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Thermal Emission from Isolated Neutron Stars

Thermal Emission from Isolated Neutron Stars. R. Turolla Dept. of Physics and Astronomy, University of Padova , Italy. Outline. Are INSs thermal emitters ? Observations of INSs Importance of thermal emission The role of magnetic field and gravity The state of the NS surface

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Thermal Emission from Isolated Neutron Stars

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  1. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Thermal Emission from Isolated Neutron Stars R. Turolla Dept. of Physics and Astronomy, University of Padova, Italy

  2. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Outline • Are INSs thermal emitters ? • Observations of INSs • Importance of thermal emission • The role of magnetic field and gravity • The state of the NS surface • Emission from NS atmospheres • Non-magnetic models • Magnetic models • Emission from “bare”NSs • The case of SXTs • Models vs. observations Lecture 1 Lecture 2

  3. Page, Geppert & Weber (2006) The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Some Like It Hot • NSs are born very hot (T ≈ 1011 K) and progressively cool down • Surface temperature drops quickly and then stays at ≈ 105 – 106 K for about 1 Myr • Thermal emission at ≈ 100 eV, L ≈ 4πR2σT4≈1031– 1032 erg/s Dima Yakovlev’s lectures Heating processes: magnetic dissipation, inflowing magnetospheric currents, accretion

  4. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 INSs in the X-rays • At present > 110 INSs detected in X-rays • Large majority are “normal” (rotation powered) radiopulsars (~ 90 sources, including HB and MPSs) • Radio-silent (quasi), X/γ-ray bright INSs • Anomalous X-ray pulsars and Soft γ-ray repeaters (AXPs and SGRs, the magnetar candidates) • Central compact objects in SNRs (CCOs) • Rotating radio transients (RRaTs) • X-ray dim neutrons stars (XDINSs) • Geminga and Geminga-like objects • “Isolated” NSs in binaries: Soft X-ray transients (SXTs) • Thermal emission detected in about 40 sources The Neutron Star Zoo

  5. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Rotation and Magnetism • Newborn neutron stars are fast rotators (P0 ≈ 10-3 – 10-2 s) • Large dipole magnetic field (B ≈ 1012 G in “normal” PSRs) • Spin-down by magneto-dipolar losses (oblique rotator in vacuo) (1 + sin2α) fromself-consistentmagnetosphericmodeling (Spitkovsky 2006)

  6. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Measuring P and Ṗ is crucial Phase-coherent timing Strictly periodic SGR 1833 (Esposito et al. 2011)

  7. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Thermally-emitting INSs (XDINSs) - I • Soft X-ray sources, seven known (hence the nickname “Magnificent Seven”, or M7) • Slow rotators, P ~ 3-11 s, Ṗ  10-13 s/s • Bp ~ 1.5-3.5x1013 G, τ ~ a fewMyr, τkin ~ 5-10 timesshorter • Faint optical counterparts • Close-by, D  150-500 pc • Radio-silent • Intrinsically radio-quiet ? Misaligned PSRs ? (Kondratiev et al. 2009)

  8. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Thermally-emitting INSs (XDINSs) - II • Thermal spectrum, T ~ 50-100 eV, RBB ~ 5-10 km • Broad absorption features @ 300-700 eV • Proton cyclotron/Atomic transitions ? (Turolla 2009, Kaplan & Van Kerkwijk 2011) • Steady, long-term spectral changes in RX J0720 • Precession (Haberl et al 2006) ? Glitch (Van Kerkwijk et al. 2007, Hohle et al. 2012) ?

  9. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Magnetar Candidates (SGRs/AXPs) - I • About 20 known • Short (0.1-1 s), energetic (1039-1041erg/s) bursts and giant flares (up to 1047erg/s) • Variable (transient) persistent emission (LX  1032-1036 erg/s) • P ~ 2-12 s, huge Ṗ  10-10-10-13 s/s • Bp  1013-1015 G, τ 1-10 kyr, LX >> Ė • Thermal + power-law spectrum (PL extends up to 200 keV), T ~ 0.5 keV, RBB < 1 km

  10. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Magnetar Candidates (SGRs/AXPs) - II • Three “low-field” magnetarsrecently discovered (Rea et al. 2010, 2012, 2013) • Bp ≤ 1013 G, τ 1 -10 Myr, • Ultra-strong, localfieldmeasured in SGR 0418 (~ 1015 G, Tiengo et al. 2013) • Magnetar-like activity detected in two RPPs (Gavriil et al. 2008, Levin et al. 2010)

