Interpreting the Relation between the Gamma-Ray and Infrared Luminosities of Star-forming Galaxies

It has been found that there is a quasi-linear scaling relationship between the gamma-ray luminosity in GeV energies and the total infrared luminosity of star-forming galaxies, i.e., with 1. However, the origin of this linear slope is not well understood. Although extreme starburst galaxies can be regarded as calorimeters for hadronic cosmic-ray interaction and thus a quasi-linear scaling may hold, it may not be the case for low star formation rate (SFR) galaxies, as the majority of cosmic rays in these galaxies are expected to escape. We calculate the gamma-ray production efficiency in star-forming galaxies by considering realistic galaxy properties, such as the gas density and galactic wind velocity in star-forming galaxies. We find that the slope for the relation between gamma-ray luminosity and the infrared luminosity gets steeper for low infrared luminosity galaxies, i.e., , due to increasingly lower efficiency for the production of gamma-ray emission. We further find that the measured data of the gamma-ray luminosity is compatible with such a steepening. The steepening in the slope suggests that cosmic-ray escape is very important in low-SFR galaxies.