  Recent observations indicate a lower Halpha to FUV ratio in dwarf galaxies
than in brighter systems, a trend that could be explained by a truncated and/or
steeper IMF in small galaxies. However, at low star formation rates (SFRs), the
Halpha 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 Halpha 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 reproduces the observed Halpha distribution at all FUV
luminosities, while a truncated IMF as implemented in current IGIMF models
underpredicts the Halpha 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, cluster mass function, 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.
