In recent years, $gamma$-ray emission has been detected from star-forming galaxies (SFGs) in the local universe, including M82, NGC 253, Arp 220 and M33. The bulk of this emission is thought to be of hadronic origin, arising from the interactions of cosmic rays (CRs) with the interstellar medium of their host galaxy. Distant SFGs are presumably also bright in $gamma$-rays. Although they would not be resolvable as point sources, distant unresolved SFG populations contribute $gamma$-rays to the extra-galactic $gamma$-ray background (EGB). Despite the wealth of high-quality all-sky EGB data collected over more than a decade of operation with the textit{Fermi}-LAT $gamma$-ray space telescope, the exact contribution of SFGs to the EGB remains unsettled. In this study, we model the $gamma$-ray emission from SFG populations and demonstrate that such emission can be characterized by just a small number of physically-motivated parameters. We further show that source populations would leave anisotropic signatures in the EGB, which could be used to yield information about the underlying properties, dynamics and evolution of CR-rich SFGs.
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