Region of the anomalous compression under Bondi-Hoyle accretion

We investigate the properties of an axisymmetric non-magnetized gas flow without angular momentum on a small compact object, in particular, on a Schwarzschild black hole in the supersonic region near the object; the velocity of the object itself is assumed to be low compared to the speed of sound at infinity. First of all, we see that the streamlines intersect (i.e., a caustic forms) on the symmetry axis at a certain distance $r_x$ from the center on the front side if the pressure gradient is neglected. The characteristic radial size of the region, in which the streamlines emerging from the sonic surface at an angle no larger than $\theta_0$ to the axis intersect, is $\Delta r= r_x\theta^2_0/3.$ To refine the flow structure in this region, we numerically compute the system in the adiabatic approximation without ignoring the pressure. We estimate the parameters of the inferred region with anomalously high matter temperature and density accompanied by anomalously high energy release.