Forward Modeling of Double Neutron Stars: Insights from Highly-Offset
  Short Gamma-Ray Bursts
  We present a detailed analysis of two well-localized, highly offset short
gamma-ray bursts---GRB~070809 and GRB~090515---investigating the kinematic
evolution of their progenitors from compact object formation until merger.
Calibrating to observations of their most probable host galaxies, we construct
semi-analytic galactic models that account for star formation history and
galaxy growth over time. We pair detailed kinematic evolution with compact
binary population modeling to infer viable post-supernova velocities and
inspiral times. By populating binary tracers according to the star formation
history of the host and kinematically evolving their post-supernova
trajectories through the time-dependent galactic potential, we find that
systems matching the observed offsets of the bursts require post-supernova
systemic velocities of hundreds of kilometers per second. Marginalizing over
uncertainties in the stellar mass--halo mass relation, we find that the
second-born neutron star in the GRB~070809 and GRB~090515 progenitor systems
received a natal kick of $\gtrsim 200~\mathrm{km\,s}^{-1}$ at the 78\% and 91\%
credible levels, respectively. Applying our analysis to the full catalog of
localized short gamma-ray bursts will provide unique constraints on their
progenitors and help unravel the selection effects inherent to observing
transients that are highly offset with respect to their hosts.
