X-ray bursts and the equation of state

Transcription

1 X-ray bursts and the equation of state Juri Poutanen (Univ. of Oulu, Finland) with Valery Suleimanov, Klaus Werner (Tuebingen University), Jari Kajava, Joonas Nättilä, Outi-Marja Latvala (U. Oulu), Mikhail Revnivtsev (IKI, Moscow), Duncan Galloway (Monash Univ.)

2 Oulu

3 Santa Claus Oulu Turku

4 Plan Atmosphere models, color corrections Touchdown and cooling tail methods to measure neutron star M, R Theory vs observations

5 Basic equations (Kompaneets approximation) Hydrostatic equilibrium Radiation transfer Radiation equilibrium Compton scattering (Kompaneets equation) - true absorption opacity (mainly free-free transitions) - Thomson electron scattering opacity

6 Basic equations (exact Compton scattering) Radiation transfer Hydrostatic equilibrium Radiative equilibrium - true absorption opacity (mainly free-free transitions) - Klein-Nishina electron scattering opacity

7 - 6 chemical compositions: H, He, solar H/He with Z = 1, 0.3,0.1,0.01 Z sun - 3 surface gravities: log g = 14.0, 14.3 and 14.6 Model atmosphere calculations (Suleimanov, Poutanen, Werner 2011, A&A 527, A139 / 2012, A&A, 545, A120) - 20 relative luminosities l = L / L edd from tо 1.08 (super-eddington luminosities for Thomson cross-section) Dashed lines Kompaneets approximation Solid lines exact Compton scattering kernel

8 Color correction f c calculations Calculated spectra are redshifted and fitted by diluted blackbody (oneand two-parameters functions) (assuming M = 1.4 M sun ) in the PCA/ RXTE energy band (3-20) kev Minimizing deviations in photon number flux

9 Color correction f c calculations Dashed lines Kompaneets approximation Solid lines exact Compton scattering kernel differences are small at L/L edd < 0.8

10 Measuring neutron star parameters from the PRE bursts using the touchdown and cooling tail methods

11 Photospheric radius expansion (PRE) bursts = Super-Eddington fluxes Measurements of the Eddington flux and the blackbody radius at the cooling tail for sources with known distances allow us to get two constraints on the neutron star mass and radius. u = R S / R = 2GM / Rc 2

12 Often it is assumed that the Eddington flux is reached during the touchdown (when blackbody normalization reaches minimum and color temperature maximum). In addition to the blackbody radius at the cooling tail, one needs the color-correction to get the apparent radius at infinity. Often it is assumed that fc=1.4 Solution exists (two curves cross) only if

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14 Touchdown method Assumption: Eddington flux = touchdown flux However, The relation between touchdown flux and Eddington flux is not clear (e.g. electron opacity is assumed to be Thomson, while at 3 kev it is 93% of Thomson) Color correction in the tail is not a unique number. Measurements of the Eddington flux and the apparent area in the tail are decoupled. Not clear whether they are consistent with each other.

15 Cooling tail method The observed evolution of K -1/4 vs. F should look similar to the theoretical relation fc vs. F/FEdd K 1/4 = A f c (F / F Edd ) From the fits a more reliable estimate of the Eddington flux and apparent radius can be obtained. Two free parameters: A and FEdd. and we use now our theoretical dependences fc vs. F/FEdd

16 Examples

17 Cooling tails of PRE bursts from 4U Suleimanov et al. (2011) Crosses: Long, >150 sec, PRE burst during hard/low state on Nov 8, Diamonds: two short PRE bursts on Feb 23 and May 22, 2004 during soft state. Spectral evolution is spectacularly different!

18 M-R relation - 4U From the best-fit A and FEdd, we can get constraints on M and R if we assume some distance distribution (we take flat in kpc with gaussian tails). 1. Radius > 13.5 km at 90% confidence for any solar composition for M<2.3 solar. 2. Hydrogen-rich atmosphere is preferred. 3. Stiff EoS is preferred. Contours are elongated along TEdd=const track Suleimanov et al. (2011)

19 4U as seen by WFC I. 24 long PRE X-ray bursts have been detected by WFC at BeppoSAX (Kuulkers et al. 2003). 2. It has 50 times less effective area than 3. Spectral evolution is consistent with that seen by RXTE from a long bursts. data by Jean in t Zand!

20 Why the apparent area is different in different bursts? Influence of accretion on the burst apparent area and the spectra

21 Two states of LMXB Soft/high state - optically thick, cool region Hard/low state - optically thin, hot region Barret et al. 2000

22 Accretion geometry Hard state - hot flow / hot optically thin boundary layer Soft state - optically thick boundary layer

23 1. Accretion disk can blocks nearly 1/2 of the star. 2. Spreading of matter on NS surface affects the atmosphere structure increasing f c Inogamov & Sunyaev (1999) Suleimanov & Poutanen (2006) radiative acceleration/ gravitational radiative / effective Spectra are nearly diluted blackbodies with color correction f c =T c / T eff = 1.8

24 Other sources

25 K 2 /K bb normalizations ratio at =1/2 touchdown flux to the touchdown F per [10-9 ergs cm -2 s -1 ] 4U (a) K 2 /K (b) ! td [s] Hard X-ray colour Evolution of blackbody normalization depends strongly on persistent flux, time until touchdown, and position on a color-color diagram Soft X-ray colour

26 Bursts from 4U at different accretion high persistent low persistent flux used by Guver, Özel Poutanen et al. (2013, in preparation)

27 4U short high persistent flux and constraints using touchdown method (Guver et al. 2010) longer low persistent flux and constraints using the cooling tail method Neutron star radii determined from short bursts are underestimated by >50%

28 M - R constraints Guver et al 2010 K= 324, FEdd, -7 = 1.541, fc=1.4, X=0 D>3.9 kpc? D10= 0.58±0.19 Amazingly close to the assumed lower limit of 3.9 kpc!

29 A posteriori distributions of parameters for short bursts with various distance cutoff

30 M-R relation for 4U from the cooling tail method causality MS0 H Solar 619 Hz Neutron star mass M/M O SQM3 PAL6 AP4 MS1 GM3 He Neutron star radius R (km)

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33 Conclusions 1. An extended set of accurate model atmospheres for X-ray bursts covering large range of luminosities, various log g and chemical composition is computed. 2. Touchdown and cooling tail methods have been used for M-R determination, only the latter is reliable. 3. Spectral evolution K -1/4 vs. F in the hard state bursts is well described by the theory. Soft state PRE bursts from 4U and 4U (and other sources) do not show the evolution of K -1/4 vs. F predicted for a passively cooling neutron star, therefore they should not be used for M-R determination. 4. Current data are consistent with rather larger neutron star radii R>13.5 km, favoring stiff equation of state (consistent with existence of the 2M pulsars). Note: rotation is not included in the model!