The Stellar Ages and Masses of Short GRB Host Galaxies: Investigating the Progenitor Delay Time Distribution and the Role of Mass and Star Formation in the Short GRB Rate

[Abridged] We present optical and NIR observations of 19 short GRB host galaxies, aimed at measuring their stellar masses and population ages. The goals of this study are to evaluate whether short GRBs track the stellar mass distribution of galaxies, to investigate the progenitor delay time distribution, and to explore any connection between long and short GRB progenitors. Using single stellar population models we infer masses of log(M/M_sun)=8.8-11.6 and population ages of tau=0.03-4.4 Gyr. We further infer maximal masses of log(M/M_sun)=9.7-11.9 by assuming stellar population ages equal to the age of the universe at each host's redshift. Comparing the distribution of stellar masses to the general galaxy mass function we find that short GRBs track the cosmic stellar mass distribution only if the late-type hosts generally have maximal masses. However, there is an apparent dearth of early-type hosts compared to the equal contribution of early- and late-type galaxies to the cosmic stellar mass budget. These results suggest that stellar mass may not be the sole parameter controlling the short GRB rate, and raise the possibility of a two-component model with both mass and star formation playing a role. If short GRBs in late-type galaxies indeed track the star formation activity, the resulting typical delay time is ~0.2 Gyr, while those in early-type hosts have a typical delay of ~3 Gyr. Using the same stellar population models we fit the data for 22 long GRB hosts and find that they have lower masses and younger population ages, with <log(M/M_sun)>=9.1 and <tau>=0.06 Gyr, respectively; their maximal masses are similarly lower, <log(M/M_sun)>=9.6. Most importantly, the two host populations remain distinct even if we consider only the star-forming hosts of short GRBs, supporting our previous findings that the progenitors of long GRBs and short GRBs in late-type galaxies are distinct.