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We present observations of the afterglows and host galaxies of threeshort-duration gamma-ray bursts (GRBs): 100625A, 101219A and 110112A. We findthat GRB 100625A occurred in a z=0.452 early-type galaxy with a stellar mass of4.6e9 M_Sun and a stellar population age of 0.7 Gyr, and GRB 101219A originatedin a star-forming galaxy at z=0.718 with a stellar mass of 1.4e9 M_Sun, a starformation rate of 16 M_Sun yr^-1, and a stellar population age of 50 Myr. Wealso report the discovery of the optical afterglow of GRB 110112A, which lacksa coincident host galaxy to i>26 mag and we cannot conclusively identify anyfield galaxy as a possible host. The bursts have inferred circumburst densitiesof ~1e-4-1 cm^-3, and isotropic-equivalent gamma-ray and kinetic energies of1e50-1e51 erg. These events highlight the diversity of galaxies that host shortGRBs. To quantify this diversity, we use the sample of 36 Swift short GRBs withrobust associations to an environment (~1/2 of 68 short bursts detected bySwift to May 2012) and classify them as follows: late-type (50%), early-type(15%), inconclusive (20%), and host-less (lacking a coincident host galaxy tolimits of >26 mag; 15%). To find likely ranges for the true late- andearly-type fractions, we assign each of the host-less bursts to the late- orearly-type category using probabilistic arguments, and consider the scenariothat all hosts in the inconclusive category are early-type galaxies to set anupper bound on the early-type fraction. The most likely ranges for the late-and early-type fractions are ~60-80% and ~20-40%, respectively. We find noclear trend between gamma-ray duration and host type, and no change to thefractions when excluding events recently claimed as possible contaminants fromthe long GRB/collapsar population. Our reported demographics are consistentwith a short GRB rate driven by both stellar mass and star formation.

Demographics of the Galaxies Hosting Short-duration Gamma-Ray Bursts