  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.
