The cluster parameters 1. Reddening 2. Distance modulus 3. Age 4. Metallicity Determination in the order: Reddening, age, distance modulus simultaneously, metallicity with possible iterations Distance:V0-MV AV k.AV Turn-off Glushkova et al., 2013, MNRAS, 429, 1102 Color – Magnitude - Diagram Different CMDs for one open cluster Grocholski & Sarajedini, 2003, MNRAS, 345, 1015 Different photometric indices Several different indices et al. are available (very much incomplete): • Sensitive to temperature: 1. Johnson: B - V, V - I, R - I, V - K, … 2. Strömgren: b - y, u - b, b 3. Sloan g - r, r - i, … 4. Geneva: B2 - V1, X, … 5. 2MASS: H - Ks, J - Ks and H - J 6. Gaia: BP - RP • „Mixture“: 1. Johnson: U - B 2. Strömgren: c1, m1, … 3. Geneva: d, D, m2, … How to derive cluster parameters? • Use as much as possible available indices • Check the literature for published values as least as a starting point • First try it with a “standard set” of data • Automatic procedures available, but be careful Absorption = Extinction = Reddening • AV = k1 E(B-V) = k2 E(V-R) = … • General extinction because of the ISM characteristics between the observer and the object • Differential extinction within one star cluster because of local environment • Both types are, in general wavelength dependent Reasons for the interstellar extinction • Light scatter at the interstellar dust • Light absorption => Heating of the ISM • Depending on the composition and density of the ISM • Main contribution due to dust • Simulations and calculations in Cardelli et al., 1989, ApJ, 345, 245 Cardelli et al., 1989, ApJ, 345, 245 Important parameter: RV = AV/E(B-V) Normalization factor Standard value used is 3.1 Be careful, different values used! Depending on the line of sight Cardelli et al., 1989, ApJ, 345, 245 Dependency of the extinction from RV How to derive the reddening? • Non-Isochrone approach: from photometric and spectroscopic observations Classical approach: Neckel & Klare, 1980, A&AS, 42, 251 Take all available UBV and Strömgren b photometry MK classifications Bailer-Jones, 1996, PhD, Cambridge University Absolute Magnitude Assume V = 10 mag and no reddening O5: -5.6 => 13 000 pc A0: +1.0 => 630 pc G0: +4.5 => 125 pc M0: +8.9 => 15 pc Assume V = 20 mag and no reddening O5: -5.6 => 1.3 Mpc A0: +1.0 => 63 kpc G0: +4.5 => 12.5 kpc M0: +8.9 => 1.5 kpc Crawford, 1976, AJ, 83, 48 Example for the b index Cut off as you like Reddening Maps Piskunov et al., 2006, A&A, 445, 545 http://argonaut.skymaps.info/ http://www.univie.ac.at/p2f Neckel & Klare, 1980, A&AS, 42, 251 Needed: Galactic coordinates Distance from Sun Haffner 18 Age about 8 Myr d = 6000 pc differential extinction within the cluster Yadav & Sagar, 2001, MNRAS, 328, 370 Differential reddening in young open clusters Determination of the reddening - Isochrones • From two temperature sensitive parameters, the determination of the reddening is not possible • You need one “other” observational index • First choices: (U – B), (u – b), [X], b • Normally, you only have V, J, H, K, and so on Reddening vector Mean values for E(B-V) and E(V-I) You would need a spectral information The reddening shifts the main sequence by a value of E(U-B) = 0.72E(B-V) + 0.05E(B-V)2 Reddening vector Mean values for E(B-V) and E(U-B) Reddening vector 1 2 1: „early type region“, hotter than A5 2: „late type region“, cooler than A5 Mean values for E(B-V) and Av Significant effect due to reddening No effect due to reddening Mean values