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Nearly 20% of short gamma-ray bursts (sGRBs) have no observed host galaxies.Combining this finding with constraints on galaxies' dark matter halo potentialwells gives strong limits on the natal kick velocity distribution for sGRBprogenitors. For the best-fitting velocity distribution, one in five sGRBprogenitors receives a natal kick above 150 km/s, consistent with mergingneutron star models but not with merging white dwarf binary models. Thisprogenitor model constraint is robust to a wide variety of systematicuncertainties, including the sGRB progenitor time-delay model, the Swiftredshift sensitivity, and the shape of the natal kick velocity distribution. Wealso use constraints on the galaxy-halo connection to determine the host haloand host galaxy demographics for sGRBs, which match extremely well withavailable data. Most sGRBs are expected to occur in halos near 10^12 Msun andin galaxies near 5x10^10 Msun (L_*); unobserved faint and high-redshift hostgalaxies contribute a small minority of the observed hostless sGRB fraction. Wefind that sGRB redshift distributions and host galaxy stellar masses weaklyconstrain the progenitor time-delay model; the active vs. passive fraction ofsGRB host galaxies may offer a stronger constraint. Finally, we discuss howsearches for gravitational wave optical counterparts in the local Universe canreduce followup times using these findings.

Interpreting Short Gamma Ray Burst Progenitor Kicks and Time Delays Using the Host Galaxy-Dark Matter Halo Connection