Spectra of the accreting neutron stars boundary layers in the spreading layer model

1. Spectra of the accreting neutron stars boundary layers in the spreading layer model V. Suleimanov1,3 in collaboration with J. Poutanen2 1- Institut fuer Astronome und Astrophysik, Tuebingen, Germany; 2 - Oulu University, Finland; 3 - Kazan State University, Russia CEA Saclay 7 February 2008

2. Outlook • Introduction. Neutron stars and X-ray binaries. • Boundary layer – region between accretion disk and neutron star. Two approaches. • Spreading layer as a boundary layer. Basic results. • Atmospheres of the bursting neutron stars – the base to understanding of the local spreading layer. • Spectra of the spreading layers. Comparison with observations. • Conclusions

3. Neutron stars – main properties and short history M ≈ 1.4 MSun R ≈ 10 km Eg ≈ GM2 / R ~ 5 1053 erg ρ≈ 7 1014 g/cc First idea – L.Landau (1932) Neutron stars arise due to Supernova outbursts W. Baade, F. Zwicky (1934) Crab nebula (Chandra) ESN ~ 1053 erg ~ Eg (NS) Discovery of Pulsars - A. Hewish, J. Bell (1968)

4. Supernova (type II) – final of a massive star life Massive star evolve along supergiant branch up to SNII explosion

5. Supernova (type II) – final of a massive star life Massive star structure before explosion SNII explosion calculations (T. Janka, MPE) Reason – gravitational collapse of Fe core due to Neutronization Photodissociation and

6. Stellar remnants From Woosley et al. (2002) NSs – final stages of massive (from 8-12 to 25-40 MSun) stars

7. Stellar remnants – White Dwarfs and Neutron Stars Maximum -mass neutron star Brown dwarfs, Giant planets Neutronstars White dwarfs Maximum-mass white dwarf Minimum-mass neutron star

8. Life of a protoneutron star Protoneutron star cooling Due to neutrino - optically thick (R – 200 km →12 km, kT – 50 →5 MeV , t~50 s) - optically thin (kT – 5 → 0.12 - 0.03 MeV , t ~ 50 - 100 yr ) Due to electromagnetic radiation (t ~ 106 yr)

9. Neutron star structure Main problem – inner core Equation of State (EoS)

10. Zoo of NS inner core EoS Prohibited by General Relativity Universal low-mass curve Special family of low-mass strange stars Solution – M and R from observations!

11. Many faces of NS

13. Masses of NS – from binaries

14. Radii of NSs – from thermal emission NS in 47 Tuc (Heinke et al 2006) XDIN RX J1856-3754 (Trümper 2005) RNS ≈ 14.5 ± 1.7 km at M = 1.4 MSun

15. NS properties – from accreting NSs in close binary systems Bursters – luminosity near Eddington limit (see Lewin et al. 1993, Galloway et al. 2007, …) Problems – distance, chemical composition… Out Attempt Boundary Layers between accretion disc and NS in Low Mass X-ray Binaries

16. X-ray Binaries Low Mass High Mass M2< MSun Old systems (Pop. II) Secondary overfilled of the Roche lobe Atoll- and Z-sources, Bursters, Millisecond X-ray Pulsars M2>> MSun Young systems (Pop. I) Accretion from wind X-ray Pulsars

17. Low Mass X-ray Binaries (LMXB) • Close binary with neutron star as a primary and a red dwarf as a secondary. • Galactic bulge sources (Population II). Most of them are located near Galactic center. • Orbital periods – few hours. • Secondary overfilled the Roche lobe and a neutron star accretes matter. X-ray radiation due to accretion. • Brightest X-ray source – Sco X-1 is a LMXB. • Neutron stars in LMXB have a relatively weak (B~108 G) magnetic field. NO magnetosphere and accretion column. Accretion disk exists up to the neutron star surface.

19. Two types of LMXB 1) Bright (Z-sources). Luminosities – few x1037 – few x10 38 erg/s ~ 0.1-1 LEdd Relatively soft two-component spectra: relatively persistent accretion disk spectrum with kTmax ~1 keV and variable black body spectrum with kT~2 keV (Mitsuda et al 1984) Figure from Gilfanov et al (2003) (RXTE) 2) Low luminosity (atoll sources). Luminosities – few x 1036 erg/s ~ 0.01 – 0.05 LEdd Two spectral states: soft (look like a Z-source) and hard (look like an X-ray binary with a black hole e.g. Cyg X-1) Figure from Natalucci et al (2004) (BeppoSAX)

20. Horizontal branch Normal branch From Done and Gerlinski 2003 From Gilfanov et al 2003 Z source Atoll source

21. Boundary layer (BL) • Region between an accretion disk and a neutron star • In BL fast rotating (with the Keplerian velocity) accretion disk matter is decelerated to the neutron star rotation velocity. • Luminosity of the BL comparable to the accretion disk luminosity Size of BL is smaller than the accretion disk size. Therefore, effective temperature of BL is larger than the effective temperature of accretion disk. Hard black body component in the soft state of LMXB – a boundary layer spectrum ?

22. Spectra of Boundary Layers Figures from Gilfanov, Revnivtsev and Molkov (2003). They shown, that frequency resolved (pulsed) spectra are spectra of boundary layers.