  11. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Radio Pulsars (including HBPSRs) • More than 2000 discovered in the radio, ~ 90 in the X-rays • Wide range of P ( 1ms-10 s) and Bp ( 108-1014 G) • X-ray emission • Thermal (~ 0.1 keV), from • hot spots (MSPs, relatively old PSRs) • the entire cooling surface (relatively young PSRs) • Non-thermal, from the magnetosphere • High-B PSRs are “normal” RPPs with a field in the magnetar range (~ 20 with Bp > 5x1013 G) but no detected magnetar-like activity

  12. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Rotating Radio Transients (RRaTs) • About 80 known, “normal” radio pulsars with an exceedingly high nulling fraction (> 99%, Burke-Spolaor 2013), i.e. they emit sporadic, single radio pulses (McLaughlin et al. 2006) • P ~ 0.5-7 s, B ~ 1012-1014 G, τ~ 0.1-3 Myr • PSR J1819-1458 (P = 4.3 s, B = 5x1013G) detected in X-rays (McLaughlin et al. 2007, Miller et al. 2013) • Thermal spectrum (T ~ 140 eV, RBB ~ 8 km) • One (two ?) absorption feature @ ~ 1 keV • LX > Ė (?) • Bright PWN (Rea et al. 2009)

  13. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Central Compact Objects (CCOs) • INS X-ray sources at the centre of SNRs, 8 found • Young (SNR age τSNR< 104yr) • Radio-silent, no counterpart at other wavelengths • Steady, thermal spectrum, quite large pulsed fraction, absorption lines in some sources • P and Ṗ measured (or constrained) in 3 sources (Pup A, Kes 79, 1E 1207; Gotthelf 2010, Halpern & Gotthelf 2010, 2011) • P ~ 0.1 -0.4 s • B  3-10x1010 G, the “anti-magnetars” • LX> Ė, τ>> τSNR

  14. X-ray emission ubiquitous over the P-Ṗdiagram Detected from objects with extremely different Ages: from young Crab-like to old PSRs Magnetic fields: from low-B ms PSRs to magnetars Kondratiev et al. (2009) The Many Faces of Compact Stars - Barcelona, September 22-26 2014

  15. LX = Ėrot from Becker (2009) The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Different mechanisms powering X-ray emission SGR+AXPs XDINSs HBPSRs RRaTs Rotation Cooling Magnetism

  16. total non-thermal thermal Old, > 1 Myr: no magnetospheric activity (XDINSs) Young, < 1 kyr: non-thermal component dominates (Crab, PSR 1509-58) Middle-aged, 10-100 kyr: thermal emission from the star surface (Vela, Geminga) The Many Faces of Compact Stars - Barcelona, September 22-26 2014 INS spectrum: thermal plus non-thermal component(magnetospheric, if rotation-powered LNT~Ė ~ t-β, β≈2-4) + SXTs

  17. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Thermal Emission from INS • Thermal radiation from a NS first detected by EXOSAT and Einstein (’80s) • Many more sources found by ROSAT (’90s), Chandra and XMM-Newton • At present about 40 sources known: PSRs, AXPs and SGRs, CCOs, RRaTs, XDINSs, Geminga and Geminga-like objects • “Isolated” NSs in binaries: Soft X-ray Transients (SXTs)

  18. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Tapping the NS surface - I Comparison of observations with theoretical models can provide Ts, Bs, chemical composition, R (and M) Consider a simple, idealized case: the NS surface emits a blackbody at TBB (≈ 100 eV) and neglect GR Fitting the observed X-ray spectrum with a BB

  19. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 provides Ts and (RBB/D)2, and, if distance is known, RBB • Beware that RBBis the linear size of the emitting region (projected onto the sky) and not necessary coincides with the NS radius RBB R

  20. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Tapping the NS Surface - II • Real life is a trifle more complicated… • Isolated NSs are highly magnetized (B ≈ 1011-1015 G) and very compact (R ≈ 10-15 km ≈ 3 RS) • The strong B field affects • Photon propagation • Surface temperature distribution • Local emission • Gravity effects are important • Ray bending • Gravitational redshift

  21. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Photons in a Magnetized Medium • Magnetized plasma is anisotropic and birefringent, radiative processes sensitive to polarization state • Two normal, elliptically polarized modes in the magnetized “vacuum+cold plasma” The extraordinary (X) and ordinary (O) modes

  22. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 B EO k EX O mode: electric field inthe k-B plane X mode: electric field perpendicular to the k-Bplane The opacities of the O mode are little affected by B, those of the X mode are substantially reduced at E << Ec Scattering cross section for the X and O modes (Ventura 1979)

