2013ApJ...773..104C

Fermi has resolved several star-forming galaxies, but the vast majority of the star-forming universe is unresolved, and thus contributes to the extragalactic gamma-ray background (EGB). Here, we calculate the contribution of star-forming galaxies to the EGB in the Fermi range from 100 MeV to 100 GeV due to inverse-Compton (IC) scattering of the interstellar photon field by cosmic-ray electrons. We first construct one-zone models for individual star-forming galaxies assuming that supernovae power the acceleration of cosmic rays. We develop templates for both normal and starburst galaxies, accounting for differences in the cosmic-ray electron propagation and in the interstellar radiation fields. For both types of star-forming galaxies, the same IC interactions leading to gamma rays also substantially contribute to the energy loss of the high-energy cosmic-ray electrons. Consequently, a galaxy's IC emission is determined by the relative importance of IC losses in the cosmic-ray electron energy budget ("partial calorimetry"). We calculate the cosmological contribution of star-forming galaxies to the EGB using our templates and the cosmic star formation rate distribution. For all of our models, we find that the IC EGB contribution is almost an order of magnitude less than the peak of the emission due to cosmic-ray ion interactions (mostly pionic p_crp_ism⟶ π⁰ ⟶ γγ); even at the highest Fermi energies, IC is subdominant. The flatter IC spectrum increases the high-energy signal of the pionic+IC sum, bringing it closer to the EGB spectral index observed by Fermi. Partial calorimetry ensures that the overall IC signal is relatively well constrained, with only uncertainties in the amplitude and spectral shape for plausible model choices. We conclude with a brief discussion on how the pionic spectral feature and other methods can be used to measure the star-forming component of the EGB.