Modelling supermassive black hole growth: towards an improved sub-grid
  prescription
  Accretion onto supermassive black holes (SMBHs) in galaxy formation
simulations is frequently modelled by the Bondi-Hoyle formalism. Here we
examine the validity of this approach analytically and numerically. We argue
that the character of the flow where one evaluates the gas properties is
unlikely to satisfy the simple Bondi-Hoyle model. Only in the specific case of
hot virialised gas with zero angular momentum and negligible radiative cooling
is the Bondi-Hoyle solution relevant. In the opposite extreme, where the gas is
in a state of free-fall at the evaluation radius due to efficient cooling and
the dominant gravity of the surrounding halo, the Bondi-Hoyle formalism can be
erroneous by orders of magnitude in either direction. This may impose
artificial trends with halo mass in cosmological simulations by being wrong by
different factors for different halo masses. We propose an expression for the
sub-grid accretion rate which interpolates between the free-fall regime and the
Bondi-Hoyle regime, therefore taking account of the contribution of the halo to
the gas dynamics.
