One of the most active fields of research of modern-day astrophysics is that
of massive black hole formation and co-evolution with the host galaxy. In these
investigations, ranging from cosmological simulations, to semi-analytical
modeling, to observational studies, the Bondi solution for accretion on a
central point mass is widely adopted. In this work we generalize the classical
Bondi accretion theory to take into account the effects of the gravitational
potential of the host galaxy, and of radiation pressure in the optically thin
limit. Then, we present the fully analytical solution, in terms of the
Lambert-Euler W-function, for isothermal accretion in Jaffe and Hernquist
galaxies with a central black hole. The flow structure is found to be sensitive
to the shape of the mass profile of the host galaxy. These results and the
formulae that are provided, mostly important the one for the critical accretion
parameter, allow for a direct evaluation of all flow properties, and are then
useful for the above mentioned studies. As an application, we examine the
departure from the true mass accretion rate of estimates obtained using the gas
properties at various distances from the black hole, under the hypothesis of
classical Bondi accretion. An overestimate is obtained from regions close to
the black hole, and an underestimate outside a few Bondi radii; the exact
position of the transition between the two kinds of departure depends on the
galaxy model.Comment: 18 pages, 6 figures, submitted to ApJ, comments welcom
