The Stellar-mass Function of Long Gamma-Ray Burst Host Galaxies

Long gamma-ray bursts (GRBs) have been discussed as a potential tool to probe the cosmic star formation rate (SFR) for a long time. Some studies found an enhancement in the GRB rate relative to the galaxy-inferred SFR at high redshifts, which indicates that GRBs may not be good tracers of star formation. However, in these studies, the GRB rate measured at any redshift is an average over all galaxies at that epoch. A deep understanding of the connection between GRB production and environment also needs to characterize the population of GRB host galaxies directly. Based on a complete sample of GRB hosts, we constrain the stellar-mass function (SMF) of GRB hosts, and examine redshift evolution in the GRB host population. Our results confirm that a strong redshift evolution in energy (with an evolution index of $\delta=2.47^{+0.73}_{-0.89}$) or in density ($\delta=1.82^{+0.22}_{-0.59}$) is needed in order to account for the observations. The GRB host SMF can be well described by the Schechter function with a power-law index $\xi\approx-1.10$ and a break mass $M_{b,0}\approx4.9\times10^{10}$ ${\rm M}_\odot$, independent of the assumed evolutionary effects. This is the first formulation of the GRB host SMF. The observed discrepancy between the GRB rate and the galaxy-inferred SFR may also be explained by an evolving SMF.