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. $L_{\gamma}\propto L_{\rm IR}^{\alpha}$ 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.
