. Optional: if there is no ancillary (effective area) file specified in the spectrum, trafo reports this
and asks if the user wants to use such an arf-file nevertheless. Default is ”no”, but if ”yes” is
entered, the name of the arf-file is prompted for.
19. As a next step, model energy bins with zero effective area are deleted from the file. Such bins
usually occur at the low and high-energy side of the matrix. Deleting them saves computing time.
Further, any necessary rebinning (if indicated by the grouping falgs) is done.
20. Trafo will tell you how many components it has found or created. It now asks you if you want to
apply a shift to your spectra. Usually you should enter here 0. Useful cases to enter a non-zero
shift s are situations where for instance your energy or wavelength scale is not yet sufficiently well
calibrated. trafo then in that case puts the data of bin nr k + s into bin s.
21. Trafo reports if the spectrum and matrix will be swapped (in case the original OGIP data were in
wavelength order). Remember that SPEX always uses energy order.
22. The pre-last question is the filename for the spectrum that has been created (without the .spo
extension, that trafo will add automatically).
23. Finally the filename for the response matrix that has been created is asked (without the .res
extension, that trafo will add automatically).
7.2 Xabsinput
For the xabs and warm models, an input file is needed that contains the temperature and ionic column
densities as a function of the ionisation parameter ξ. The standard input file provided by SPEX is based
on a run with an older version of Cloudy, using the spectral energy distribution of NGC 5548 as used in
Steenbrugge et al. (2005a).
7.2 Xabsinput 137
The present program xabsinput allows the user to create such a file. The user basically needs to provide the
following information, discussed in more detail below: spectral energy distribution (SED), abundances,
root directory, and how to call Cloudy.
The SED should be provided in an ascii-file with two columns. The first column gives the energy in
Rydberg units (note these units!), and the second column gives the spectral energy distribution in terms
of E dN/dE (for instance, in units of keV m−2
s−1
keV−1
or Ryd m−2
s−1
Ryd−1
, or Jansky, etc. Note
that the absolute normalisation of the SED does not matter here, only the shape is used, so therefore all
these units can be used as long as it corresponds to energy per area per time per unit energy.
Warning: In order to have a sufficiently broad energy band, xabsinput adds a value of 10−10
at energies
of 10−8
and 109
Ryd. Take care that the SED scaling would essentially imply 10−10
to be a very small
value. Also, the energies in the file should be in increasing order, and within the 10−8
and 109
Ryd
interval.
Default abundances are presently the Lodders et al. (2009) proto-Solar values, presently the default of
SPEX.
Warning: These default abundances are not equal to the default abundances of Cloudy
The user is prompted for a file that contains the abundances relative to these standard abundances. This
ascii files should have one line for each element with non-standard abundances. Each such line has two
numbers: the atomic number of the element and the abundance relative to standard (in linear units, i.e.
if you have iron two times solar, enter ”26 2.0”, without the quotes, of course). If all abundances are
standard, simply use an empty but existing file.
The user also should provide the name of a directory where the files that are calculated will be stored.
Basically, the following files will appear in this directory:
• a file ”run.in”, which contains the input file for Cloudy; at the end of the program, it contains the
input of the last Cloudy run (with the highest ξ).
• a file ”run.out”, which contains the output of Cloudy; at the end of the program, it contains the
output of the last Cloudy run (with the highest ξ).
• a file ”xabs inputfile”, which is the input file that you will need for the xabs and warm models of
SPEX; you can rename or move that file after finishing this program. The format of that file is
as follows: first part two columns (log ξ (in cgs, bah) and temperature (in eV); this is followed by
blocks for each ion from H i to Zn xxxi, with as first entry the nuclear charge and ionisation stage,
and then simply the logs of the column densities, scaled to 28 for hydrogen.
• ascii files named ”column01.dat”, ”column02.dat”, . . . ”column30.dat” containing for each element
with nuclear charge Z = 1 − 30 the ion concentrations as a function of ξ. SPEX does not need
those files, but it can be educative to look at them (or to plot using qdp). The format of those files
is log ξ, followed by the logs of the column densities for each ion (1 is neutral, 2 is singly ionised
etc). The column densities take account of the abundances and have, for practical reasons, been
scaled in such a way that Hydrogen has log column 10; values below 0 are cut-off to 0.
Finally, the user should provide the name of a script that runs Cloudy. At SRON, this is /opt/local/bin/cloudy,
and the script is given as:
#!/bin/csh -f
#
setenv CLOUDY_DATA_PATH /opt/local/HEA/cloudy/c13.01/data
setenv LD_LIBRARY_PATH
/opt/local/HEA/cloudy/c13.01/source/cloudy.exe < ${1}
Warning: We presently run Cloudy version 13. When newer versions of Cloudy become available, the
Cloudy input or output formats may change, and the present program would need updates.
Finally, our runs with Cloudy are done using the following default settings (apart from the SED and
abundances that are entered by the user):
138 Auxilary programs
• Hydrogen density small, i.e. 1014
m−3
(108
cm−3
)
• Column density small, i.e. 1020
m−2
(1016
cm−2
)
• Use the ”iterate to convergence” command of Cloudy
• Values of log ξ between −8.5 and +6.5 with steps of 0.1
Note that, depending on the computer used, thi program may run for several hours; during execution it
displays the present value of log ξ and the electron temperature in eV for each step of log ξ between −8.5
and +6.5.
Warning: We note that up to and including version 13.03 of Cloudy, Lion in the definition of ξ was
actually the total bolometric ionising luminosity. However, from the upcoming version 13.04 of Cloudy
this is corrected in the Cloudy code to be consistent with the commonly used definition, where Lion ranges
between 1 to 1000 Ryd. Thus, we recommend using the xabsinput program with Cloudy version 13.04.
