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Anisotropy of X-ray bursts from neutron stars with concave accretion disks

Emission from neutron stars and accretion disks in low-mass X-ray binaries is not isotropic. The non-spherical shape of the disk as well as blocking of the neutron star by the disk and vice versa cause the observed flux to depend on the inclination angle of the disk with respect to the line of sight. This is of special importance for the interpretation of Type I X-ray bursts, which are powered by the thermonuclear burning of matter accreted onto the neutron star. Because part of the X-ray burst is reflected off the disk, the observed burst flux depends on the anisotropies for both direct emission from the neutron star and reflection off the disk. This influences measurements of source distance, mass accretion rate, and constraints on the neutron star equation of state. Previous studies made predictions of the anisotropy factor for the total burst flux, assuming a geometrically flat disk. Recently, detailed observations of two exceptionally long bursts (so-called superbursts) allowed for the first time for the direct and the reflected burst flux to each be measured, as opposed to just their sum. The ratio of the reflected and direct flux (the reflection fraction) was much higher than what the anisotropies of a flat disk can account for. We create numerical models to calculate the anisotropy factors for different disk shapes, including concave disks. We present the anisotropy factors of the direct and reflected burst flux separately, as well as the anisotropy of the persistent flux. Reflection fractions substantially larger than unity are produced in case the inner accretion disk steeply increases in height, such that part of the star is blocked from view. Such a geometry could possibly be induced by the X-ray burst, if X-ray heating causes the inner disk to puff up.