Cocoon breakout and escape from the ejecta of neutron star mergers

The cocoon is an inevitable product of a jet propagating through ambient matter, and takes a fair fraction of the jet energy. In short gamma-ray bursts, the ambient matter is the ejecta from the merger of neutron stars, expanding with a high velocity $\sim 0.2 c$, in contrast to the static stellar envelope in collapsars. Using 2D relativistic hydrodynamic simulations with the ejecta density profile as $\rho \propto r^{-2}$, we find that the expansion makes a big difference; only 0.5--5\% of the cocoon mass escapes from (faster than) the ejecta, with an opening angle $20^{\circ}$--$30^{\circ}$, while it is $\sim 100\%$ and spherical in collapsars. We also analytically obtain the shares of mass and energies for the escaped and trapped cocoons. Because the mass of the escaped cocoon is small and the trapped cocoon is concealed by the ejecta and the escaped cocoon, we conclude that it is unlikely that the cocoon emission was observed as a counterpart to the gravitational wave event GW170817.