7.3 RGS fluxcombine
Program RGS fluxcombine combines fluxed spectra, created by the XMM-Newton SAS task rgsfluxer. It
has two options:
1. Option 1: combine RGS spectra of the same detector and spectral order
2. Option 2: combine spectra of RGS1, RGS2 and first and second order of both (4 spectra) into one
spectrum.
This is not a trivial task, due to the presence of bad pixels, CCD gaps etc, that for each individual
spectrum can be slightly different, for instance because of the use of the multi-pointing mode (MPM) of
the RGS, so that the same bad pixel falls at a different wavelength for each individual spectrum, or due
to the transient nature of some bad pixels/columns.
We discuss both options separately. In general, if you have RGS data for multiple epochs of a source,
you may have to run this program first four times with option 1 (RGS1 and 2, orders 1 and 2), and then
run it ones with option 2 to get a single stacked RGS spectrum.
Warning: You must run the SAS task rgsfluxer with 3400 wavelength bins between 5–38 ˚A. Thus, do
not use the former β-bins!. Also, do not change these wavelength limits or number of bins.
The program needs an input file, basically telling it how many spectra should be combined, followed by
one line for each spectrum (fixed format, in fortran (F9.2,1X,A) for option 1), containing the exposure
time in s (unfortunately not contained in the output of rgsfluxer, but you can get it from the spectral
files) and the name of the relevant output file of rgsfluxer. For option 2 there are two additional numbers,
namely the RGS (1 or 2 for RGS1 and RGS2), and the spectral order (1 or 2 for first and second spectral
order), in such a way that the format is (I1,1X,I1,1X,F9.2,1X,A).
7.3.1 Option 1: combining RGS spectra of the same detector and spectral
order
It is important to realise that when data of a time-variable source are combined, artifacts due to missing
data (bad pixels) will arise. This can be simply illustrated by an example. Suppose that source X is
observed twice with RGS, with exactly the same exposure time, the first time with 100 counts/bin, the
second time with 20 counts/bin. Suppose that at wavelength bin j the first observation has a bad pixel,
hence no counts, while the second observation has no bad pixel at bin j. The averaged spectrum will
have (100+20)/2=60 counts per bin, except for bin j where the average value is (0+20)/2=10. Now since
both exposure times are the same, the model will predict 60 counts for all bins (as required), except for
bin j where it will predict 30 counts (the pixel is dead for half of the exposure). Thus, the model has
7.3 RGS fluxcombine 139
30 counts while the data have only 10 counts. An innocent observeer might therefore think there is an
absorption line at bin j taking awat 20 counts, but it is obvious that that is not true.
For this reason, when we combine spectra, we will weigh with the exposure time for all ”normal” bins,
but when in some of the datasets there is a bad pixel j, we will use a different procedure. In that case, we
look to the neighbouring pixels, and assume that the spectral shape in this local neighbourhoud remains
the same. From the neighbours with complete data we can estimate how much flux the spectra with good
data contribute to the total flux, and we use this fraction to estimate with what factor we should scale
the flux measured at pixel j in these good data sets, to obtain the best estimate of the flux at pixel j for
the total spectrum.
This procedure gives reliable results as long as the spectral shape does not change locally; as there is less
exposure at pixel j, only the error bar on the flux will be larger.
Warning: When there is reason to suspect that the bad pixel is at the location of a spectral line that
changes in equivalent width, this procedure cannot be applied!
To alleviate this problem, the user has to enter a minimum exposure fraction. If this value is zero, for
spectra with constant shape the best result is obtained. On the other hand, if this value is 1, only bins
will be included that have no bad pixel in any of the observations that are combined. Advantage in that
case is that there is no bias in the stacked spectrum, but a disadvantage may be that a significant part
of the spectrum may be lost near important diagnostic lines (in particular for the multi-pointing mode).
Due to the binning and randomisation procedures within the SAS task rgsfluxer, it is still possible that
despite careful screening on bad pixels, a few bad pixels remain in the fluxed spectrum, often adjacent
or close to discarded pixels. For this reason, the present program checks for any bins that are more
than 3σ below their right or left neighbouring bin (taking the statistical errors in both into account).
Typically, the algorithm finds a few additional bad pixels in an individual observation that is discarded
for combination.
The program further allows to apply two other corrections (both are done in the same step). The first
correction is an effective area correction. In very high signal to noise data, there are broadband flux
differences between RGS1 and RGS2 and first and second order spectra, in some parts of the spectrum,
at the few percent level. A simpel model has been produced to correct for this, in the sense that when
RGS1 and RGS2 are combined, the true spectrum is assumed to be the average of both. The correction
is based on the monitoring campaign on Mrk 509, taken in 2009, and is found to be consistent with a
large data set of Mrk 421 spectra that are present in the archive.
Local continuum fits to spectral bands that are poor of lines yield in general χ2
values that are too low.
This is an artifact of the SAS procedures related to the rebinning of the data. Data have to be binned
from the detector pixel grid to the fixed wavelength grid that we use in our analysis. The bin boundaries
of both grids do not match. As a consequence of this process, the natural Poissonian fluctuations on the
spectrum as a function of detector pixel are distributed over the wavelength bin coinciding most with
the detector pixel and its neighbours. In addition, there is a small smoothing effect caused by pointing
fluctuations of the satellite. Due to this tempering of the Poissonian fluctuations, chi2
values will be
lower for a ”perfect” spectral fit.
We have quantified the effect by fitting a linear model Fλ = a+bλ to fluxed spectra in relatively line-poor
spectral regions, in 1 ˚A wide bins in the 7–10, 17–18 and 35–38 ˚A ranges. The median reduced χ2
is
0.72, with a 67 % confidence range between 0.65 and 0.79.
