  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.
