  At present, all physical models of diffuse Galactic gamma-ray emission assume
that the distribution of cosmic-ray sources traces the observed populations of
either OB stars, pulsars, or supernova remnants. However, since H2-rich regions
host significant star formation and numerous supernova remnants, the morphology
of observed H2 gas should also provide a physically motivated, high-resolution
tracer for cosmic-ray injection. We assess the impact of utilizing H2 as a
tracer for cosmic-ray injection on models of diffuse Galactic gamma-ray
emission. We employ state-of-the-art 3D particle diffusion and gas density
models, along with a physical model for the star-formation rate based on global
Schmidt laws. Allowing a fraction, f_H2, of cosmic-ray sources to trace the
observed H2 density, we find that a theoretically well-motivated value f_H2 ~
0.20 -- 0.25 (i) provides a significantly better global fit to the diffuse
Galactic gamma-ray sky and (ii) highly suppresses the intensity of the residual
gamma-ray emission from the Galactic center region. Specifically, in models
utilizing our best global fit values of f_H2 ~ 0.20 -- 0.25, the spectrum of
the galactic center gamma-ray excess is drastically affected, and the
morphology of the excess becomes inconsistent with predictions for dark matter
annihilation.
