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 . L _ { \gamma } \propto L _ { IR } ^ { \alpha } with \alpha \simeq 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 . \alpha \rightarrow 1.6 , 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 .