  We have categorized possible transonic solutions of galactic outflows in the
gravitational potential of DMH and SMBH using the isothermal, spherically
symmetric and steady model. We conclude that the gravitational potential of
SMBH generates a new transonic branch while Tsuchiya et al. (2013) concluded
that the gravitational potential of DMH forms one transonic solution. Because
these two transonic solutions have different mass fluxes and starting points,
these solutions will make different influences to the star formation rate, the
evolution of galaxies, and the chemical evolution of the intergalactic medium.
Therefore, we conclude that the influence of galactic outflows to the
intergalactic medium depends not only on the mass distribution but also on the
selected transonic solution. In addition, we have estimated range of parameters
(KDMH; KBH) for actual galaxies. Moreover, it may be possible to estimate the
galactic mass distributions of DMH and SMBH applying the model to the observed
profile of the outflow velocity. Although it is difficult to determine the
velocity of hot gas in the galactic halos from the current X-ray observations,
but the next-generation X-ray observatory will be able to detect the detailed
profiles of outflow velocities.
