Introduction to Physics of Neutron Stars Pulsars — Magnetars Jan Benáček 11. 11. 2024 Institute for Physics and Astronomy, University of Potsdam, DE Me • 2010–2015 – Bachelor in physics + Master in astrophysics at MU • 2015–2019 – PhD in astrophysics at MU • 2014–2019 – Work in industry • 2020–2022 – Research assistant at Technical University of Berlin: GAČR–DFG project on solar/pulsar coherent (at kinetic scales) radio emission processes • 2023–2025 – Research assistant at University of Potsdam: PI of a DFG grant — pulsar coherent radio emission processes Scientific interests: Solar flares, magnetospheres of stars/compact objects, pulsars, fast radio bursts MU IS email: jbenacek@physics.muni.cz Uni Potsdam email: jan.benacek@uni-potsdam.de 1 Recommended literature Books • Beskin et al., “Physics of the pulsar magnetosphere,” 1993 • Lorimer & Kramer, “Handbook of pulsar astronomy,” 2005 • Rezolla et al., “The Physics and Astrophysics of Neutron Stars,” 2018 Papers • Petri, “Theory of pulsar magnetosphere and wind”, JPP, 2016 • Kaspi & Beloborodov, “Magnetars”, ARAA, 2017 • Zhang, “Physical Mechanism of fast radio bursts”, Nature, 2020 • Philippov and Kramer, “Pulsar Magnetospheres and their radiation”, ARAA, 2022 2 1. Introduction to neutron stars Discovery • Jocelyn Bell in 1967 • 2000 wires as dipole antennas • Analyzing roles of paper • Advisor: Anthony Hewish & Martin Ryle • Nobel price 1974 3 Neutron star Neutron star properties • Remnants of supernovae • Composed of compressed matter, neutrons • Very dense ∼ 5 × 1017 kg m−3, > 10natomcore • Short rotation periods ≲ 1 s • Radius ∼10 km • Hot surface (∼105 K) • M ∼ 1.1–2.1 M∗ • Strong magnetic fields ∼108 T (1012 G) • Radio to γ-rays • Plasma heating, particle acceleration • Reliability of shown figures 4 Neutron stars provide insights into a broad range of various astrophysical phenomena Pulsars Magnetars Extreme physical environments Gravitational waves X-ray binaries Microqusars Fast radio bursts 5 1. Introduction to neutron stars Neutron star Formation 6 Formation • Initial star mass ≳ 8 M∗ • Inner core exceeds Chandrasekhar limit (1.4 M∗) • Core-collapse supernovae (Type II, or Type Ib,c) • Central core collapse into a compact object (NS or BH) • Implosion → shock wave • Outer layers outflow • Electrons and protons combine p+ + e− → n + νe (reversed β-decay) • Initial temperature 1011 − 1012 K drops in few years to 106 K (BB in X-rays) • Compact object kicked (∼100 km s−1) NS = neutron star; BH = black hole 7 Mass of neutron star (Latimer & Prakash, 2005) (Ozel & Freire 2016) 8 Neutron star inner structure • Main problem: Equation of state • Superconductivity and superfluidity of matter • Strong frozen magnetic fields • Two main models (AP4 and MS2), Many more existing • Neutrons hold from decay by strong pressures (otherwise decay in ∼15 minutes) 9 Neutron star models 10 Magnetosphere Toy/book model: Properties: • Magnetic dipole • Higher pole moments under debate • Inclination between rotation and magnetic axes • Light cylinder – RLC = Pc/2π, RLC ∼ 500 R⋆ • Open and closed magnetic fields • Atmosphere only a fraction of millimeter thickness 11 Gravitation effect – Light deflection • Bending of radiation from surface • Effect of spaghettification • Red shift of light from star surface 12 Spin down • Rotational kinetic energy of star decreases • Rotation periods increase • Measuring slow down → amount of energy release • Spin-down luminosity ˙E = d(IΩ2/2) dt = IΩ ˙Ω = 4π2 ˙PP−3 (1) I = 1045 g cm−2 ˙E ∼ 1025 W (1032 erg s−1) (Other