  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. 
Transonic Galactic Outflows and Their Influences to the Chemical   Evolution of Galaxies and Intergalactic Space