Abstract
The joint detection of GW~170817/GRB 170817 confirmed the long-standing
theory that binary neutron star mergers produce short gamma-ray burst (sGRB)
jets that can successfully break out of the surrounding ejecta. At the same
time, the association with a kilonova provided unprecedented information
regarding the physical properties (such as masses and velocities) of the
different ejecta constituents. Combining this knowledge with the observed
luminosities and durations of cosmological sGRBs detected by the Burst Alert
Telescope (BAT) onboard the Neil Gehrels Swift Observatory, we revisit the
breakout conditions of sGRB jets. Assuming self-collimation of sGRB jets does
not play a critical role, we find that the time interval between the binary
merger and the launching of a typical sGRB jet is $\lesssim0.1$~s. We also show
that for a fraction of at least $\sim 30\%$ of sGRBs, the usually adopted
assumption of static ejecta is inconsistent with observations, even if the
polar ejecta mass is an order of magnitude smaller than the one in GRB 170817.
Our results disfavour magnetar central engines for powering cosmological sGRBs,
limit the amount of energy deposited in the cocoon prior to breakout, and
suggest that the observed delay of $\sim 1.$7~s in GW 170817 /GRB 170817
between the gravitational wave and $\gamma$-ray signals is likely dominated by
the propagation time of the jet to the $\gamma$-ray production site.