Stochasticity, a variable stellar upper mass limit, binaries and star formation rate indicators

Using our Binary Population And Spectral Synthesis (bpass) code we explore the effects on star formation rate indicators of stochastically sampling the stellar initial mass function (IMF), adding a cluster-mass-dependent stellar upper mass limit and including binary stars. We create synthetic spectra of young clusters and star-forming galaxies and compare these to observations of Hα emission from isolated clusters and the relation between Hα and far-ultraviolet (FUV) emission from nearby galaxies. We find that observations of clusters tend to favour a purely stochastic sampling of the IMF for clusters less than 100 M⊙, rather than the maximum stellar mass being dependent on the total cluster mass. It is more difficult to determine whether the same is true for more massive clusters. We also find that binary stars blur some of the observational differences that occur when a cluster-mass-dependent stellar upper mass limit is imposed when filling the IMF. The effect is greatest when modelling the observed Hα-to-FUV star formation rate ratios in galaxies. This is because mass transfer and merging of stars owing to binary evolution create more massive stars and stars that have greater mass than the initial maximum imposed on the stellar population.