Flow morphology of a supersonic gravitating sphere

Stars and planets move supersonically in a gaseous medium during planetary engulfment, stellar interactions, and within protoplanetary discs. For a nearly uniform medium, the relevant parameters are the Mach number and the size of the body, R, relative to its accretion radius, R-A. Over many decades, numerical and analytical work has characterized the flow, the drag on the body, and the possible suite of instabilities. Only a limited amount of work has treated the stellar boundary as it is in many of these astrophysical settings, a hard sphere at R. Thus, we present new 3D athena++ hydrodynamic calculations for a large range of parameters. For R-A << R, the results are as expected for pure hydrodynamics with minimal impact from gravity, which we verify by comparing to experimental wind tunnel data in air. When R-A approximate to R, a hydrostatically supported separation bubble forms behind the gravitating body, exerting significant pressure on the sphere and driving a recompression shock, which intersects with the bow shock. For R-A >> R, the bubble transitions into an isentropic, spherically symmetric halo, as seen in earlier works. These two distinct regimes of flow morphology may be treated separately in terms of their shock stand-off distance and drag coefficients. Most importantly for astrophysical applications, we propose a new formula for the dynamical friction, which depends on the ratio of the shock stand-off distance to R-A. That exploration also reveals the minimum size of the simulation domain needed to accurately capture the deflection of incoming streamlines due to gravity.