Modeling Atmospheres of Neutron Stars

Transcription

1 Moeling Atmospheres of Neutron Stars Isolate NSs: solitary NSs or those in binaries without accretion Slava Zavlin (NASA/MSFC) The 363- Heraeus Seminar, Ba Honnef, May 5-9, 2006

2 Short history Chiu & Salpeter (964) an Tsuruta (964): thermal raiation from the surface of a hot NS may be a source of cosmic X-rays First etections with Einstein (978-8) an EXOSAT (983-86): mile-age PSRs B0656+4, Geminga an B central compact sources in the SNRs RCW 03, Puppis A, PKS a few AXPs since 99, X-ray stuies with ROSAT, ASCA, EUVE, BeppoSax, Chanra an XMM-Newton In total, thermal emission etecte from about 30 NSs: from the whole surface (atmospheres?) of cooling NSs from polar caps heate by relativistic particles streaming own onto the surface from pulsar s magnetosphere

3 Thermal vs. Nonthermal emission in pulsars of ifferent ages Nonthermal (magnetospheric) emission, ~ ~ t -β, β ~ 2 4 NSs cool own from T 0 K (at birth) to MK in 0.- Myr E opt opt Young active (< kyr): Mile-age (0-00 kyr): Ol (> Myr): nonthermal raiation thermal component from thermal emission from ominates; the whole surface; hot polar caps; Crab, B509-58, Vela, B0656+4, B055-5, 6-ms J , B Geminga, J B

4 Main questions Why is stuying thermal emission neee? What is the state of the NS surface? Gaseuos or liqui, or soli? What is the chemical composition of the NS surface? Hyrogen or heavier elements (e.g., iron)? What is the proper moel for the thermal raiation?

5 Why is stuying thermal emission neee? Comparing observe emission with theoretical moels T surf, B, R, M T surf (t) thermal evolution R, M constraints on EOS an internal structure surface chemical composition formation of NSs an their interaction with environment What is the state of the NS surface? It epens on T surf, B an chemical composition. For hyrogen, the surface is in a conense state if: T surf < 0 5 B = 0 3 G T surf < B = 0 4 G (Lai & Salpeter 997) T surf < 0 6 B = G

6 What is the chemical composition of the NS surface? Heavy elements or hyrogen? A small amount of H, surface ensity g/cm² total amount g, ue to accretion from ISM or fallback of material eecte uring the SNR explosion. Otherwise, heavier elements may be present. What is the proper moel for the thermal raiation? Whatever is the physical state of the surface, its raiation shoul not be that of a black boy.

7 Main aspects of the NS atmosphere moeling What s special about NS atmospheres? Why not to use stanar stellar atmosphere moels?. Enormous gravity at the surface (M.4 M, R 0 km) g 0 4 vs. 0 4 cm²/s for usual stars NS atmospheres are strongly compresse ρ vs. 0-7 g/cm³ height kt sur /m P g 0-0 vs. 0 8 cm stratification of chemical elements non-ieality effects (pressure ionization, smoothe spectral features)

8 2. Huge magnetic fiels, B = G E ce =.6 (B/0 2 G) kev» kt sur 0. kev, E 0. kev NS atmospheres are essentially anisotropic opacities epen on irection an polarization of raiation raiation is polarize an epens on B γ = E ce / (Z² Ry) = 850 Z 2 (B/0 2 G)» atomic structure is istorte by B increase of bining (ionization) energies of boun states I/(Z²Ry) ln²(γ/z²)», I H 0.2 kev at B = 0 3 G altere ionization equilibrium an equation of state

9 NS atmosphere moels with low magnetic fiels, B < G (millisecon pulsars, NS transients in quiescence) General scheme (Mihalas 978): (Romani 987, Zavlin et al. 996, Gänsike et al. 200, Zavlin & Pavlov 2002) raiative transfer in isotropic -D meium for specific raiative intensity I ( z, μ) μ I = k [ I S ], μ = cosθ = n r, y = ρ z y k = σ + α S J [ J B ] = σ + α k = I μ 2 total raiative opacity, scattering+absorption mean intensity source function Comptonization is not important at T < K

10 [ ] B J J f y k y α = 0 = = y J h J f y k = y B J Most common (iffusion) approach: no incient emission equilibrium solution ) ( ] [ ] [ 2 ) ( ) ( = μ μ μ μ I I J h the Eington factors (accounting for anisotropy of raiation): spectral (monochromatic) flux 4 J f y k F π = ) ( ] [, = y I J f μ μ

11 raiative equilibrium (electron conuctivity is not important) 0 4 μ I μ = σ [ ] SB eff T α J B - 0 = 0 hyrostatic equilibrium (raiative force is not important) P = k B N T = g y ionization equilibrium base on the occupation-probability formalism for non-ieal plasmas (e.g., Hummer & Mihalas 988)

12 raiative opacities: absorption ue to free-free, boun-free an boun-boun transitions the Thomson scattering on electrons k E -3

