The Starburst Contribution to the Extra-Galactic Gamma-Ray Background

Cosmic ray protons interacting with gas at the mean density of the interstellar medium in starburst galaxies lose energy rapidly via inelastic collisions with ambient nuclei. The resulting pions produce secondary electrons and positrons, high-energy neutrinos, and gamma-ray photons. We estimate the cumulative gamma-ray emission from starburst galaxies. We find a total integrated background above 100 MeV of F_gamma ~ 10^{-6} GeV/cm^2/s/sr and a corresponding specific intensity at GeV energies of nuI_nu ~ 10^{-7} GeV/cm^2/s/sr. Starbursts may thus account for a significant fraction of the extra-galactic $\gamma$-ray background. We show that the FIR-radio correlation provides a strong constraint on the gamma-ray emission from starburst galaxies because pions decay into both gamma-rays and radio-emitting electron/positron pairs. We identify several nearby systems where the potential for observing gamma-ray emission is the most favorable (M82, NGC 253, and IC 342), predict their fluxes, and predict a linear FIR-gamma-ray correlation for the densest starbursts. If established, the FIR-gamma-ray correlation would provide strong evidence for the ``calorimeter'' theory of the FIR-radio correlation and would imply that cosmic rays in starburst galaxies interact with gas at approximately the mean density of the interstellar medium (ISM), thereby providing an important constraint on the physics of the ISM in starbursts.