Flow Morphology of a Supersonic Gravitating Sphere

Stars and planets move supersonically in a gaseous medium during planetary engulfment, stellar interactions and within protoplanetary disks. 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 3-D Athena++ hydrodynamic calculations for a large range of parameters. For $R_A\ll R$, 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 $R_A\approx R$, 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 $R_A\gg R$, 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.