The rebinning process conserves the number of counts, hence the nominal error bars (square root of the
number of counts) are properly determined. The lower reduced χ2
is caused by the smoothing effect on
the data. For correct inferences about the spectrum, such a bias in χ2
is not appropriate. As we cannot
change the observed flux values, we opt to multiply the nominal errors on the fluxes by (0.72) = 0.85,
in order to get get acceptable fits for ideal data and models.
140 Auxilary programs
7.3.2 Option 2: combine spectra of RGS1, RGS2 and first and second order
of both (4 spectra) into one spectrum
This procedure is similar to option 1, but with some differences.
No corrections for effective area or binning bias are allowed here, as this should be taken into account in
the steps that use option 1. In case there is only one observation, the present program can also be run
with only one spectrum for option 1, to get the efective area and binning corrections in.
Further, the spectra are not combined according to exposure time (that should be in general almost the
same for RGS1 and RGS2), but according to signal to noise ratio at each bin. Reason is that ofteh the
second order spectra have poorer statistics than the first order spectra, hence they should be weighted
less in the combined spectra.
Warning: Spectra created with rgsfluxcombine can only be fitted using χ2
statistics. C-statistics will
produce wrong values.
7.4 RGS fmat
Program RGS fmat produces a response matrix for a fluxed spectrum created by the XMM-Newton SAS
task rgsfluxer.
The user should provide an FITS file that is the output of the rgsfluxer program. That program must be
run with 3600 equidistant wavelength bins between 4 and 40 ˚A. The program takes this fluxed spectrum,
and creates a response matrix with effective area 1 m2
for each wavelength, and a redistribution function
normalised to unity for each wavelength.
This redistribution function is slightly different for RGS1 and RGS2, and also different for the second
order spectra. Hence, the user must provide RGS fmat the information about which RGS and spectral
order is used.
In addition, it is also possible to make a single response matrix for combined RGS1 and RGS2 data, first
and second order. In this case, first the program RGS fluxcombine must have been run with option=2.
That program then creates the rgsfluxer-compatible file, with the addition of four extra columns, containing
for each wavelength the relative weight of the different instrument/order to the total spectrum.
These weights are used to weigh the redistribution functions in the combined spectra.
The redistribution function has been parametrised as the sum of three (first order) or 4 (second order)
Gaussians, with wavelength-dependent width and relative normalisations. These parametrisations have
been obtained by fitting the ”true” redistribution function as it is in SAS in 2014 after having reinvestigated
the RGS line-spread-function by the RGS consortium.
The model energy grid used for the matrix has a uniform spacing of 1/9th of the instrumental FWHM,
approxinmated here simply by 0.06/|m|, where m is the spectral order. The matrix is fully SPEXcompatible,
in the sense that it also uses the derivatives of the matrix with respect to energy to get the
most accurate results. There is no way back from this to OGIP-typs spectra!
Warning: The redistribution function is limited to ±1 ˚A around the central wavelength. For most
continuum and absorption line spectra this is sufficient. In a few rare cases of very bright emission line
sources, the user is advised to compare the resulting fit with a direct fit using the original SAS response
matrices and spectral files.
The matrix is much smaller: the combined RGS matrix has a size of 8.2 Mbyte. This should be compared
to the total size of the four matrices in OGIP format, which is over 200 Mbyte.
7.5 Hydro driver
Some users run complex and computationally expensive hydrodynamical simulations, and want to be
able to calculate the corresponding X-ray spectrum. Without having to implement these hydro-codes
7.6 Rgsvprof 141
into SPEX it is now possible to do this.
For that purpose we offer the fortran90 subroutine hydro driver. The source code of that routine is
available in the SPEX distribution. Basically, it does the following:
1. It reads the needed parameters as subroutine arguments.
2. It does a few sanity checks (ion concentrations should be non-negative, and the total H i+H ii
column density must be 1.
3. It then creates a file called ”spexicon.dat” containing the ion concentrations.
4. It also creates a file called ”spexgrid.egr” containing the energy grid.
5. It then creates a file called ”spexdriver.com” that contains the commands to run SPEX in batch
mode.
6. This file is executed, and SPEX creates a file ”spexoutput.asc” containing the emitted spectrum.
7. SPEX terminates.
8. The subroutine reads the file ”spexoutput.asc” and puts the spectrum in the appropriate output
array of the subroutine.
The input arguments of the subroutine are as follows:
hden - The Hydrogen density in SPEX units of 1020
m−3
. Real number.
t - The electron temperature in keV. Real number.
it - The ion temperature in keV, used for line broadening. Real number.
vmic - The microturbulence velocity, in km s−1
, used for line broadening. Real number.
volume - The emitting volume, in SPEX units of 1024
m3
. Real number.
con(31,30) - Array with ion concentrations relative to hydrogen (number densities). The abundances
of the metals should be taken into account in this; thus, for example, for cosmic abundances, oxygen
has a number density of about 0.001 per hydrogen atom, hence the sum of all oxygen ion concentrations
should then be 0.001. The array con(jz,iz) contains for each element (labeled with atomic number iz,
H=1, He=2 etc.) the concentration; jz indicates the ionisation stage (1=I=neutral, 2=II=singly ionized,
etc.; do not forget to include the bare nucleus as the last one. Array elements with jz > iz + 1 will be
ignored. Note that as things are normalised to hydrogen, con(1, 1) + con(2, 1) = 1 is obligatory! Real
array.
neg - Number of energy bins. Integer number.
eg(0:neg) - Energy bin boundaries in keV; the boundaries of the first bin are stored in eg(0) and eg(1);
the second bin in eg(1) and eg(2); etc. Real array.
The output arguments of the subroutine are as follows:
spec(neg) - The emitted spectrum in units of 1044
photons/s/keV. Divide this number by 4πd2
with d
the source distance to get the flux at Earth. Real array
.
