The gamma-ray / infrared luminosity correlation of star-forming galaxies

Context. Near a dozen star-forming galaxies have been detected in gamma-rays by the Fermi observatory in the last decade. A remarkable property of this sample is the quasi-linear relation between the gamma-ray luminosity and the star formation rate, obtained assuming that the latter is well traced by the infra-red luminosity of the galaxies. The non-linearity of this relation has not been fully explained yet. Aims. We aim at determining the biases derived from the use of the infrared luminosity as a proxy for the star formation rate, and shed light onto the more fundamental relation between the latter and the gamma-ray luminosity. We expect to quantify and explain some trends observed in this relation. Methods. We compile from the literature a near-homogeneous set of distances, ultraviolet, optical, infra-red, and gamma-ray fluxes for all known gamma-ray emitting star-forming galaxies. From these data we compute the infra-red and gamma-ray luminosities, and star formation rates. We determine the best-fitting relation between the latter two, and describe the trend using simple, population-oriented models for cosmic-ray transport and cooling. Results. We find that the gamma-ray luminosity-star formation rate relation obtained from infra-red luminosities is biased to shallower slopes. The actual relation is steeper than previous estimates, having a power-law index of 1.35 +- 0.05, in contrast to 1.23 +- 0.06. Conclusions. The unbiased gamma-ray luminosity-star formation rate relation can be explained at high star formation rates by assuming that the cosmic ray cooling region is kiloparsec-sized, and pervaded by mild to fast winds. Combined with previous results about the scaling of wind velocity with star formation rate, our work provides support to advection as the dominant cosmic ray escape mechanism in low-star formation rate galaxies.