for E(B-V) and Av No stars hotter than A0 Good estimate for the reddening and distance Distance modulus • Apparent DM: (V - MV) which still includes the reddening • Absolute DM: (V - MV)0 or (V0 - MV) which not includes the reddening • Be careful there is always a mixture in the literature! How to determine the DM? • Direct isochrone fitting • Calibrate MV directly via photometry and spectroscopy with known reddening and V magnitude => distance directly • Advantage: statistical sample Balaguer-Núñez et al., 2007, A&A, 470, 585 Guerrero et al., 2011, RMxAA, 47, 185 Distance:V0-MV AV k.AV Turn-off Turn off point • Where is the turn-off point located? –Color/temperature –Absolute/apparent magnitude/luminosity • Direct correlation with the age • Difficult to define for young star clusters • First, classical method, just „to look“ at color-magnitude-diagram Mermilliod, 1981, A&A, 97, 235: no newer paper available! Dereddened indices „Bluest“ (U – B)0 at main sequence MV of red giants Mermilliod, 1981, A&A, 97, 235 No direct error estimation possible Possible to use for star clusters between 20 Myr and 800 Myr Mermilliod, 1981, A&A, 97, 235 Very precise method Possible to use between for star clusters between 20 Myr and 300 Myr (U – B)0 for cooler stars = older ages is almost constant Not very accurate but still useful, never done for 2MASS and NIR Calculation of Isochrones The calculation of theoretical isochrone (= lines of equal age) is done with stellar atmospheres Free parameter : Metallicity [X, Y, Z] 1. Zero Age Main Sequence [Teff , L]0 2. Chemical and gravitational evolution 3. [Teff , L](t) 4. Adequate stellar atmosphere = PHYSICS 5. Absolute fluxes 6. Folding with filter curves 7. Colors, absolute magnitudes and so on Which astrophysical “parameters” are important? • Equations of state • Opacities • Model of convection • Rotation • Mass loss • Magnetic field • Core Overshooting • Abundance of helium • … Maeder & Mermilliod, 1981, A&A, 93, 136 Maeder & Mermilliod, 1981, A&A, 93, 136 Different treatment of convection A comparison of isochrone sets • Grocholski & Sarajedini (2003, MNRAS, 345, 1015) compared the following isochrones: 1.“Padova”: Girardi et al., 2002, A&A, 391, 195 2.Baraffe: Baraffe et al., 1998, A&A, 337, 403 3.“Geneva”: Lejeune & Schaerer, 2001, A&A, 366, 538 4.Y2: Yi et al., 2001, ApJS, 136, 417 5.Siess: Siess et al., 2000, A&A, 358, 593 For Pop II The location of the Sun with isochrones of 5 Gyr Isochrones by Siess et al. (1997) seem “to have a problem” Comparison of different masses for a constant MV 100% M5 Zero line is the isochrone of the Padova group Comparison of different color indices for a constant MV Zero line is the isochrone of the Padova group M0 Used Photometry Parameters from the literature log t, E(B-V) and [Fe/H] fixed, only Distance modulus determined Value from the literature Transformation in distances [pc] • M35: 1148 [916,1208]; -20% +5% • M37: 2042 [1905,2239]; -7% +10% • NGC 1817: 2692 [2344,2884]; -13% +7% • NGC 2477: 2042 [1698,2089]; -17% +2% • NGC 2420: 2630 [2399,3090]; -9% +17% • M67: 912 [776,912]; -15% +0% • Mean values: -13(5)% +7(6)%, for one free parameter! In a statistical point-of-view: significant For a given reddening, metallicity and age, the isochrones by Baraffe et al. yield significantly brighter and Yi et al. significantly fainter absolute magnitudes . In addition, the isochrones by Siess et al. do not reproduce the location of the Sun correctly. Grocholski & Sarajedini, 2003, MNRAS, 345, 1015 Age determination ONLY based on these three stars Isochrones for [Z] = 0.040 and log t = 8.0, 8.1 und 8.2 Result: t = 130+40 -30 Myr E(B-V) = 0.75(5) mag V – MV = 14.00(25) mag log t = 7.0 Automatic Methods Jorgensen & Lindegren, 2005, A&A, 436, 127 Definition of different „important“ areas (Box) in the CMD. Do this allocation as you like. Turn-off point, location of the red giant clump, and so on. Count the number of stars in each box. Warning: you always „lose“ stars because of discrete boxes. Only for t > 300 Myr 1 Gyr Other methods • https://github.com/hektor-monteiro/OCFit • http://asteca.readthedocs.io/en/latest/index.html • An et al., 2007, ApJ, 655, 233 • Buckner & Froebrich, 2013, MNRAS, 436, 1465 • Fernandes et al., 2012, A&A, 541, A95 • Frayn & Gilmore, 2003, MNRAS, 339, 887 • Kharchenko et al., 2005, A&A, 438, 1136 • Monteiro et al., 2010, A&A, 516, A2 • Oliveira et al., 2013, A&A, 557, A14 • Pinsonneault et al., 2003, ApJ, 598, 588 Metallicity - Basics • Metallicity as [X:Y:Z] • X = Hydrogen • Y = Helium • Z = „the rest“ 𝑋 ≡ 𝑚 𝐻 𝑀 Y ≡ 𝑚 𝐻𝑒 𝑀 Z = 𝑚𝑖 𝑀𝑖>𝐻𝑒 = 1 – X – Y Metallicity - designations • In the literature you will find – [Z] – [Fe/H] – [M/H] – [Element 1 / Element 2] • Relations for the transformation are necessary Metallicity – designations Metallicity - designations • [dex], e.g. [Fe/H] = -0,5 dex dex factor dex factor -2 0,01 0,1 1,26 -1,5 0,03 0,2 1,58 -1 0,10 0,3 2,00 -0,9 0,13 0,4 2,51 -0,8 0,16 0,5 3,16 -0,7 0,20 0,6 3,98 -0,6 0,25 0,7 5,01 -0,5 0,32 0,8 6,31 -0,4 0,40 0,9 7,94 -0,3 0,50 1 10,00 -0,2 0,63 1,5 31,62 -0,1 0,79 2 100,00 The Sun as standard star • „Our“ standard star for the normalisation of the metallicity is the Sun • We define: – Mass – Luminosity = absolute (bolometric) magnitude – Temperature = spectral type = color – Age – Chemical composition – Internal structure (rotation, magnetic field, convection, diffusion, pulsation, …) Abundance analysis - Sun • Review article: Asplund et al., 2009, Annual Review of Astronomy & Astrophysics, 47, 481 • Ingredients: – Stellar atmosphere – Atomic line data – High resolution spectra – Analysis method – Starting parameter • Gray, 2005, The Observation and Analysis of Stellar Photospheres, Cambridge University Press Stellar atmospheres • ATLAS, http://atmos.obspm.fr/ • MARCS, http://marcs.astro.uu.se/ • NEMO, http://www.univie.ac.at/nemo • PHOENIX, http://www.hs.uni- hamburg.de/EN/For/ThA/phoenix/index.html • TLUSTY, http://nova.astro.umd.edu/ • iSpec, https://www.blancocuaresma.com/s/iSpec • Workshop: http://astro.physics.muni.cz/events/spec_ws_2017/ Stellar atmospheres Different synthesized stellar spectra “for the same star“ Abundance - Sun • Problems with –Hydrogen –Helium –Elements with only a few lines –Elements with only weak lines • LTE versus NLTE (Local Thermodynamic Equilibrium ) Abundance - Sun Asplund et al. Abundance - Sun Asplund et al. Abundance - Sun PhD thesis – U. Heiter Abundance - Sun Asplund et al. Determination of the metallicity • The determination of the metallicity can be done in three ways: 1. Spectroscopic abundance analysis 2. Fitting of isochrones 3. Photometric calibrations • ESO- Gaia survey: https://www.gaia-eso.eu/ „Metalls“ in stars Photometric calibrations Martell & Laughlin, 2002, ApJ, 577, L45 Error: +-0.10 dex Metallicity => different opacity Isochrones for 10 Myr Metallicity - isochrones Schaller et al., 1993, A&AS, 101, 415 Different He abundances – [Z] constant