  23. Greenstein & Hartke (1983) The Many Faces of Compact Stars - Barcelona, September 22-26 2014 NS Thermal Maps • Electrons move much more easily along B than across B • Thermal conduction is highly anisotropic inside a NS: Kpar >> Kperpuntil EF >> hνcor ρ >> 104(B/1012 G)3/2 g/cm3 • EnvelopescaleheightL ≈ 10 m << R, B ~ const and heat transport locally 1D

  24. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Core centered dipole Core centered quadrupole

  25. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Gravity Effects - I • NSs are highly relativistic objects • GM/Rc2~ 0.15 (M/M)(R/10 km)-1 • (J/Mc)/(GM/c2) ~ 4x10-4 (P/1 s)-1 (M/M)-1(R/10 km)2 (the Kerr solution does not describe spacetime outside a rotating star though) • Schwarzschild spacetime • Radiation emitted at frequency νatthe NS surface (r = R) is redshifted (Δν/ν≈ 0.2) • For BB radiation (uniform T on the surface)

  26. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Gravity Effects - II • R is the circumferential radius (i.e. Lcirc= 2πR for a localobserveratrest). An observeratinfinitymeasures a radius • The luminosity at infinity is lower • For a non-uniform surface temperature compute the (monochromatic) fluxfrom dS = R2sinθdθdφ (rememberthatthereis a single raywhichleavesdS and reach the observer) 2 4

  27. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 More Than Meets the Eye • Oops, light rays are not straight lines ! • Because of light bending, the ray which hits your eye leaves dS at an angle α ≠ θ More than half the surface is visible • The total flux is obtained by integrating over the visible part of the emitting region • Dependence of αon θsomehowcomplicated. Simple, accurate approximation (Beloborodov 2002)

  28. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 The terminator is at α = π/2, cos θF = (1-2GM/Rc2)-1 R = 15 km M = 1.4 M No gravity 112° LOS 90°

  29. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 LOS Hot spot

  30. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 STEP 2 Compute emission from each surface patch STEP 3 GR ray-tracing to obtain the spectrum at infinity STEP 1 Specify viewing geometry and B-field topology; compute the surface temperature distribution STEP 4 Predict lightcurve and phase-resolved spectrum Compare with observations

  31. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 What is the correct model for surface thermal emission ?

  32. Fe H condensation (Lai 2001) FeC He condensation (Medin & Lai 2006, 2007) H Fe The Many Faces of Compact Stars - Barcelona, September 22-26 2014 A “Hard” Surface ? • NS surface composition: either H (accreted from ISM or from fallback of SN material) or heavy elements (C, Ne, Fe) • Under typical conditions surface layers are in gaseous state: NS atmosphere • For sufficiently low T and large B (and depending on composition) the surface can be in a condensed state: “bare” NS adapted from Turolla et al (2004) Whatever the state of the surface, the emitted thermal radiation is NOT a blackbody

  33. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 NS Atmospheres • For a NS: M ~ 1.4 M, R ~ 10 km • Huge surface gravity, g = GM/R2 ≈ 1014 cm/s2 • Pressure scale-height, H ~ kTs/mpg ≈ 1 cm • Large densities, ρ ≈ 0.01 – 10 g/cm3 Very different from atmospheres around normal stars In NSs 108 G < B < 1015G Magnetic effects important if Ece> kT, Eion → B > 1010 (T/106 K) G

  34. z n Iν(z,μ) θ The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Low-B Atmospheres • H << R → plane-parallel approximation • Isotropic medium: P=P(z), T=T(z),… • Radiation field: monochromatic intensity Iν(z,μ) (μ=cosθ)

  35. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Radiative transfer equation total opacity (absorption plus scattering) Hydrostatic equilibrium Radiative energy equilibrium + EOS, ionization balance,…

  36. Zavlin & Pavlov (2002) The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Opacity depends on density, temperature and chemical composition Free-free, free-bound, bound-bound transitions Thomson scattering (σν = σT) κν ~ ν-3

  37. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Specify model parameters: M, R (or g) and L (or Teff = [L/4πR2σB]1/4); chemical composition Solve transfer equation, hydrostatic and energy balance; dz → dτ = -σρdz(0 < τ < τmax» 1) RTE integro-differential: moment methods, Λ-iteration Obtain Iν(τ,μ), T(τ), ρ(τ) Compute emergent flux Model atmospheres investigated e.g. in Romani (1987), Zavlin et al. (1996), Rajagopal & Romani (1996), Gänsicke, Braje & Romani (2002), Pons et al. (2002)

  38. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Non-magnetic Spectra g = 2.4x1014 cm s-2 g = 2.4x1014 cm s-2 Zavlin & Pavlov (2002)