7.6 Rgsvprof
In SPEX, the lpro component (see Section 4.24) can be used to fold the spectrum with a user defined
broadening profile. This is particularly useful for the analysis of extended sources with grating spectrometers,
like RGS aboard XMM-Newton. The rgsvprof program creates an input file (usually called
vprof.dat) for the lpro component from a MOS1 detector image.
The program will ask for the following input:
• MOS1 detector image. In order to obtain a profile along the dispersion direction of RGS within
the same field of view, the program asks for a MOS1 image of the source in detector coordinates
142 Auxilary programs
(DETX,DETY) created by, for example, the XMM-Newton SAS task evselect. Rgsvprof does not
require a particular resolution for the image, but a resolution of about 1/3 of the XMM-Newton
PSF, i.e. 4′′
, is recommended. It is recommended to extract an image using events with energies
falling in the RGS band: ∼0.3-2.0 keV.
• Cross-dispersion selection region. If the RGS spectrum is extracted from a certain area in the
cross-dispersion direction, then provide the lower and upper boundary here in arcminutes with
respect to the centre of the field of view. The full RGS strip corresponds to a range between -2.5
and 2.5 arcminutes.
• Source width in the dispersion direction. This parameter determines the boundaries of the resulting
profile in wavelength space. Rgsvprof asks for the width of the source in arcmin centred on the
peak of the emission. Choose this width to be somewhat larger than the actual width of the source
to be sure that the brightest parts are included in the profile. A width of >10 arcmin is typically
enough, but a larger width will increase the size of the vprof.dat file and increase processing times.
• Output file name. The name of the output file (usually vprof.dat). Note that rgsvprof does not
overwrite files that already exist.
Rgsvprof creates an ASCII file with two columns. The left column consists of the grid of wavelengths
that the profile is based upon and the right column gives the normalised cumulative profile over this
range starting with 0 and ending at 1. The profile will be centred on the peak of the emission.
Note: The cross-dispersion axis in RGS is parallel to the DETX coordinate axis in MOS1 and has the
same direction. This is particularly helpful when one extracts spatial regions in the cross-dispersion
direction of RGS.
Warning: This program works best for bright extended sources, where the background contribution is
negligible. For sources with a low surface brightness, in principle a background subtracted image should
be used. This program, however, cannot deal with negative values in the MOS1 image.
Warning: This program does not take into account vignetting and chip gaps. For offset observations
or very extended sources, this may start to play a role.
7.6.1 Theory
The wavelength scale corresponding to the angular width of the source in RGS can be calculated using
the dispersion equation defined in e.g. Peterson et al. (2004):
mλ = d(cosβ − cosα), (7.1)
where m is the spectral order, λ the wavelength, d the grating spacing, α the incidence angle of a photon,
and β the diffracted angle. The wavelength shift ∆λ due to an offset angle ∆θ relative to the telescope
boresight can be derived by differentiating the equation above with respect to θ = F
L (α − α0), where F
is the distance between the gratings (RGA) and the camera (RFC), L the focal length of the telescope,
and α0 the incidence angle corresponding to the telescope boresight. The resulting relation for ∆λ is:
∆λ =
dL
mF
sin(α0)∆θ. (7.2)
We then use the following numbers from den Herder et al. (2001): d is 1/645.6 mm, L is 7.5 m, F is 6.7
m, and α0 is 1.5762◦
to calculate the typical conversion factor from ∆θ in arcmin:
∆λ = 0.1387 ˚A ∆θ (7.3)
Note that the value in Peterson et al. (2004) is not correct, because the factor L
F was not applied. The
value in the above equation is used in rgsvprof to convert the spatial profile from arcminute scales to
wavelength scales.
7.7 Stepcontour 143
7.7 Stepcontour
The stepcontour task produces 1D and contour plots of step searches produced using the step commands.
At the end of the step command definitions (see 3.28), add the text file and a file name to the step
command to write out the step results to a .stp file.
For example:
SPEX> step dimension 2
SPEX> step axis 1 parameter 1 1 norm range 0.5 1.5 n 10
SPEX> step axis 2 parameter 1 1 t range 0.75 1.25 n 10
SPEX> step file norm-kt
These commands will produce a norm-kt.stp file. Subsequently, the stepcontour command can be run
from the command line or the SPEX¿ prompt:
linux:~> stepcontour
or
SPEX> sys exe "spexcontour"
The program will start and ask the user for the name of the .stp file:
Program stepcontour version 1.0.
Use this program to plot contours from SPEX steppar (.stp) files.
Enter filename of SPEX steppar file (.stp): norm-kt.stp
Then provide a PGPLOT device to show the plot. For example ’/xw’ for X output or ’file.ps/ps’ for
Postscript plots:
Number of axes in your steppar file: 2
Graphics device/type (? to see list, default /NULL): /xw
PGPLOT device type: XWINDOW
Plotting contours for: 68.3%, 90%, 95.4%, 99%, 99.99%.
If you would like to write the plot data to QDP format, say yes to the following question:
Would you like to write this plot to a QDP file (y/n)? y
The program asks for an output QDP filename and writes the data to that file.
Warning: The stepcontour program does not support logarithmic axes on 2D plots. Use another program
to plot these or perform the step command on a linear grid.
144 Auxilary programs
Chapter 8
Response matrices
8.1 Optimal definition of respons matrices
The SPEX FITS format allows us to bin spectra and response matrices on arbitrary grids, which enables
us to bin spectra and responses in an optimal way. In Kaastra & Bleeker (2016) a theoretical framework
is developed in order to estimate the optimum binning of X-ray spectra. Expressions are derived for
the optimum bin size for the model spectra as well as for the observed data using different levels of
sophistication. It is shown that by not only taking into account the number of photons in a given
spectral model bin but also its average energy (not necessarily equal to the bin center) the number of
model energy bins and the size of the response matrix can be reduced by a factor of 10–100. The response
matrix should then not only contain the response at the bin center, but also its derivative with respect
to the incoming photon energy. In the coming sections we describe practical guidelines how to construct
the optimum energy grids as well as how to structure the response matrix. Finally a few examples are
given to illustrate the present methods.
