1. Continuum correlations in accreting X-ray pulsars Mikhail Gornostaev, Konstantin Postnov (SAI), Dmitry Klochkov (IAAT, Germany) 2015, MNRAS, 452, 1601 22.12.2015 International Conference on Particle Physics and Astrophysics, Moscow-2015

2. 22.12.2015 Outline Motivating observations 2D accretion column modeling Spectral calculations: saturated Comptonization + reflected emission Conclusions ICPPA, Moscow-2015

3. 22.12.2015 Rossi X-ray Time Explorer (1995-2012) All-Sky Monitor (ASM) 1-12 keV Continuous monitoring Bright transient XRP EXO 2030+375, GX304−1, 4U 0115+63, V 0332+63, A 0535+26 and MXB 0656−072) Credit: MIT/NASA ICPPA, Moscow-2015

4. 22.12.2015 Observations In all bright transient XRPs spectral hardness increases with luminosity and saturates above some value Postnov, Gornostaev+’15 ICPPA, Moscow-2015

5. 22.12.2015 Accretion columns At low accretion rates – braking by Coulomb interaction with NS atmosphere At high accretion rates – braking by radiation (Davidson’73, Basko & Sunyaev’75, Wang & Frank’81… Mushtukov+’15) ICPPA, Moscow-2015

6. 22.12.2015 Two models of the accretion columns. Boundary conditions Shock wave Deceleration zone Magnetic field lines Magnetic pole Basko M. M., Sunyaev R. A., 1976, MNRAS, 175, 395 cm/s ICPPA, Moscow-2015

7. 22.12.2015 ICPPA, Moscow-2015 Basic equations (cylindrical geometry) steady-state momentum equation for accretion braking by radiation with energy density U S = ρv is the accreting matter flux energy equation radiation transfer equation in the diffusion approximation mass continuity equation

8. 22.12.2015 ICPPA, Moscow-2015 Reduce to one 2D equation Dimensionless variables (cf. Davidson 1973, Wang & Frank 1981)

9. 22.12.2015 ICPPA, Moscow-2015 Filled-column geometry Hollow-column geometry, wall thickness is 0.1r 0 (r 0 is the radius of corresponding filled column)

10. 22.12.2015 ICPPA, Moscow-2015 Lines of equal optical depth Filled column, accretion rate is 10 17 g/s Column appears as a cylinder wall!

11. 22.12.2015 ICPPA, Moscow-2015 Radial bolometric flux F r (z) from filled accretion column Lines from bottom to up correspond to mass accretion rate 2, 3, 5, 8, 12 x 10 17 g/s

12. Photon modes in strong magnetic field 22.12.2015 ICPPA, Moscow-2015 X O

13. 22.12.2015 ICPPA, Moscow-2015 Extraordinary photons in proper plasma frame for ν<<ν g (Lyubarsky’86) With fixed total flux Ф Take Ф(z)~F r (z)/2 Integrate along z Saturated comptonization in strong magnetic field

14. 22.12.2015 ICPPA, Moscow-2015 Spectra of accretion columns (in the accreting plasma rest-frame) Left: the spectrum of sidewall emission from optically thick filled-cylinder accretion column, as seen by the local observer, for mass accretion rates 2, 3, 5, 8, 12 (from bottom to up, respectively) Right: the spectral hardness ratio HR as a function of mass accretion rate

15. 22.12.2015 ICPPA, Moscow-2015 Single-scattering Compton X-ray albedo from a NS atmosphere with strong magnetic field The electron number density is n e = 5 × 10 25 cm −3, electron temperature T = 3 keV, magnetic field B = 3 × 10 12 G, photon incident angle to the magnetic field π/ 4 (NB weak dependence on the incident angle!) Extraordinary and ordinary photon spectra are shown by the solid and dashed lines, respectively. The cyclotron line is ignored

16. 22.12.2015 ICPPA, Moscow-2015 Doppler boosting  significant reflection from the neutron star surface Fraction of the reflected component (hard) in the total spectrum decreases with accretion rate  effective spectral softening

17. 22.12.2015 ICPPA, Moscow-2015 Spectra of accretion columns with account for radiation reflected from NS atmosphere Left: the total spectrum of direct sidewall and reflected from the NS atmosphere from the optically thick filled accretion column for mass accretion rates (from bottom to up, respectively) Right: the hardness ratio HR of the total spectrum. Shown are calculations for the NS radius R NS = 10 km (squares) and R NS = 13 km (circles)

18. 22.12.2015 ICPPA, Moscow-2015 Hardness ratio of the total emission (direct plus reflected from the NS atmosphere) from a hollow-cylinder accretion column as a function of mass accretion rate

19. 22.12.2015 ICPPA, Moscow-2015 Conclusions Spectral hardness of transient accreting XRP increases with luminosity and saturates (decreases) above some value ~10 37-38 erg/s Sidewall emission from optically thick accretion columns (saturated Comptonized spectra X-photons) always gets harder with L x Addition of the reflected emission from NS surface allows to explain observations Even with account for reflection, hollow columns should be harder and saturate at higher accretion rates than filled columns