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Star-forming galaxies (SFGs) have been established as an important sourcepopulation in the extra-galactic $\gamma$-ray background (EGB). Their intensivestar-formation creates an abundance of environments able to accelerateparticles, and these build-up a rich sea of cosmic rays (CRs). Above GeVenergies, CR protons can undergo hadronic interactions with their environmentto produce $\gamma$-rays. SFGs can operate as CR proton "calorimeters", where alarge fraction of the CR energy is converted to $\gamma$-rays. However, CRsalso deposit energy and momentum to modify the thermal and hydrodynamicconditions of the gas in SFGs, and can become a powerful driver of outflows.Such outflows are ubiquitous among some types of SFGs, and have the potentialto severely degrade their CR proton calorimetry. This diminishes theircontribution to the EGB. In this work, we adopt a self-consistent treatment ofparticle transport in outflows from SFGs to assess their calorimetry. We use 1Dnumerical treatments of galactic outflows driven by CRs and thermal gaspressure, accounting for the dynamical effects and interactions of CRs. We showthe impact CR-driven flows have on the relative contribution of SFG populationsto the EGB, and investigate the properties of SFGs that contribute moststrongly.

Cosmic ray calorimetry in star-forming galaxy populations and implications for their contribution to the extra-galactic $\gamma$-ray background