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We carry out three-dimensional computations of the accretion rate onto an object (of sizeR_sinkand massm) as it moves through a uniform medium at a subsonic speedv_∞. The object is treated as a fully absorbing boundary (e.g., a black hole). In contrast to early conjectures, we show that for an accretor with$R_{\mathrm{sink}}\ll R_A=2\mathit{Gm}/v_{\infty }^2$in a gaseous medium with adiabatic indexγ= 5/3, the accretion rate is independent of Mach number and is determined only bymand the gas entropy. Our numerical simulations are conducted using two different numerical schemes via the Athena++ and Arepo hydrodynamics solvers, which reach nearly identical steady-state solutions. We find that pressure gradients generated by the isentropic compression of the flow near the accretor are sufficient to suspend much of the surrounding gas in a near-hydrostatic equilibrium, just as predicted from the spherical Bondi–Hoyle calculation. Indeed, the accretion rates for steady flow match the Bondi–Hoyle rate, and are indicative of isentropic flow for subsonic motion where no shocks occur. We also find that the accretion drag may be predicted using the Safronov number, Θ =R_A/R_sink, and is much less than the dynamical friction for sufficiently small accretors (R_sink≪R_A).

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, RA. 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 RA ≪ 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 RA ≈ 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 RA ≫ 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 RA. That exploration also reveals the minimum size of the simulation domain needed to accurately capture the deflection of incoming streamlines due to gravity.

We conduct a long-time-scale ($5000\,$ d) 3D simulation of a common-envelope event with a $2\, {\rm M}_{\odot }$ red giant and a $1\, {\rm M}_{\odot }$ main-sequence companion, using the moving-mesh hydrodynamic solver manga. Starting with an orbital radius of $52\, \mathrm{ R}_{\odot }$, our binary shrinks to an orbital radius of $5\, \mathrm{ R}_{\odot }$ in $200\,$ d. We show that over a time-scale of about $1500\,$ d, the envelope is completely ejected, while 80 per cent is ejected in about $400\,$ d. The complete ejection of the envelope is solely powered by the orbital energy of the binary, without the need for late-time reheating from recombination or jets. Motivated by recent theoretical and observational results, we also find that the envelope enters a phase of homologous expansion about $550\, \rm d$ after the start of our simulation. We also run a simplified 1D model to show that heating from the central binary in the envelope at late times does not influence the ejection. This homologous expansion of the envelope would likely simplify calculations of the observational implications such as light curves.