energy releases neglected) • Dependence of spin down on period • Dependence of energy release on period • Spin down caused by dipole radiation power ˙Erad = 2 3c3 (BsurfaceR3 ⋆ sin α) ( 2π P )4 (2) • α is the dipole inclination angle 13 P ˙P diagram Small dots: Radio pulsars HE: High energy pulsars AXP: Anomalous X-ray pulsars RRAT: Radio transients XINS: Thermally emitting isolated neutron stars 14 Glitches • Sudden changes of rotational period • 1. Changes in structure of star core • 2. Changes in structure of mg. fields The mg. field disturbance propagate along field lines • More often for young NS (Lyne et al. 1999) 15 Braking index • Quantifies the spin down • Dipole emission ˙Edipole = 2 3c3 |m|2 Ω4 sin2 α (3) • Change of NS rotational frequency ˙ν = −Kνn (4) • n is braking index • Measured as n = ν¨ν/ ˙ν2 • Values: 1.4 – 2.9 Estimation of pulsar age T = P (n − 1) ˙P [ 1 − ( P0 P )n−1 ] (5) Characteristic age τ = P 2 ˙P (6) • Crab: τ = 1240 yr, known: 970 • Born periods P0 = 14 − 140 ms Magnetic fields at surface B0 = √ 3c3 8π2 I R6 ⋆ sin2 α P ˙P (7) • B0 ∼ 1012 G (108 T) 16 Braking index 17 Pulsar death • As NS period increases, efficiency of energy conversion decreases • For large periods, their emission vanishes • Can be recycled if in binary 18 2. Pulsar Observations Radio telescopes GBT Effelsberg FAST Arecibo 19 Radio telescopes MeerCAT ALMA VLA 20 Telescopes Chandra Fermi Integral NICER 21 Average pulses (Lorimer & Kramer 2005) – Effelsberg • PSR B1913+16 separate epochs • PSR B1237+25 only part of rotation phase • PSR B1934+21 1.4 GHz • Others 430 MHz • Interpulses, 2 explanations • Duty cycle 22 Individual pulses PSR B0301+19, Arecibo, Lorimer & Kramer 2005 23 Vela pulsar spectrum (Mignani et al. 2017) 24 Crab pulsar (Hankins & Eilek 2015) 25 Dispersion measure • Signal delay ∆t = 1 c (∫ d 0 dl vg ) − d c (8) • Group velocity vg = cN = c √ 1 − ( fp f )2 (9) (N – refractive index, fp – plasma frequency) • Signal delay (after expansion of N) ∆t = e2 2mec ∫ d 0 nedl f2 = C DM f2 (10) DM = ∫ d 0 nedl (11) 26 Faraday rotation • Difference in phase between left and right polarization ∆ΨFar(f) = ∫ d 0 (kR(f) − kL(f))dl, (12) where k(f) = 2π c f √ 1 − f2 p f2 ∓ f2 p fB f3 (13) Then ∆ΨFar(f) = 2e3 m2 ecf2 ∫ d 0 neB∥dl (14) ∆ΨPPA = ∆ΨFar(f)/2 ≡ RM/f2 (15) RM = e3 m2 ecf2 ∫ d 0 neB∥dl (16) ⟨B∥⟩ = ∫ d 0 neB∥dl ∫ d 0 nedl = 1.2µG ( RM rad m−2 ) ( DM cm−3 pc )−1 27 Submicrosecond pulses (Hankins & Eilek 2016) – Crab 28 Nanoshots (Hankins et al. 2003) (Hankins & Eilek 2007) 29 Brightness temperature Tb • Black body radiation dI(ν) dν = 2hν3 c2 1 e hν kT − 1 (17) • Temperature Tb = hν kB ln−1 ( 1 + 2hν3 I(ν)c2 ) (18) • For hν < kT • Brighness temperature Tb = I(ν)c2 2kBν2 (19) 30 X-ray observations NICER (X-ray) + Nançay (1.4 GHz) (Guillot et al. 2019) 31 Gamma rays Vela (Kuiper & Hermsen 2015) – Vela Crab Vela (Rudak 2018) – Crab 32 3. Physical applications High precision timing • Precide measurements of times of pulse arrivals • Depends on time resolution and S/N ratio • Low variance between individual pulses • Millisecond pulsars are ideal • Precision ∼ 100 ns for over > 1 year • Stability of pulsar internal clock limited (due to “unknown” slow down mechanism) • Cross-check with terrestrial clocks (Hotan 2005) 33 Testing general theory of relativity Shift of periastron (Weisberg & Taylor 2005) Window of opportunity 34 Gravitational waves • Continuous gravitational waves • Compact binary gravitational waves • (Stochastic gravitational wave) • (Burst gravitational waves) (Lorimer & Kramer 2005) 