Star formation in galaxies is observed to be associated with gamma-ray emission, presumably from non-thermal processes connected to the acceleration of cosmic-ray nuclei and electrons. The detection of gamma rays from starburst galaxies by the Fermi Large Area Telescope (LAT) has allowed the determination of a functional relationship between star formation rate and gamma-ray luminosity. Since star formation is known to scale with total infrared (8-1000 $mu$m) and radio (1.4 GHz) luminosity, the observed infrared and radio emission from a star-forming galaxy can be used to quantitatively infer the galaxy's gamma-ray luminosity. Similarly, star-forming galaxies within galaxy clusters allow us to derive lower limits on the gamma-ray emission from clusters, which have not yet been conclusively detected in gamma rays.
In this study, we apply the functional relationships between gamma-ray luminosity and radio and IR luminosities of galaxies derived by the Fermi Collaboration to a sample of the best candidate galaxy clusters for detection in gamma rays in order to place lower limits on the gamma-ray emission associated with star formation in galaxy clusters. We find that several clusters have predicted gamma-ray emission from star formation that are within an order of magnitude of the upper limits derived in Ackermann et al. based on non-detection by Fermi-LAT. Given the current gamma-ray limits, star formation likely plays a significant role in the gamma-ray emission in some clusters, especially those with cool cores. We predict that both Fermi-LAT over the course of its lifetime and the future Cerenkov Telescope Array will be able to detect gamma-ray emission from star-forming galaxies in clusters.