Thermal Emission from Isolated Neutron Stars

Transcription

1 Thermal Emission from Isolated Neutron Stars R. Turolla Dept. of Physics, University of Padova, Italy IWARA09 - Maresias, October

2 Outline Are INSs thermal emitters? Observations of INSs Importance of thermal emission The state of the NS surface (gaseous/solid-liquid) Emission from NS atmospheres Non-magnetic models Magnetic models Emission from bare NSs Model spectra and observations IWARA09 - Maresias, October

3 Some Like It Hot NSs are born very hot (T K) and progressively cool down Surface temperature drops quickly and then stays at K for about 1 Myr Thermal emission at 100 ev, L erg/s Page, Geppert & Weber (2006) Heating processes: magnetic dissipation, inflowing magnetospheric currents, accretion IWARA09 - Maresias, October

4 INS Observations 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 (the magnetar candidates), CCOs, RRaTs, XDINSs, Geminga and Geminga-like objects Isolated NSs in binaries: SXTs IWARA09 - Maresias, October

5 INS spectrum: thermal plus non-thermal component (magnetospheric, if rotation-powered L NT ~ Ė ~ t -β, β 2-4) total non-thermal thermal Young, < 1 kyr: non-thermal component dominates (Crab, PSR ) Middle-aged, kyr: thermal emission from the star surface (Vela, Geminga) Old, > 1 Myr: no magnetospheric activity (XDINSs) + SXTs IWARA09 - Maresias, October

6 Tapping the NS surface Comparison of observations with theoretical models provides T s, B s, chemical composition, R (and M) T s (t) thermal evolution R, M NS matter equation of state Chemical composition NS formation and interaction with surrounding medium What is the correct model for thermal emission? IWARA09 - Maresias, October

7 A Hard Surface? NS surface composition: either H (accreted from ISM or from fallback of SN material) or adapted from Turolla et al (2004) heavy elements (C, Ne, Fe) Fe H condensation (Lai 2001) Under typical conditions surface layers are in gaseous state: NS atmosphere For sufficiently low T and large B (and Fe depending on composition) the H surface can Fe be in a condensed state: bare NS Whatever the state of the surface, the emitted thermal radiation is NOT a blackbody C He condensation (Medin & Lai 2006, 2007) IWARA09 - Maresias, October

8 NS Atmospheres Very different from atmospheres around normal stars For a NS: M ~ 1.4 M, R ~ 10 km Huge surface gravity, g = GM/R cm/s 2 Pressure scale-height, H ~ kt s /m p g 1 cm Large densities, ρ g/cm 3 In NSs 10 8 G < B < G Magnetic effects important if E ce > kt, E ion B > G IWARA09 - Maresias, October

9 Low B Atmospheres H «R plane-parallel approximation Isotropic medium: P=P(z), T=T(z), Radiation field: monochromatic intensity I ν (z,μ) (μ=cosθ) z θ n I ν (z,μ) IWARA09 - Maresias, October

10 IWARA09 - Maresias, October Radiative transfer equation total opacity (absorption plus scattering) Hydrostatic equilibrium g dz dp Radiative energy equilibrium , ) ( d I J B J S d J at ) ( S I z I + EOS, ionization balance,

11 Opacity depends on density, temperature and chemical composition Free-free, free-bound, bound-bound transitions Thomson scattering (σ ν = σ) κ ν ~ ν -3 Zavlin & Pavlov (2002) IWARA09 - Maresias, October

12 Specify model parameters: M, R (or g) and L (or T eff = [L/4πR 2 σ B ] 1/4 ); chemical composition Solve transfer equation, hydrostatic and energy balance; dz dτ = -σρdz (0 < τ < τ max» 1) RTE integro-differential: moment methods, Λ-iteration Obtain I ν (τ,μ), T(τ), ρ(τ) Compute emergent flux F 1 1 ( 0) 2 di (0, ) Model atmosperes investigated e.g. in Romani (1987), Zavlin et al. (1996), Rajagopal & Romani (1996), Gänsicke, Braje & Romani (2002), Pons et al. (2002) IWARA09 - Maresias, October

13 Non-magnetic Spectra Zavlin & Pavlov (2002) IWARA09 - Maresias, October

14 H, He spectra are typically broader (harder) than the blackbody at T eff Fe spectra are closer to a blackbody but show many lines and edges Because of the frequency-dependent opacity (κ ν ~ ν -3 ) higher-energy photons decouple in the deep layers which are hotter Emerging spectrum like the superposition of blackbodies at different temperatures IWARA09 - Maresias, October

15 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 IWARA09 - Maresias, October