13 Moel input: T eff, M, R (or g ), chemical composition Moel output: F I = 4π h J spectral (monochromatic) flux at y = μ S k exp [ k x] μ y 0 0 y = 0 specific intensity atmospheric structure: T ( y), ρ( y)

14 Spectra of nonmagnetic NS atmospheres

15 Spectra of nonmagnetic NS atmospheres with various abunances of heavy elements

16 Angular epenences of specific intensities Fe raiation is anisotropic even in nonmagnetic case limb-arkening effect

17 NS atmosphere moels with strong magnetic fiels, B = G (all orinary pulsars, magnetars, raio-quiet INSs [?]) raiative transfer for two polarization moes, extra- an orinary ones, with ortogonal polarizations (Gnein & Pavlov 974) + = = 2 ) ( ), ( ) ( ) ( ) ( ) ( i i 2 i B I I k I y α σ μ n n n n n n n n ), (, ) ( i 2 n n n n = + = = σ σ σ α i k total raiative opacity, scattering+absorption raiative an hyrostatic equilibrium

18 Diffusion approximation: ] [ ] [ 2 3 B J J J J y D y α σ = ) ( 4 n n α π α = ), ( 4 2 n n n n = σ π σ μ μ μ μ ) ( 2,, sin cos = = Θ + Θ = k D k D D D D B B cos r B Moel output: specific intensity an spectral flux at = ΘB y x k J B I y exp 2 ] [ ] [ i i = + = μ σ α μ = 0 y μ μ 0 = I F

19 NS atmosphere moels with strong magnetic fiels, B = G

20 Angular epenence of raiation from a magnetize NS atmosphere: B r pencil -like structure along fan -like structure at larger angles B

21 proton cyclotron line B = 0 4 G electron cyclotron line B = 3 0 G atomic transitions T eff < K B=2 0 2 G

22 Iron magnetize NS atmosphere moels (Raagopal et al. 997)

23 More on hyrogen NS moels for B > G, fully ionize case: Özel 200, Zane et al. 200, Ho & Lai 200 stuying vacuum-polarization effects (Gnein et al. 977): conversion of normal moes of raiation in particular, it affects cyclotron lines (makes them very narrow) More on partially ionize hyrogen atmosphere moels: Ho et al. 2003, Ho & Lai 2004 spectral features ue to boun-free an boun-boun transitions First magnetize NS atmosphere moels for C, O, Ne chemical compositions (Mori et al. 2006)

24 Thermal emission as seen by a istant observer General case: F( E) = g r I( g r E) S 2 S μ [ exp( nhσ )] 2GM / 2 g r = [ 2 ] reshift parameter c R E observe (reshifte) energy S visible emitting area istance to the obect nonuniform surface temerature an magnetic fiel gravitational bening of photon traectories Doppler shifts of photon energies (for fast rotators) Small heate spots (polar caps): F( E) S a = g I( g r r E 2 μ, )

25 Gravitational bening of photon traectories 2GM / 2 g r = [ 2 ] c R the whole surface is visible if g r < 0.66

26 Effect of the Doppler shift Spectra from the whole surface of a nonmagnetize NS (iron atmosphere)

27 Light curves of raiation from a magnetize NS

28 Practical aspect: NS atmosphere vs. blackboy moel T bb / T atm 2-3 S atm / S bb

29 Successful applications of hyrogen atmosphere moels: young pulsars, Vela, J , B (0 30 kyr), whose thermal emission originates from the whole NS surface of T> MK millisecon an ol pulsars with thermal X-ray component emitte from heate polar caps, J , J , J , J , B , J compact central sources in the SNR Puppis A, RX J , an in the SNR CTA, RX J thermal emission from the whole NS surface transiently accreting NSs in X-ray binaries, Aql X-, Cen X-4, KS , 4U , MXB quiescent raiation is interprete as emitte from the whole NS surface ue to heat release in the compresse material hyrogen atmosphere moels can be useful for istinguishing between transiently accreting NSs an black holes, in quiescence

30 XSPEC coes: NSA, NSAGRAV spectral fluxes for a wie range of surface temperature, magnetic fiel, surface gravitational acceleration

31 NS atmospheres o not work: mile-age pulsars ( kyr), Geminga, PSRs , PSR J9-627 (toay s talk) ol raio-quiet isolate NSs, RX J , J , J These have lower surface temperatures, ( ) MK, an high magnetic fiels atmospheres may not exist

32 Problems, future work boun-boun transitions in superstrong fiel B > 0 4 G, when the lines get into observable X-ray range molecules an molecular chains in strong magnetic fiels reliable moels for partially ionize atmospheres for for various chemical compositions raiative transfer approach base on two polarization moes is inaccurate for partially ionize plasma solving the raiative transfer equations for the four Stokes parameters using the polarizability tensor constracte with ai of the Kramers-Kronig relation thin atmosphere moels optically thick only at lower energies

33 From atmospheres to conense surfaces solis an liquis in strong magnetic fiels phase transition from atmospheres to conense surface reliable moels for emissivity of conense surface Everyone is welcome to contribute...