8.2 Proposed file formats
In Kaastra & Bleeker (2016) it was shown how the optimum data and model binning can be determined,
and what the corresponding optimum way to create the instrumental response is. Now I focus upon the
possible data formats for these files.
For large data sets, the fastest and most transparant way to save a response matrix to a file would be to
use direct fortran or C write statements. Unfortunately not all computer systems use the same binary
data representation. Therefore the FITS-format has become the de facto standard in many fields of
astronomical data analysis. For that reason I propose here to save the response matrix in FITS-format.
A widely used response matrix format is NASA’s OGIP format. This is used e.g. as the data format
for XSPEC. There are a few reasons that we propose not to adhere to the OGIP format here, as listed
below:
1. The OGIP response file format as it is currently defined does not account for the possibility of
response derivatives. As was shown in the previous sections, these derivatives are needed for the
optimum binning. Thus, the OGIP format would need to be updated.
2. In the later versions of OGIP new possibilities of defining the energy grid have been introduced
that are prone to errors. In particular the possibility of letting grids start at another index than
1 may (and has led) often to errors. The sofware also becomes unncessarily complicated, having
to account for different possible starting indices. Moreover, the splitting into arf and rmf files
makes it necessary to check if the indexing in both files is consistent, and also if the indexing in
the corresponding spectra is consistent.
146 Response matrices
3. There are some redundant quantities in the OGIP format, like the ”areascal” keyword. When the
effective area should be scaled by a given factor, this can be done explicitly in the matrix.
4. As was shown in this work, it is more efficient to do the grouping within the response matrix
differently, splitting the matrix into components where each component may have its own energy
grid. This is not possible within the present OGIP format.
8.2.1 Proposed response format
I propose to give all response files the extension ”.res”, in order not to confuse with the ”.rmf” or ”.arf”
files used within the OGIP format.
The file consists of the mandatory primary array that will remain empty, plus a number of extensions.
In principle, we could define an extension for each response component. However, this may result into
practical problems. For example, the fitsio-package allows a maximum of 1000 extensions. The documentation
of fitsio says that this number can be increased, but that the access time to later extensions
in the file may become very long.
In principle we want to allow for data sets with an unlimited number of response components. For
example, when a cluster spectrum is analysed in 4 quadrants and 10 radial annuli, one might want
to extract the spectrum in 40 detector regions and model the spectrum in 40 sky sectors, resulting in
principle in at least 1600 response components (this may be more if the response for each sky sector and
detector region has more components).
Therefore I propose to use only three additional and mandatory extensions.
The first extension is a binary table with 4 columns and contains for each component the number of data
channels, model energy bins, sky sector number and detector region number (see table 8.1).
The second extension is a binary table with 5 columns and contains for each model energy bin for each
component the lower model energy bin boundary (keV), the upper model energy bin boundary (keV),
the starting data channel, end data channel and total number of data channels for the response group
(see table 8.2).
The third extension is a binary table with 2 columns and contains for each data channel, for each model
energy bin for each component the value of the response at the bin center and its derivative with respect
to energy (see table 8.3). SI units are mandatory (i.e. m2
for the response, m2
keV−1
for the response
derivative).
Any other information that is not needed for the spectral analysis may be put into additional file extensions,
but will be ignored by the spectral analysis program.
Finally I note that the proposed response format is used as the standard format by version 2.0 of the
SPEX spectral analysis package.
8.2.2 Proposed spectral file format
There exists also a standard OGIP FITS-type format for spectra. As for the OGIP response file format,
this format has a few redundant parameters and not absolutely necessary options.
There is some information that is absolutely necessary to have. In the first place the net source count
rate Si (counts/s) and its statistical uncertainty ∆Si (counts/s) are needed. These quantities are used
e.g. in a classical χ2
-minimization procedure during spectral fitting.
In some cases the count rate may be rather low; for example, in a thermal plasma model at high energies
the source flux is low, resulting in only a few counts per data channel. In such cases it is often desirable
to use different statistics for the spectral fitting, for example maximum likelihood fitting. Such methods
are often based upon the number of counts; in particular the difference between Poissonian and Gaussian
statistics might be taken into account. In order to allow for these situations, also the exposure time ti per
data channel is needed. This exposure time needs not to be the same for all data channels; for example,
a part of the detector might be switched off during a part of the observation, or the observer might want
to use only a part of the data for some reason.
8.2 Proposed file formats 147
Table 8.1: First extension to the response file
keyword description
EXTNAME (=RESP INDEX) Contains the basic indices for the components in the form
of a binary table
NAXIS1 = 16 There are 16 bytes in one row
NAXIS2 = This number corresponds to the total number of components
(the number of rows in the table)
NSECTOR = This 4-byte integer is the number of sky sectors used.
NREGION = This 4-byte integer is the number of detector regions used.
NCOMP = This 4-byte integer is the totalnumber of response components
used (should be equal to NAXIS2).
TFIELDS = 4 The table has 4 columns; all columns are written as 4-byte
integers (TFORM=’1J’)
TTYPE1 = ’NCHAN’ First column contains the number of data channels for each
component. Not necessarily the same for all components,
but it must agree with the number of data channels as
present in the corresponding spectrum file.
TTYPE2 = ’NEG’ Second column contains the number of model energy grid
bins for each component. Not necessarily the same for all
components.
TTYPE3 = ’SECTOR’ Third column contains the sky sector number as defined by
the user for this component. In case of simple spectra, this
number should be 1.