16 IWARA09 - Maresias, October 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, T eff, chemical composition, B and obtain 1,2 ), ( ) ( ), ( ) ( ) ( ) ( ) ( ) ( i I d B I z I j j i j i i i i ] ) (0, ) (0, [ 2 (0) 1 1 (2) (1) I I d F

17 Magnetic Spectra Ionized H Not too different from non-magnetic models. Magnetic opacities higher: spectra more BB-like Proton cyclotron line E cp B 0.63 kev G Zavlin & Pavlov (2002) IWARA09 - Maresias, October

18 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) Partial ionization complicated even for H (e.g. Ho et al. 2003; 2008); models for heavier elements coming (Mori & Ho 2007) For B > B QED = 4.4x10 13 G model need to account for vacuum polarization and mode switching Magnetized models are local : B and T change on the surface IWARA09 - Maresias, October

19 Condensed Surface Commonplace: the surface of a body at temperature T always emits The a way blackbody a metallic at T mirror works! j ( n) ( n) B ( T) In general the emissivity is or j ( ) [1 ( )] B ( T) where α, ρ are the absoptivity, n n reflectivity In a metal conduction electrons are unable to oscillate in response to an incident wave with ν > ν pe : the wave is absorbed, α = 1 and blackbody emission The opposite occurs below ν pe : the wave is reflected, ρ ~ 1, α ~ 0 and no emission IWARA09 - Maresias, October

20 The condensed surface works much in the same way (after all it is made of iron ) Zero-pressure density of the condensate: ρ s 560AZ -3/5 B 12 6/5 g/cm 3 Plasma frequency in the surface layers: hν pe 0.7Z 1/5 B 12 3/5 (ρ/ρ s ) 1/2 kev Emissivity strongly suppressed at ν ν pe (Lenzen & Trümper 1978, Brinkmann 1980) NSs with condensed surface are cold: hν kt 100 ev, soft X-ray/UV-optical spectrum depressed wrt a blackbody IWARA09 - Maresias, October

21 Spectra from a Condensed Surface Compute the Bare reflectivity NS spectra - fixed in ions a highly (Turolla, Zane magnetized & Drake 2004) medium (Turolla et al. 2004; Pons et al. 2005; Van Adelsberg et al. 2005) X-ray spectra (0.1 2 kev) close to a blackbody in shape but depressed by a factor of ~ 3 IWARA09 - Maresias, October

22 Models and Observations H atmosphere models work for youngish PSRs (10-30 kyr, T > 10 6 K): Vela, J , B Do not work for older, cooler PSRs: Geminga, , H atmosphere models work for SXTs in quiescence: Aql X-1, omega Cen, Do not work for the XDINSs Models of emission from a condensed surface work for the XDINSs IWARA09 - Maresias, October

23 Future Perspectives Detailed X-ray spectroscopy (and X-ray polarimetry) Multiband optical/uv observations More detailed modelling of condensed surface emission H atmospheres including molecules, He atmospheres, partial ionization for heavy elements Beyond the normal mode description: radiative transfer for the 4 Stokes parameters IWARA09 - Maresias, October

24 Soft X-ray Transients SXTs: a subset of the low-mass X-ray binaries (LMXBs, compact object+low mass star); many found in globular clusters Large X-ray outbursts (weeks, L X erg/s) followed by quiescent phases (L X erg/s) Outbursts driven by accretion instabilities Accretion switched off in quiescence IWARA09 - Maresias, October

25 Quiescent Emission Thermal + power-law spectra, kt ~ kev, Γ ~ 1-2, L pl /L tot < 0.1 for L tot ~ erg/s (PL may be absent) NSs in Aql SXTs X-1 too old to retain formation heat (Campana et al. 1998) Accretion heats them up! Heat is deposited in the crust by nuclear reactions and then transferred to the (cold) core Stationary state attained in ~ 10 4 yr (Haensel & Zdunik 1990; Bildstein & Rutledge 2000) IWARA09 - Maresias, October

26 Measuring NS Radii in SXTs In quiescence SXTs behave much like isolated cooling NSs There are advantages, however: The magnetic field is low (it has been buried by accretion), B G The surface layers are nearly pure H (metals settle below the photosphere because of gravity, Bildstein 1990) The surface is at same T Being in GCs the distance is fairly well known IWARA09 - Maresias, October

27 One can use unmagnetized, H, constant T atmosphere models to fit the thermal component Source omega Cen (Chandra) omega Cen (XMM) R (km/d) D (kpc) kt eff, (ev) % % 67 2 Ref. Rutledge et al (2002) Gendre et al (2003) M % Tuc X % M % Gendre et al (2003) Heinke et al (2006) Becker et al (2003) IWARA09 - Maresias, October