What Can Galaxy Evolution Tell Us About Short Gamma-Ray Bursts?

We use recent constraints on the star formation rate---halo mass---redshift relation to model the host halo environments where short Gamma-Ray Burst (sGRB) progenitors are created.  These halo environments set minimum energy requirements for sGRB progenitors to leave the vicinity of their original galaxy.  We find that the fraction of sGRBs which are hostless is a robust probe of the underlying velocity kick distribution for sGRB progenitors, regardless of uncertainties in the sGRB time-delay distribution and observational systematics.  We use observed constraints on the hostless fraction of sGRBs to rule out several sGRB progenitor classes which cannot supply the necessary velocity kicks.  Finally, we discuss the ability of sGRB galaxy host properties (e.g., stellar mass and morphology) to further constrain model uncertainties.