The gravitational wave event from the binary neutron star (BNS) merger GW170817 and the following multi-messenger observations present strong evidence for i) merger ejecta expanding with substantial velocities and ii) a relativistic jet which had to propagate through the merger ejecta. The ejecta's expansion velocity is not negligible for the jet head motion, which is a fundamental difference from the other systems like collapsars and active galactic nuclei. Here we present an analytic model of the jet propagation in an expanding medium. In particular, we notice a new term in the expression of the breakout time and velocity. In parallel, we perform a series of over a hundred 2D numerical simulations of jet propagation. The BNS merger ejecta is prepared based on numerical relativity simulations of a BNS merger with the highestresolution to date. We show that our analytic results agree with numerical simulations over a wide parameter space. Then we apply our analytic model to GW170817, and obtain two solid constraints on: i) the central engine luminosity as L iso,0 ∼ 3 × 10 49 − 2.5 × 10 52 erg s −1 , and on ii) the delay time between the merger and engine activation t 0 − t m < 1.3 s. The engine power implies that the apparently-faint short gamma-ray burst (sGRB) sGRB 170817A is similar to typical sGRBs if observed on-axis.

The binary neutron star (BNS) merger event GW170817 clearly shows that a BNS merger launches a short Gamma-Ray Burst (sGRB) jet. Unlike collapsars, where the ambient medium is static, in BNS mergers the jet propagates through the merger ejecta that is expanding outward at substantial velocities (∼0.2c). Here, we present semi-analytic and analytic models to solve the propagation of GRB jets through their surrounding media. These models improve our previous model by including the jet collimation by the cocoon self-consistently. We also perform a series of 2D numerical simulations of jet propagation in BNS mergers and in collapsars to test our models. Our models are consistent with numerical simulations in every aspect (the jet head radius, the cocoon’s lateral width, the jet opening angle including collimation, the cocoon pressure, and the jet-cocoon morphology). The energy composition of the cocoon is found to be different depending on whether the ambient medium is expanding or not; in the case of BNS merger jets, the cocoon energy is dominated by kinetic energy, while it is dominated by internal energy in collapsars. Our model will be useful for estimating electromagnetic counterparts to gravitational waves.

In the gravitational wave event GW170817, there was a ∼10 hours gap before electromagnetic (EM) observations, without detection of the cocoon. The cocoon is heated by a short gamma-ray burst (sGRB) jet propagating through the ejecta of a Neutron Star (NS) merger, and a part of the cocoon escapes the ejecta with an opening angle of 20○–30○. Here we model the cocoon and calculate its EM emission. Our 2D hydrodynamic simulations suggest that the density and energy distributions, after entering homologous expansion, are well-fitted with power-law functions, in each of the relativistic and non-relativistic parts of the escaped cocoon. Modeling these features, we calculate the cooling emission analytically. We find that the cocoon outshines the r-process kilonova/macronova at early times (10–103 s), peaking at UV bands. The relativistic velocity of the cocoon’s photosphere is measurable with instruments such as Swift, ULTRASAT and LSST. We also imply that energetic cocoons, including failed jets, might be detected as X-ray flashes. Our model clarifies the physics and parameter dependence, covering a wide variety of central engines and ejecta of NS mergers and sGRBs in the multi-messenger era.

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 (sGRBs), the ambient matter is the ejecta from the merger of neutron stars, expanding with a high velocity ∼0.2c, in contrast to the static stellar envelope in collapsars. Using 2D relativistic hydrodynamic simulations with the ejecta density profile as ρ∝r−2, we find that the expansion makes a big difference; only 0.5–5 per cent of the cocoon mass escapes from (faster than) the ejecta, with an opening angle 20○–30○, 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 suggest that it is unlikely that cooling emission from the sGRB-jet heated cocoon was observed as a counterpart to the gravitational wave event GW170817.