TTYPE4 = ’REGION’ Fourth column contains the detector region number as defined
by the user for this component. In case of simple spectra,
this number should be 1.
Further, in several situations the spectrum will contain a contribution from background events. The
observed spectrum can be corrected for this by subtracting the background spectrum Bi scaled at the
source position. In cases where one needs to use Poissonian statistics, including the background level,
this subtracted background Bi must be available to the spectral fitting program. Also for spectral
simulations it is necessary to include the background in the statistics.
The background can be determined in different ways, depending upon the instrument. For the spectrum
of a point-source obtained by an imaging detector one could extract the spectrum for example from a
circular region, and the background from a surrounding annulus and scale the background to be subtracted
using the area fractions. Alternatively, one could take an observation of an ”empty” field, and using a
similar extraction region as for ther source spectrum, one could use the empty field observation scaled
by the exposure times to estimate the background.
The background level Bi may also contain noise, e.g. due to Poissonion noise in the background observation.
In some cases (e.g. when the raw background count rate is low) it is sometimes desirable to smooth
the background to be subtracted first; in this case the nominal background uncertainty ∆Bi no longer
has a Poissonian distribution, but its value can nevertheless be determined. In spectral simulations one
may account for the background uncertainty by e.g. simply assuming that the square of the background
signal-to-noise ratio (Bi/∆Bi)2
has a Poissonian distribution.
Furthermore, there may be systematic calibration uncertainties, for example in the instrumental effective
148 Response matrices
Table 8.2: Second extension to the response file
keyword description
EXTNAME (=RESP COMP) Binary table with for each row relevant index information for
a single energy of a component; stored sequentially, starting
at the lowest component and within each component at the
lowest energy.
NAXIS1 = 20 There are 20 bytes in one row
NAXIS2 = This number must be the sum of the number of model energy
bins added for all components (the number of rows in the
table).
TFIELDS = 5 The table has 5 columns
TTYPE1 = ’EG1’ The lower energy (keV) as a 4-byte real of the relevant model
energy bin
TTYPE2 = ’EG2’ The upper energy (keV) as a 4-byte real of the relevant
model energy bin
TTYPE3 = ’IC1’ The lowest data channel number (as a 4-byte integer) for
which the response at this model energy bin will be given.
The response for all data channels below IC1 is zero. Note
that IC1 should be at least 1 (i.e. start counting at channel
1!).
TTYPE4 = ’IC2’ The highest data channel number (as a 4-byte integer) for
which the response at this model energy bin will be given.
The response for all data channels above IC2 is zero.
TTYPE5 = ’NC’ The total number of non-zero response elements for this
model energy bin (as a 4-byte integer). NC is redundant,
and should equal IC2-IC1+1, but it is convenient to have
directly available in order to allocate memory for the response
group.
area or in the background subtraction. These systematic errors may be expressed as a fraction of the
source count rate (such that the total systematic source uncertainty is ǫsiSi) and/or as a fraction of
the subtracted background (such that the total systematic background uncertainty is ǫbiBi). Again, these
systematic errors may vary from data channel to data channel. They should also be treated different than
the statistical errors in spectral simulations: they must be applied to the simulated spectra after that the
statistical errors have been taken into account by drawing random realisations. Also, whenever spectral
rebinning is done, the systematic errors should be averaged and applied to the rebinned spectrum: a 10 %
systematic uncertainty over a given spectral range may not become 1 % by just rebinning by a factor of
100, but remains 10 %, while a statistical error of 10 % becomes 1 % after rebinning by a factor of 100.
In the previous sections we have shown how to choose the optimal data binning. The observer may want
to rebin further in order to increase the significance of some low-statistics regions in the spectrum, or
may want to inspect the unbinned spectrum. Also, during spectral analysis or beforehand the observer
may wish to discard certain parts of the spectrum, e.g. data with bad quality or parts of the spectrum
that he is not interested in. For these reasons it is also usefull to have the proposed rebinning scheme
available in the spectral file.
I propose to add to each data channel three logical flags (either true or false): first, if the data channel is
8.2 Proposed file formats 149
Table 8.3: Third extension to the response file
keyword description
EXTNAME (=RESP RESP) Contains the response matrix elements and their derivatives
with respect to model energy. The data are stored sequentially,
starting at the lowest component, within each component
at the lowest energy bin, and within each energy bin
at the lowest channel number.
NAXIS1 = 8 There are 8 bytes in one row
NAXIS2 = This number must be the sum of the NC values, added for
all model energy bins and all components (the number of
rows in the table).
TFIELDS = 2 The table has 2 columns
TTYPE1 = ’Response’ The response values Rij,0, stored as a 4-byte real in SI units
i.e. in units of m2.
TTYPE1 = ’Response Der’ The response derivative values Rij,1, stored as a 4-byte real
in SI units i.e. in units of m2keV−1.
the first channel of a group (fi); next, if the data channel is the last channel of a group (li); and finally,
if the data channel is to be used (ui). A channel may be both first and last of a rebinning group (fi
and li both true) in the case of no rebinning. The first data channel i = 1 always must have fi true,
and the last data channel li true. Whenever there are data channels that are not used (ui false), the
programmer should check that the first data channel after this bin that is used gets fi true and the last
data channel before this bin taht is used gets li true. The spectral analysis package needs also to check
for these conditions upon reading a data set, and to return an error condition whenever this is violated.
