Bondi or not Bondi: the impact of resolution on accretion and drag force
  modelling for Supermassive Black Holes
  Whilst in galaxy-size simulations, supermassive black holes (SMBH) are
entirely handled by sub-grid algorithms, computational power now allows the
accretion radius of such objects to be resolved in smaller scale simulations.
In this paper, we investigate the impact of resolution on two commonly used
SMBH sub-grid algorithms; the Bondi-Hoyle-Lyttleton (BHL) formula for accretion
onto a point mass, and the related estimate of the drag force exerted onto a
point mass by a gaseous medium. We find that when the accretion region around
the black hole scales with resolution, and the BHL formula is evaluated using
local mass-averaged quantities, the accretion algorithm smoothly transitions
from the analytic BHL formula (at low resolution) to a supply limited accretion
(SLA) scheme (at high resolution). However, when a similar procedure is
employed to estimate the drag force it can lead to significant errors in its
magnitude, and/or apply this force in the wrong direction in highly resolved
simulations. At high Mach numbers and for small accretors, we also find
evidence of the advective-acoustic instability operating in the adiabatic case,
and of an instability developing around the wake's stagnation point in the
quasi-isothermal case. Moreover, at very high resolution, and Mach numbers
above $\mathcal{M}_\infty \geq 3$, the flow behind the accretion bow shock
becomes entirely dominated by these instabilities. As a result, accretion rates
onto the black hole drop by about an order of magnitude in the adiabatic case,
compared to the analytic BHL formula.
