Transonic galactic wind model including stellar feedbacks and application to outflows in high/low-$z$ galaxies

Galactic winds play a crucial role in the ejection of the interstellar medium (ISM) into intergalactic space. This study presents a model that classifies possible transonic solutions of galactic winds in the gravitational potential of the dark matter halo and stellar component under spherically symmetric and steady assumptions. Our model includes injections of mass and energy resulting from supernovae feedback along a flow line. The mass flux in galactic winds is a critical factor in determining the acceleration process of the flow and revealing the impact of galactic winds on galaxy evolution. We apply the transonic galactic wind model to the observed outflow velocities of star-forming galaxies to estimate the mass flux. Dividing the mass flux by the star formation rate (SFR) yields the mass loading rate (and mass loading factor), which indicates the entrainment effect of the ISM by the hot gas flow. Our results demonstrate that the mass loading rate is inversely correlated with galaxy mass and SFR. In less massive galaxies (stellar mass $\sim 10^{7-8} M_\odot$), the mass loading rate exceeds unity, indicating effective ejection of the ISM into intergalactic space. However, in massive galaxies (stellar mass $\sim 10^{10-11} M_\odot$), the mass loading rate falls below unity, meaning that the mass flux cannot exceed the injected mass by supernovae, thus resulting in the ineffective ejection of the ISM.