Continuum correlations in accreting X-ray pulsars

Mikhail Gornostaev, Konstantin Postnov (SAI),Dmitry Klochkov (IAAT, Germany)

2015, MNRAS, 452, 1601

21.04.23International Conference on Particle Physics and Astrophysics,

Moscow-2015

21.04.23

Outline

• Motivating observations• 2D accretion column modeling• Spectral calculations: saturated

Comptonization + reflected emission• Conclusions

ICPPA, Moscow-2015

21.04.23

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

21.04.23

Observations

In all bright transient XRPs spectral hardness increases with luminosity and saturates above some value

Postnov, Gornostaev+’15ICPPA, Moscow-2015

21.04.23

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

21.04.23

Two models of the accretion columns.Boundary conditions

Shockwave

Decelerationzone

Magnetic field lines

Magnetic pole

Basko M. M., Sunyaev R. A.,1976, MNRAS, 175, 395

10

0 0 0

( ) 10

(0)

)

3

0

)

2

( (r r

v

v

F r rF

U

d

c

cm/s

ICPPA, Moscow-2015

21.04.23 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

21.04.23 ICPPA, Moscow-2015

Reduce to one 2D equation

Dimensionless variables0

0

/ /

/ /T T

T T

r S r c rv c

z S z c zv c

(cf. Davidson 1973, Wang & Frank 1981)

21.04.23 ICPPA, Moscow-2015

Filled-column geometry

z

Hollow-columngeometry,wall thickness is 0.1r0

(r0 is the radius of corresponding filled column)

21.04.23 ICPPA, Moscow-2015

Lines of equal optical depth

Filled column, accretion rate is 1017 g/s

Column appears as a cylinder wall!

21.04.23 ICPPA, Moscow-2015

Radial bolometric flux Fr(z) from filled accretion column

Lines from bottom to up correspond to mass accretion rate 2, 3, 5, 8, 12 x 1017 g/s

Photon modes in strong magnetic field

21.04.23 ICPPA, Moscow-2015

X

O

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• Extraordinary photons in proper plasma frame for ν<<νg

(Lyubarsky’86)

• With fixed total flux Ф• Take Ф(z)~Fr(z)/2

• Integrate along z

Saturated comptonization in strong magnetic field

21.04.23 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 rates2, 3, 5, 8, 12 (from bottom to up, respectively)• Right: the spectral hardness ratio HR as a function of mass accretion rate

21.04.23 ICPPA, Moscow-2015

Single-scattering Compton X-ray albedo from a NS atmosphere with strong magnetic field

• The electron number density is ne = 5 × 1025 cm−3, electron temperature T = 3 keV, magnetic field B = 3 × 1012 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 dashedlines, respectively. The cyclotron line is ignored

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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

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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 RNS = 10 km (squares) and RNS = 13 km (circles)

21.04.23 ICPPA, Moscow-2015

Hardness ratio of the total emission(direct plus reflected from the NS atmosphere)

from a hollow-cylinder accretion columnas a function of mass accretion rate

21.04.23 ICPPA, Moscow-2015

Conclusions

• Spectral hardness of transient accreting XRP increases with luminosity and saturates (decreases) above some value ~1037-38 erg/s

• Sidewall emission from optically thick accretion columns (saturated Comptonized spectra X-photons) always gets harder with Lx

• 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