Free-fall accretion and emitting caustics in wind-fed X-ray sources

In wind-fed X-ray binaries the accreting matter is Compton cooled and falls freely onto the compact object. The matter has a modest angular momentum $l$ and accretion is quasi-spherical at large distances from the compact object. Initially small non-radial velocities grow in the converging supersonic flow and become substantial in the vicinity of the accretor. The streamlines with $l>(GMR_*)^{1/2}$ (where $M$ and $R_*$ are the mass and radius of the compact object) intersect outside $R_*$ and form a two-dimensional caustic which emits X-rays. The streamlines with low angular momentum, $l<(GMR_*)^{1/2}$, run into the accretor. If the accretor is a neutron star, a large X-ray luminosity results. We show that the distribution of accretion rate/luminosity over the star surface is sensitive to the angular momentum distribution of the accreting matter. The apparent luminosity depends on the side from which the star is observed and can change periodically with the orbital phase of the binary. The accretor then appears as a `Moon-like' X-ray source.