23. Spectra of Boundary Layers Figures taken from Gilfanov, Revnivtsev and Molkov (2003). They shown that shape of boundary layer spectra are independent on luminosity. BL spectra are close to Planck spectrum with a color temperature 2.4 ± 0.1 keV

24. Theory of Boundary Layers “Classical” BL BL as a part of the accretion disk NO vertical (latitude) velocity component of the matter In this case Figure from Inogamov and Sunyaev (1999)

25. Theory of Boundary Layers BL as a spreading layer (SL) Picture suggested by Inogamov & Sunyaev (1999), below IS99 Matter has a significant latitude velocity component, spreading above the neutron star surface and decelerating due to friction at the neutron star surface (wind above the sea). Figures from Inogamov and Sunyaev (1999)

26. Kley, 1989 Fisker et al. 2005 Numerical calculations confirm this picture

27. We slightly modified the Inogamov-Sunyaev model. The GR effects and chemical composition were taken into account. Pseudo-Newtonian potential

28. Continuity equation Euler equation Energy equation Geometry of the problem Model suggestions

29. We obtained the same equations as IS99 with one exception Energy equation Input parameters of the model Model distributions

30. Surface density and temperature distribution of the spreading layers with luminosities L=0.1, 0.2, 04 and 0.8 LEdd along the latitude.

31. Scheme of the SL spectrum calculation • For each ring the model along height and emergent spectrum • SL are divided onto N rings • are calculated • 3. Spectra of the each rings are summed with all relativistic corrections

32. Basic equations Hydrostatic equilibrium Radiation transfer Radiation equilibrium - true-absorption coefficient (mainly free-free transitions) - Thomson electron scattering coefficient

33. X-ray bursting neutron star model atmospheres • X-ray bursting NSs – LMXBs with nuclear explosions at the neutron star surface • Close to Eddington limit during the burst • Burst duration ~10 sec, time between bursts ~1 day Figure from Pavlinsky et al (2001)

34. Compton scattering is very important! Photons which we observe are emitted at the depth - thermalization depth At this depth, electron scattering optical depth In the case of Thomson scattering, the radiation and the gas are weakly coupled in the surface layers of atmosphere → low surface temperature. If Compton scattering is taken into account, hard photons heat electrons at the surface up to T>Teff. This results in the emergent spectrum close to the diluted black body. Surface density which correspond to thermalization depth ~ 10 g/cm2

35. Diluted blackbody spectrum Bν– Planck function fc – color correction (hardness factor) Tc= fcTeff - color temperature fc ~(1.3 – 1.9) mainly depend on L / LEdd Pavlov et al. 1991

36. X-ray bursting NS model atmosphere spectra and temperature structures

37. SL structure along height 1) IS99, X-ray bursting NS 2) parameter of IS99 model Analogy with classical hydrodynamic boundary layers 3)

38. Temperature structure of the local SL models X-ray bursting NS (IS99) Second caseΣS=630 g/cm2 Second caseΣS=63 g/cm2 Third case

39. Spectra of local SL models from previous figure

40. Pavlov et al. (1991)

41. SL spectra slightly depend on the luminosity and the inclination angle to line of sight

42. Spectra of Boundary Layers Figures taken from Gilfanov, Revnivtsev and Molkov (2003). They shown that shape of boundary layer spectra are independent on luminosity. BL spectra are close to Planck spectrum with a color temperature 2.4 ± 0.1 keV

43. Comparison of the observed spectra of the BLs and the model spectra of the SL. Black circles – GX 340+0 in the normal branch, green circles – 5 Z and atoll sources in horizontal branch (Suleimanov & Poutanen 2006).

44. Main Idea fc Teff fc , T Tc=fcTeff Latitude, θ No dependence on distance! On chemical composition only (H or solar)

45. Allowed areas (shaded) for the NS mass and radii, which can have SLs with color temperatures 2.4 +/- 0.1 keV. Various theoretical mass-radius relations for neutron and strange stars are shown for comparison. Red dashed curve corresponds to the NS with the apparent radius 16.5 km (Suleimanov & Poutanen 2006).

47. X7 R=14.5 +/- 1.7 km (1.4 M_sun) Our Result R=14.9 +/- 1.5 km (1.4 M_sun) Contours at 68% (dotted curves), 90% (dashed curves), and 99% (long-dashed curves) confidence in the mass-radius plane derived for X7 (NS in 47 Tuc) by spectral fitting (Heinke et al. 06). Allowed area from our model and limitations from the apparent radius of RX J1856 and from the rotation period of B1937 are added.

48. Conclusions • Local spectra of the optically thick (ΣS > 100 g/cm2) spreading layers weakly depend on details of SL structure along height and close to X-ray bursting NS spectra with the same Teff , log g andY. • Integral spectra of the high luminosity spreading layers (LSL> 0.2 LEdd )are close to diluted Planck spectra. • Radiation spectra of the spreading layers on the surface of the neutron stars with stiff equations of state are compatible with the observed spectra of boundary layers inLMXBs.

49. Future work … 2D radiation hydrodynamic modeling - transition region between accretion disk and SL - vertical structure effects on global structure of SL - non-axisymmetric models - instabilities (QPO in LMXBs ?!)

50. The same accretion rate !