35 Gravitational waves • Continuous gravitational waves • Compact binary gravitational waves • (Stochastic gravitational wave) • (Burst gravitational waves) (Haskell & Schwenzer 2021) 36 Merging neutron stars • Source of gravitational waves • Might produce short gamma ray bursts or kilonovae • Produce a neutron star or a black hole (Tolman–Oppenheimer–Volkoff limit) • First detection on 17th August 2017 by gravitational waves, later short gamma ray burst • Total mass 2.82 M∗ • It collapsed into a black hole or a magnetar in milliseconds • Direct evidence of production of heavier elements and that neutron star is composed of neutrons 37 Extrasolar planets (Marcy & Buttler 2000) 38 Plasma physics in extreme conditions • Relativistic temperatures ρ = mc2 kBT ≲ 1 • Relativistic particle velocity distributions – e.g. Maxwell–Jüttner • Magnetic fields 1014 G (ωce ∼ 1020 Hz) • Particle Lorentz factors γ up to 107, typical 103 (v/c = 0.9999995) • Large kinetic energy densities • Huge field energy densities • Plasma beta parameter β ≪ 1 39 4. Magnetospheres of Pulsars 4. Magnetospheres of Pulsars Physics of the magnetosphere Pulsar model • 40 Force free magnetosphere • Force ratio fEM fG = eE∥R2 ∗ GM∗mp ≈ 109 (20) • Goldreich–Julian density ρe = ϵ0∇ · E = −2ϵ0Ω · B (21) • Particle (EB) drift vE,d = E × B B2 (22) → No currents between e− and p+. And drift along mg. fields (+ stationarity) For deviation from charge-neutrality → currents • Ideal MHD vE,d = Ω × r − B · (Ω × r) B2 B. (23) From ideal Ohm’s law E + v × B = 0 (24) Problem between open and closed fields. 41 2D magnetospheric simulations (Chen & Beloborodov 2014) 42 3D magnetospheric simulations (Philippov et al. 2015) 43 Electron-positron production • Breaking of force–free magnetospheric models in regions called gaps • Electric currents do not compensate plasma co-rotation ∇ × B = j + ϵ0µ0 ∂E ∂t (25) • Electric fields can reach ∼ 1013 V/m • “Primary particles accelerated” (107 MeV) • Curvature emission of γ-photons • Inverse Compton scattering may occur γ + B → e+ + e− + B (26) • Production of “secondary particles” (102 − 104 MeV) • Multiplicity factor κ ∼ 102 − 105. Other electron-positron sources • γ photons from hot star surface • photon-photon interactions 44 Formation of relativistic beams (Gurevich et al. 1993) (Usov 2002, ArXiv) 45 Model of pulsar wind Types of wind: • Quasi-neutral (MHD) wind of relativistic particles, currents between species, large particle density required • Relativistic charged wind, species separated, questions about effectiveness, current only one species • Large-amplitude low-frequency elmg. wave in a low density plasma Focus mainly on propagation effects. (Petri, 2016) 46 Outer magnetosphere (Cerutti et al. 2020) 47 5. Magnetars Discovery Soft gamma repeaters (SGRs) • (Vegnera 11 and 12) detection of hard X-ray / soft gamma-ray repeater (SGR 1900+14) • Softer spectra than gamma ray bursts (GRBs) • New class of high energy sources • 8 s period (SGR 0526-66) suggests a neutron star, but much larger than other newly born pulsars (<100 ms) • Ultrastrong magnetic fields needed for such decay in 104 years • Fields provide energy source for large activity • Magnetic fields confirmed from spin-down measurements in 1998 Anomalous X-ray pulsars (AXPs) • Indipendent theory evolution • 1980 ”an extraordinary new celestial X-ray source” • Pulsations with period ∼3.5 s (Later 7 s) • Later suggested as a new type of accretion powered X-ray (neutron star) binary (Mazets 1979a,b; Thompson & Duncan 1992,1996) 48 Main parameters • Periods 2–12 s • Born with periods ∼100 ms → rapid magnetic breaking • Large spin-down rates ∼ 10−3 yr−1 • Mg. fields from spind down rates > 1014 G • Spin down energy < X-ray luminosity • X-ray luminosity 1030 − 1035 erg s−1 (2–10 keV) • Soft X-ray – black body radiation • Hard X-ray – hardening • Sometimes observed at other wavelength (radio to UV) • Located in galactic plane → young sources • Spatial velocities ∼ 200 km s−1 • Some associated with supernova remnants (Olausen & Kaspi 2014) 49 Activity Generally vary strongly between magnetars. Bursts: • Durations ms – s, typically 100 ms • Energies 1036 − 1044 erg s−1 • More common during outbursts Outbursts: • 10 − 103 time increase of X-ray flux • Energy flux < 1036 erg s−1 • Accompanied by glitches • Rapid initial decay in minutes – hours • Slow decay of days – years (Woods et al. 2004) 50 Giant flares Giant flares • Three sources detected • Power 1044 − 1047 erg s−1 Pulsations • Star pulsations (magnetosphere) 51 Mechanism of a burst (Beloborodov 2013) 52 6. Fast radio bursts Discovery • First burst detected 24th July 2001 – Parkes 64-m telescope • Published by Lorimer et al. 2007 • Debate about “Lorimer burst” or “peryton” • Originating from “microwave-ovens” • Other reported by Petroff in 2013 • Telescope: Parkes, Arecibo, GBT, ASKAP, CHIME, FAST, STARE2 • Every 6 months “quamtum leap” 53 Observed properties 1/2 • Duration of 1 ms → L = ct ∼ 105 − 106 m → compact sources • Repetition, > 20 repeating sources → can be majority repeating? • Repetition ms – s → pulsars? – no such source • Typical repetition after days → binary/precession models? • Pulse structure complex • Subpulse down frequency drifts • DM ∼ 100 − 2600, typical 300 − 400 • Luminosities 1038 − 1046 erg s−1 • Reduction by a beaming factor • Luminosity large for pulsars, but low for GRB 54 Observed properties 2/2 • Not clear association to SGR • Brighness temperatures ∼ 1036 K → coherent source • Detection range 300 MHz – 8 GHz, No LOFAR detection → hard spectral pulses • Linear polarization > 50 % • No polarization swing across pulse • Some FRBs constant polarization angle in all pulses • Large rotation measures 1 − 105 rad m−2 • Isotropic over sky • Rate ∼ 103 events per day (> 1 mJy) • Massive galaxies 55 Repeating FRB 121102 (z = 0.19) • DM ∼ 560 pc cm−3 • Establishing extragalactic/cosmological origin (Spitler et al. 2016) 56 Combines radio and X-ray detection – Galactic magnetar • CHIME & STARE2 • Soft-gamma-repeater SGR 1935+2154 • During its active phase • Magnetars are origin of, at least some, FRBs (Tavani et al. 2020) 57 FRB Effective Isotropic Luminosity (Nimmo et al. 2022) 58 Open Questions • Are there multiple species? • Where are they from? • What creates/produces them? (Zhang et al. 2018) 59 FRB models • Pulsar-like models • GRB-like models • Main energy source is magnetic energy (not spin-down energy) 60 List of FRB models (not all) 61 List of FRB models (not all) 62 List of FRB models (not all) 63 Probability of source of FRBs Observational facts – blue Speculations – grey Speculated multi-messenger – green (Zhang et al. 2020) 64 Conclusions to neutron stars • Neutron stars, pulsars, millisecond pulsars, magnetars, soft gamma repeaters, active X-ray pulsars, γ-ray sources, fast radio bursts • Observational and theoretical approaches • Large variety and uncertainty in emission processes of electromagnetic waves • Dynamics of the magnetosphere • Supergiant pulses and FRBs have same mechanism • Now is the time of first global magnetopsheric simulations 65