The role of the galaxy stellar mass function in determining the cosmological distribution of astrophysical transients with applications to fast radio bursts and merging binary black holes

The cosmological distribution and formation rate of compact astrophysical objects such as fast radio bursts (FRBs) are typically assumed to be proportional to a linear combination of cosmological star formation rate and stellar mass. In the literature, a template for star formation rate, which is just a function of redshift, is typically used. In this work, we point out the importance of galaxy stellar mass function which captures the host galaxy information of observed FRBs as well as the redshift evolution of galaxy stellar mass. Using this information and taking the stellar mass distribution of a sample of localized FRBs at face value, we find that FRB formation efficiency per stellar mass may have to be more efficient (by a factor of $\approx 3$) than previously calculated, in order to reproduce the observed volumetric rate of FRBs at $z=0$. We show that cosmological population studies of FRBs have to include host galaxy information along with its redshift evolution in order to obtain unbiased results. This consideration is also applicable to other transients, e.g. gamma-ray bursts and merging binary black hole events. We show that our approach may open up the possibility to distinguish between different scenarios of merging binary black holes formation with a detection of few thousand gravitational wave events.