  The classical Bondi model is adopted to study accretion onto the finite
luminous region around the central massive black hole (MBH) in an elliptical
galaxy. Unlike Bondi (1952), we define the boundary conditions at a certain
finite radius ($r_f$) instead of at the infinity and examine the variation of
solutions for a simple case. In the following, we consider the special case of
an MBH at the center of a Hernquist galaxy and involve the gravity and
luminosity of its own galaxy. Our results in the first part show that kinetic
energy at the final radius is ignorable even for not so far away from the
center. Moreover, the mass accretion rate will be approximately equal to its
Bondi value if the final radius ($r_f$) becomes about 2-3 orders of magnitude
larger than semi-Bondi radius, i.e. $GM/c_{sf}^2$ (where $M$ and $c_{sf}$ are
the mass of the central object and the sound speed at $r_f$). In the second
part, adding the two extra forces of gravity and radiation in the momentum
equation let us know that the maximum possible of accretion rate increases with
a greater characteristic linear density of galaxy and lower radiation. e.g.:
