H$\alpha$ Emission and the Dependence of the Circumgalactic Cool Gas
  Fraction on Halo Mass
  We continue our empirical study of the emission line flux originating in the
cool ($T\sim10^4$ K) gas that populates the halos of galaxies and their
environments. Specifically, we present results obtained for a sample of nearly
half a million individual galaxies, groups, and clusters of galaxies,
intersected by more than two million SDSS lines of sight at projected
separations of up to a quarter of the virial radius. Adopting simple power law
relationships between the circumgalactic (CGM) cool gas fraction and either the
halo or stellar mass, we present expressions for the CGM cool gas fraction as a
function of either halo or stellar mass, $f_{\rm cool}(M_h) =
(0.25^{+0.07}_{-0.06}) \times (M_h/10^{12}M_\odot)^{(-0.39^{+0.06}_{-0.07})}$
or $f_{\rm cool}(M_{*}) = (0.28^{+0.07}_{-0.06}) \times (M_{\rm
*}/10^{10.0}M_\odot)^{(-0.33\pm 0.06)}$. Where we can compare, our results are
consistent with previous constraints from absorption line studies, our own
previous emission line work, and simulations. The cool gas can be the dominant
baryonic CGM component, comprising a fraction as high as $> 90\%$ of halo
gaseous baryons, in low mass halos, $M_h\sim$ $10^{10.5} M_\odot$, and a minor
fraction, $<$ 5\%, in groups and clusters, $M_h > 10^{14} M_\odot$.
