  In many investigations involving accretion on a central point mass, ranging
from observational studies to cosmological simulations, including
semi-analytical modelling, the classical Bondi accretion theory is the standard
tool widely adopted. Previous works generalised the theory to include the
effects of the gravitational field of the galaxy hosting a central black hole,
and of electron scattering in the optically thin limit. Here we apply this
extended Bondi problem, in the general polytropic case, to a class of new
two-component galaxy models recently presented. In these models, a Jaffe
stellar density profile is embedded in a dark matter halo such that the total
density distribution follows a $r^{-3}$ profile at large radii; the stellar
dynamical quantities can be expressed in a fully analytical way. The
hydrodynamical properties of the flow are set by imposing that the gas
temperature at infinity is proportional to the virial temperature of the
stellar component. The isothermal and adiabatic (monoatomic) cases can be
solved analytically, in the other cases we explore the accretion solution
numerically. As non-adiabatic accretion inevitably leads to an exchange of heat
with the ambient, we also discuss some important thermodynamical properties of
the polytropic Bondi accretion, and provide the expressions needed to compute
the amount of heat exchanged with the environment, as a function of radius. The
results can be useful for the subgrid treatment of accretion in numerical
simulations, as well as for the interpretation of observational data.
