  Using a sample of nearly half a million galaxies, intersected by over 8
million lines of sight from the Sloan Digital Sky Survey Data Release 12, we
extend our previous study of the recombination radiation emitted by the gaseous
halos of nearby galaxies. We identify an inflection in the radial profile of
the H$\alpha$+N[{\small II}] radial emission profile at a projected radius of
$\sim 50$ kpc and suggest that beyond this radius the emission from ionized gas
in spatially correlated halos dominates the profile. We confirm that this is a
viable hypothesis using results from a highly simplified theoretical treatment
in which the dark matter halo distribution from cosmological simulations is
straightforwardly populated with gas. Whether we fit the fraction of halo gas
in a cooler (T $= 12,000$ K), smooth ($c = 1$) component (0.26 for galaxies
with M$_* = 10^{10.88}$ M$_\odot$ and 0.34 for those with M$_* = 10^{10.18}$
M$_\odot$) or take independent values of this fraction from published
hydrodynamical simulations (0.19 and 0.38, respectively), this model
successfully reproduces the radial location and amplitude of the observed
inflection. We also observe that the physical nature of the gaseous halo
connects to primary galaxy morphology beyond any relationship to the galaxy's
stellar mass and star formation rate. We explore whether the model reproduces
behavior related to the central galaxy's stellar mass, star formation rate, and
morphology. We find that it is unsuccessful in reproducing the observations at
this level of detail and discuss various shortcomings of our simple model that
may be responsible.
