Ready, set, launch: time interval between BNS merger and short GRB jet formation

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.