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.
