Interpreting short gamma-ray burst progenitor kicks and time delays using the host galaxy-dark matter halo connection

Nearly 20% of short gamma-ray bursts (sGRBs) have no observed host galaxies. Combining this finding with constraints on galaxies' dark matter halo potential wells gives strong limits on the natal kick velocity distribution for sGRB progenitors. For the best-fitting velocity distribution, one in five sGRB progenitors receives a natal kick above 150 km s^-1, consistent with merging neutron star models but not with merging white dwarf binary models. This progenitor model constraint is robust to a wide variety of systematic uncertainties, including the sGRB progenitor time-delay model, the Swift redshift sensitivity, and the shape of the natal kick velocity distribution. We also use constraints on the galaxy-halo connection to determine the host halo and host galaxy demographics for sGRBs, which match extremely well with available data. Most sGRBs are expected to occur in halos near 10¹² M and in galaxies near 5 × 10¹⁰ M (L _*); unobserved faint and high-redshift host galaxies contribute a small minority of the observed hostless sGRB fraction. We find that sGRB redshift distributions and host galaxy stellar masses weakly constrain the progenitor time-delay model; the active versus passive fraction of sGRB host galaxies may offer a stronger constraint. Finally, we discuss how searches for gravitational wave optical counterparts in the local universe can reduce follow-up times using these findings.