  We have classified possible transonic solutions of galactic outflows in the
gravitational potential of the dark matter halo (DMH) and super massive black
hole (SMBH) under the assumptions of isothermal, spherically symmetric and
steady state. It is clarified that the gravity of SMBH adds a new branch of
transonic solutions with the transonic point in very close proximity to the
centre in addition to the outer transonic point generated by the gravity of
DMH. Because these two transonic solutions have substantially different mass
fluxes and starting points, these solutions may have different influences on
the evolution of galaxies and the release of metals into intergalactic space.
We have applied our model to the Sombrero galaxy and obtained a new type of
galactic outflow: a slowly accelerated transonic outflow through the transonic
point at very distant region ($\simeq 126$\ kpc). In this galaxy, previous
works reported that although the trace of the galactic outflow is observed by
X-ray, the gas density distribution is consistent with the hydrostatic state.
We have clarified that the slowly accelerating outflow has a gas density
profile quite similar to that of the hydrostatic solution in the widely spread
subsonic region. Thus, the slowly accelerating transonic solution cannot be
distinguished from the hydrostatic solution in the observed region ($\leq 25$\
kpc) even if slow transonic flow exists. Our model provides a new perspective
of galactic outflows and is applicable even to quiescent galaxies with inactive
star formation.