Finally, I propose to add the nominal energies of the data bin boundaries ci1 and ci2 to the data file. This
is very usefull if for example the observed spectrum is plotted outside the spectral fitting program. In the
OGIP format, this information is contained in the response matrix. I know that sometimes objections are
made against the use of these data bin boundaries, expressed as energies. Of course, formally speaking
the observed data bin boundaries often do not have energy units; it may be for example a detector
voltage, or for grating spectra a detector position. However, given a proper response. However given
a corresponding response matrix there is a one-to-one mapping of photon energy to data channel with
maximum response, and it is this mapping that needs to be given here. In the case of only a single data
channel (e.g. the DS detector of EUVE) one might simply put here the energies corresponding to the
FWHM of the response. Another reason to put the data bin boundaries in the spectral file and not in
the response file is that the response file might contain several components, all of which relate to the
same data bins. And finally, it is impossible to analyse a spectrum without knowing simultaneously the
response. Therefore, the spectral analysis program should read the spectrum and response together.
As a last step we must deal with multiple spectra, i.e. spectra of different detector regions that are
related through the response matrix. In this case the maximum number of FITS-file extensions of 1000
is a much smaller problem then for the response matrix. It is hard to imagine that anybody might wish
to fit more than 1000 spectra simultaneously; but maybe future will prove me to be wrong. An example
could be the following. The supernova remnant Cas A has a radius of about 3′
. With a spatial resolution
of 10′′
, this would offer the possibility of analysing XMM-EPIC spectra of 1018 detector regions. At the
scale of 10′′
the responses of neighbouring regions overlap so fitting all spectra simultaneously could be
an option· · ·.
Therefore it is wise to stay here on the conservative side, and to write the all spectra of different detector
regions into one extension. As a result we propose the following spectral file format.
150 Response matrices
After the null primary array the first extension contains the number of regions for the spectra, as well
as a binary table with the number of data channels per region (see table 8.4). This helps to allocate
memory for the spectra, that are stored as one continuous block in the second extension (see table 8.5).
Table 8.4: First extension to the spectrum file
keyword description
EXTNAME (=SPEC REGIONS) Contains the spectral regions in the form of a binary table
NAXIS1 = 4 There are 4 bytes in one row
NAXIS2 = This number corresponds to the total number of regions
(spectra) contained in the file (the number of rows in the
table)
TFIELDS = 1 The table has 1 column, written as 4-byte integer
(TFORM=’1J’).
TTYPE1 = ’NCHAN’ Number of data channels for this spectrum.
8.2 Proposed file formats 151
Table 8.5: Second extension to the spectrum file
keyword description
EXTNAME
(=SPEC SPECTRUM)
Contains the basic spectral data in the form of a binary table
NAXIS1 = 28 There are 28 bytes in one row
NAXIS2 = This number corresponds to the total number of data channels
as added over all regions (the number of rows in the
table)
TFIELDS = 12 The table has 12 columns.
TTYPE1 = ’Lower Energy’ Nominal lower energy of the data channel ci1 in keV; 4-byte
real.
TTYPE2 = ’Upper Energy’ Nominal upper energy of the data channel ci2 in keV; 4-byte
real.
TTYPE3 = ’Exposure Time’ Net exposure time ti in s; 4-byte real.
TTYPE4 = ’Source Rate’ Background-subtracted source count rate Si of the data
channel in counts/s; 4-byte real.
TTYPE5 = ’Err Source Rate’ Background-subtracted source count rate error ∆Si of the
data channel in counts/s (i.e. the statistical error on
’Source Rate’); 4-byte real.
TTYPE6 = ’Back Rate’ The background count rate Bi that was subtracted from the
raw source count rate in order to get the net source count
rate Si; in counts/s; 4-byte real.
TTYPE7 = ’Err Back Rate’ The statistical uncertainty ∆Bi of ’Back Rate’ in counts/s;
4-byte real.
TTYPE8 = ’Sys Source’ Systematic uncertainty ǫsi as a fraction of the net source
count rate Si; dimensionless; 4-byte real.
TTYPE9 = ’Sys Back’ Systematic uncertainty ǫbi as a fraction of the subtracted
background count rate Bi; dimensionless; 4-byte real.
TTYPE10 = ’First’ True if it is the first channel of a group; otherwise false.
4-byte logical.
TTYPE11 = ’Last’ True if it is the last channel of a group; otherwise false.
4-byte logical.
TTYPE12 = ’Used’ True if the channel is to be used; otherwise false. 4-byte
logical.
152 Response matrices
Chapter 9
Installation
9.1 Installation
We support SPEX on two platforms: Linux 64-bit and Mac OSX 64-bit. Please consult our website for
the most recent list of (http://www.sron.nl/spex). For instructions, please follow the steps below for
your operating system.
9.1.1 Installation on Linux
These are the steps to install SPEX on Linux 64-bit (Intel/AMD) systems:
1. Download the tar file from our web site named SPEX-<version>-Linux.tar.gz where ¡version¿ is
the current version number (for example 3.00.00). Copy this file into the directory where you want
to install SPEX, like /home/user/software/.
2. Extract the tar file in the desired directory:
linux:~/software> tar xvfz SPEX-3.00.00-Linux.tar.gz
Tar will create the directory ~/software/SPEX-3.00.00-Linux.
3. For SPEX to function, the environment needs to be set. The SPEX90 variable should point to the
top SPEX directory (/path/to/your/SPEX-3.00.00). Then source the included environment file
called spexdist.sh or spexdist.csh:
For BASH shells:
linux:~/software> export SPEX90=/path/to/your/SPEX-3.00.00-Linux
linux:~/software> source $SPEX90/spexdist.sh
For CSH shells:
linux:~/software> setenv SPEX90 /path/to/your/SPEX-3.00.00-Linux
linux:~/software> source $SPEX90/spexdist.csh
4. To automate the setting of the environments, you can add the commands for your shell to either
~/.bashrc (bash) or ~/.cshrc (csh).
If you encounter problems or if you have questions, please visit the troubleshooting and frequently asked
questions sections on our website first, before consulting us directly.
154 Installation
9.1.2 Installation on Mac OSX
We always compile SPEX on one of the most recent Mac OSX versions and try to make the executables
compatible with earlier OSX versions. However, due to the dependency on X-windows (XQuartz), this
compatibility is limited. Please consult our web site for the list of supported Mac OSX versions.
SPEX can be installed following these steps:
1. Download and install on your system first (if you have not done so already) from http://www.xquartz.org/
2. Download the SPEX-3.00.00-OSX.dmg file from our web site http://www.sron.nl/spex
3. Click the downloaded file and open the installation package. You can walk through the graphical
installer. The default settings will be fine.
4. SPEX will be installed in /opt/spex, but the still needs to be set. The included spexdist.sh and
spexdist.csh files can be found in the directory /opt/spex:
For BASH shells:
darwin:~> source /opt/spex/spexdist.sh
For CSH shells:
darwin:~> source /opt/spex/spexdist.csh
5. To automate the setting of the environments, you can add the command for your shell to either
~/.bashrc (bash) or ~/.cshrc (csh).
If you encounter problems or if you have questions, please visit the troubleshooting and frequently asked
questions sections on our website first, before consulting us directly.
Chapter 10
Acknowledgements
We would like to express our special thanks to numerous people who have substantially contributed to
the development of various aspects of this work, in alphabetical order:
Frans Alkemade, Gert-Jan Bartelds, Ehud Behar, Alex Blustin, Elisa Costantini, Max Duysens, Jacobo
Ebrero, Irma Eggenkamp, Andrzej Fludra, Yan Grange, Ed Gronenschild, Liyi Gu, Theo Gunsing, J¨orgen
Hansen, Wouter Hartmann, Kurt van der Heyden. Fred Jansen, Jelle Kaastra, Jim Lemen, Duane Liedahl,
Junjie Mao, Pasquale Mazzotta, Missagh Mehdipour, Rolf Mewe, Hans Nieuwenhuijzen, Bert van den
Oord, Ken Phillips, Ciro Pinto, Ton Raassen, Remco van der Rijst, Makoto Sawada, Hans Schrijver,
Karel Schrijver, Tiemen Schut, Janusz Sylwester, Rob Smeets, Katrien Steenbrugge, Jeroen Stil, Igone
Urdampilleta, Dima Verner, Jacco Vink, Frank van der Wolf, Piotr Zycki.
During the years the many people have contributed as follows:
Software:
Most software is written by Kaastra. Nieuwenhuijzen contributed to the software design.
De Plaa maintains the software on different platforms.
The philosophy of the fitting procedure is based on the experiences obtained with the fitting of EXOSAT
data, especially on the software package ERRFIT designed by Jansen and Kaastra.
Tiemen Schut has initiated the parallelisation of important parts of the code.
Plasma model:
The line and continuum emission routines were written by Kaastra, based on previous routines by Mewe,
Gronenschild, van den Oord, and Lemen (1981-1986).
The original line and continuum emission data are based on the work by Mewe and Kaastra.
Raassen has calculated and compiled a large amount of atomic data for the models.
Nieuwenhuijzen, Hansen, Duysens and Van der Rijst contributed to the extension of the atomic database.
Phillips contributed to improvements of the wavelengths of strong lines.
Liedahl contributed to the Fe-L calculations.
The photo-ionization cross-sections have been provided by Verner. Behar and Raassen contributed to
the atomic data for the absorption models.
Missagh Mehdipour helped with the pion model.
Mazzotta and Urdampilleta worked on the ionization balance.
Mao incorporated new radiative recombination data.
Gu developed the charge exchange models.
The non-equilibrium ionization balance routine was developed by Jansen, based on earlier work by Hans
Schrijver (1974) and Gronenschild (1981). It was extended and updated together with Sawada (2014).
SPEX models:
156 Acknowledgements
The SNR models are based on the work by Kaastra and Jansen (1992), with further extensions and
testing by Stil, Eggenkamp and Vink.
Costantini and Pinto contributed to the dust models.
Lemen, Smeets, and Alkemade developed an earlier version (1986-1990) of a spectrum synthesis program.
The original DEM modelling was based on the work by Sylwester and Fludra (1980), while the current
DEM regularisation algorithm has been designed by Karel Schrijver and Alkemade. Bartelds contributed
to the testing of these models.
Piotr Zycki provided us the refl model code.
Documentation:
The first version (1.0) of the documentation has been prepared – with starting help by Gunsing – by
van der Wolf and Nieuwenhuijzen. The second version was set-up by Kaastra with contributions from
Steenbrugge, van der Heyden and Blustin. The later versions were managed by de Plaa.
The cookbook contains contributions from De Plaa, Ebrero, Grange, Pinto, Kaastra, Steenbrugge, Gu,
and Mehdipour.
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Index
abundance, 23
ASCA, 21
ascdump, 25
BeppoSAX, 21
bin, 27
calculate, 28
clusters of galaxies, 21
command files, 44
comp, 28
data, 30
dem, 31
distance, 33
distance units, 33
Doppler broadening, 61
egrid, 35
elim, 36
environment, 154
error, 37
file formats, 145
fit, 38
flux, 33
free-bound emission, 61
ibal, 41
ignore, 41
installation, 153
ion, 42
log, 44
mekal, 62
menu, 45
multiply, 46
obin, 47
par, 47
plot, 50
plot, axis scales, 126
plot, axis units, 124
plot, captions, 122
plot, colours, 120
plot, devices, 119
plot, line types, 120
plot, symbols, 124
plot, text, 121
plot, types, 119
quit, 54
Response matrix, 145
sector, 55
shiftplot, 55
show model, 46
simulate, 56
sky sector, 33
step, 57
supernova remnants, 21
supported systems, 153
syserr, 58
system, 59
use, 60
vbin, 63
watch, 64
XMM-Newton, 21
XQuartz, 154