Extragalactic Gamma-ray Background from Star-forming Galaxies: Will
  Empirical Scalings Suffice?
  Despite the influx of unprecedented-quality data from the Fermi Gamma-Ray
Space Telescope that have been collected over nine years of operation, the
contribution of normal star-forming galaxies to the extragalactic gamma-ray
background (EGRB) remains poorly constrained. Different estimates are
discrepant both their underlying physical assumptions and their results. With
several detections and many upper limits for the gamma-ray fluxes of nearby
starforming galaxies now available, estimates that rely on empirical scalings
between gamma-ray and longer-wavelength luminosities have become possible and
increasingly popular. In this paper we examine factors that can bias such
estimates, including: a) possible sources of nontrivial redshift dependence; b)
dependence on the choice of star-formation tracer; c) uncertainties in the
slope and normalisation of empirical scalings. We find that such biases can be
significant, pointing towards the need for more sophisticated models for the
star-forming galaxy contribution to the gamma-ray background, implementing
more, and more confident, physics in their buildup. Finally, we show that there
are large regions of acceptable parameter space in observational inputs that
significantly overproduce the gamma-ray background, implying that the observed
level of the background can yield significant constraints on models of the
average cosmic gamma-ray emissivity associated with star formation.