  39. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 H, He spectra are typically broader (harder) than the blackbody at Teff Fe spectra are closer to a blackbody but show many lines and edges Because of the frequency-dependent opacity (κν~ ν-3) higher-energy photons decouple in the deep layers which are hotter Emerging spectrum like the superposition of blackbodies at different temperatures

  40. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Magnetized Atmospheres • Magnetized plasma is anisotropic and birefringent, radiative processes sensitive to polarization state • Two normal, elliptically polarized modes in the magnetized “vacuum+cold plasma”: ordinary and extraordinary • Radiative transfer for both modes • Heat transfer in the crust mainly along B → surface temperature inhomogeneous

  41. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Opacities are different for the two modes and depend on n·B/B Assume B along the z-axis (n·B/B = μ) Radiative transfer equations Hydrostatic and radiative energy equilibrium Fix g, Teff, chemical composition, B and obtain

  42. Ionized H Proton cyclotron line The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Magnetic Spectra Not too different from non-magnetic models. Magnetic opacities higher: spectra more BB-like Zavlin & Pavlov (2002)

  43. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 • Ionized, H atmospheres investigated e.g. in Shibanov et al. (1992), Pavlov et al. (1994; 1995), Zavlin et al. (1995), Zane et al. (2001), Ho & Lai (2001) • Ionization affected by B: at the atoms binding energy increases and their size along B decreases. Light elements which are fully ionized at low B are not in NS atmospheres • H (e.g. Ho et al. 2003; 2008)and heavier elements (Z < 10) (Mori & Hailey 2006; Mori & Ho 2007) models with partial ionization

  44. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 hydrogen Mori & Ho (2007) Ho et al (2008) • For B > 1013 G models need to account for vacuum polarization and mode switching • Magnetized models are “local”: B and Tchange on thesurface

  45. The way a metallic mirror works ! The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Condensed Surface Commonplace: the surface of a body at temperature T always emits a blackbody at T In general the emissivity is or where α(ρ)are the absorbitivity (reflectivity) In a metal conduction electrons are unable to oscillate in response to an incident wave with ν > νpe: the wave is absorbed, α = 1 and blackbody emission The opposite occurs below νpe: the wave is reflected, ρ ~ 1, α~ 0 and no emission

  46. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 • The condensed surface works much in the same way (after all it is made of iron ) • Zero-pressure density of the condensate: ρs≈ 560 AZ3/5B126/5 g/cm3 • Plasma frequency in the surface layers: hνpe ≈ 0.7Z1/5B123/5(ρ/ρs)1/2keV • Emissivity strongly suppressed at ν ≲ νpe (Lenzen & Trümper 1978, Brinkmann 1980) • NSs with condensed surface are cold: hν ≈ kT ≈ 100 eV, soft X-ray/UV-opticalspectrumdepressedwrt a blackbody

  47. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Spectra from a Condensed Surface Compute the emissivity in a highly magnetized medium (Turolla et al. 2004; Pons et al. 2005; Van Adelsberg et al. 2005) Potekhin (2014) Free ions Fixed ions

  48. Bare NS spectra - fixed ions (Turolla, Zane & Drake 2004) The Many Faces of Compact Stars - Barcelona, September 22-26 2014 X-ray spectra (0.1 – 2 keV) close to a blackbody in shape but depressed by a factor of ~ 3

  49. The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Absorption Features - I • Detection of spectral “lines” is crucial: information on chemical composition, B, … • And M/R ! If the physical process responsible for the line is known, the line energy (in the lab) is known and the ratio Eline,∞/Eline = (1-2GM/Rc2)1/2 gives M/R • Broad absorption features observed in the thermal spectrum of several INSs (XDINSs, with the exception of RX J1853.5-3754, the RRAT PSR J1819-1458, SGR 0418+5729, the CCO 1E 1207.4-5209 and PSR J1740+1000) • Multiple lines and (phase/long-term) line variability reported in a few sources

  50. RX J0720.4-3125 (Haberl et al 2004) The Many Faces of Compact Stars - Barcelona, September 22-26 2014 Absorption Features - II • No convincing explanation for the features exists (and their origin is likely different in different INS classes…) • Consider the XDINSs (and possibly the RRAT PSR J1819-1458) • proton cyclotron lines (e.g. Zane et al. 2001) • Ec,p → B in fair agreement with the spin-down measure • need an atmosphere • cannot work for multiple lines: higher harmonics strongly suppressed • Atomic transitions in light (H, He) elements (e.g. Van Kerkwijk & Kaplan 2007) • Etrans→ B in fair agreement with the spin-down measure • need an atmosphere • cannot work for sources with larger Eline Van Kerkwijk & Kaplan (2007)

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