  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.
