Jet Dynamics in Compact Object Mergers: GW170817 Likely Had a Successful Jet

We use relativistic hydrodynamic numerical calculations to study the interaction between a jet and a homologous outflow produced dynamically during binary neutron star mergers. We quantify how the thermal energy imparted by the jet and the ability of the jet to escape the ejecta depend on the parameters of the jet engine and the ejecta. Under our assumptions, a collimated jet initiated at early times compared to the engine duration, we show that successful breakout of the forward cocoon shock necessitates a jet that successfully escapes the ejecta. This is because the ejecta is expanding, and the forward shock from a failed jet stalls before it reaches the edge of the ejecta. This conclusion can be circumvented only for very energetic wide angle jets, with parameters that are uncomfortable given short-duration GRB observations. For successful jets, we find two regimes of jet breakout from the ejecta: early breakout on timescales shorter than the engine duration, and late breakout well after the engine shuts off. A late breakout can explain the observed delay between gravitational waves and gamma rays in GW170817. We show that for the entire parameter space of jet parameters surveyed here (covering energies ∼10⁴⁸-10⁵¹ erg and opening angles θ _j ∼ 0.07-0.4) the thermal energy deposited by the jet is less than that produced by r-process heating on second timescales by at least an order of magnitude. Shock heating is thus energetically subdominant in setting the luminosity of thermally powered transients coincident with neutron star mergers (kilonovae).