Stochastic star formation and a (nearly) uniform stellar initial mass function

Recent observations indicate a lower Hα to FUV ratio in dwarf galaxies than in brighter systems, a trend that could be explained by a truncated and/or steeper initial mass function (IMF) in small galaxies. However, at low star formation rates (SFRs), the Hα to FUV ratio can vary due to stochastic sampling even for a universal IMF, a hypothesis that has, prior to this work, received limited investigation. Using SLUG, a fully stochastic code for synthetic photometry in star clusters and galaxies, we compare the Hα and FUV luminosity in a sample of 450 nearby galaxies with models drawn from a universal Kroupa IMF and a modified IMF, the integrated galactic initial mass function (IGIMF). Once random sampling and time evolution are included, a Kroupa IMF convolved with the cluster mass function (CMF) reproduces the observed Hα distribution at all FUV luminosities, while a truncated IMF as implemented in current IGIMF models underpredicts the Hα luminosity by more than an order of magnitude at the lowest SFRs. We conclude that the observed luminosity is the result of the joint probability distribution function of the SFR, CMF, and a universal IMF, consistent with parts of the IGIMF theory, but that a truncation in the IMF in clusters is inconsistent with the observations. Future work will examine stochastic star formation and its time dependence in detail to study whether random sampling can explain other observations that suggest a varying IMF.