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Inverse Compton Contribution to the Star-Forming Extragalactic Gamma-Ray Background

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 from 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 a one-zone model for a single star-forming galaxy, assuming supernovae power the acceleration of cosmic rays. 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 use our template for galactic IC luminosity to find the cosmological contribution of star-forming galaxies to the EGB. For all of our models, we find 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_cr p_ism \rightarrow π_0 \rightarrow γγ); even at the highest Fermi energies, IC is subdominant. Moreover, the flatter IC spectrum increases the high-energy signal of the pionic+IC sum, bringing it into better agreement with the EGB spectral index observed by Fermi . Partial calorimetry ensures that the overall IC signal is well constrained, with only modest uncertainties in the amplitude and spectral shape for plausible model choices. Partial calorimetry of cosmic-ray electrons should hold true in both normal and starburst galaxies, and thus we include starbursts in our calculation. 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.