An Empirical Determination of the Dependence of the Circumgalactic Mass Cooling Rate and Feedback Mass Loading Factor on Galactic Stellar Mass

Using our measurements of the H$\alpha$ emission line flux originating in the cool (T $\sim10^4$ K) gas that populates the halos of galaxies, we build a joint model to describe mass of the cool circumgalactic medium (CGM) as a function of galactic stellar mass ($10^{9.5} < ({\rm M_*/M}_\odot) < 10^{11}$) and environment. Because the H$\alpha$ emission correlates with the main cooling channel for this gas, we are able to estimate the rate at which the CGM cools and becomes fuel for star formation in the central galaxy. We describe this calculation, which uses our observations, previous measurements of some critical CGM properties, and modeling of the cooling mechanism using the \cloudy modeling suite. We find that the mass cooling rate is larger than the star formation rates of the central galaxies by a factor of $\sim 4 - 90$, empirically confirming that there is sufficient fuel to resolve the gas consumption problem and that feedback is needed to avoid collecting too much cold gas in galaxies. We find excellent agreement between our estimates of both the mass cooling rates and mass loading factors and the predictions of independent theoretical studies. The convergence in results that we find from several completely different treatments of the problem, particularly at the lower end of the galactic mass range, is a strong indication that we have a relatively robust understanding of the quantitative effects of feedback across this mass range.