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We use relativistic hydrodynamic numerical calculations to study theinteraction between a jet and a homologous outflow produced dynamically duringbinary neutron star mergers. We quantify how the thermal energy supplied by thejet to the ejecta and the ability of a jet to escape the homologous ejectadepend on the parameters of the jet engine and the ejecta. For collimated jetsinitiated at early times compared to the engine duration, we show thatsuccessful breakout of the forward cocoon shock necessitates a jet thatsuccessfully escapes the ejecta. This is because the ejecta is expanding andabsorbing thermal energy, so that the forward shock from a failed jet stallsbefore it reaches the edge of the ejecta. This conclusion can be circumventedonly for very energetic wide angle jets, with parameters that are uncomfortablegiven short-duration GRB observations. For successful jets, we find two regimesof jet breakout from the ejecta, early breakout on timescales shorter than theengine duration, and late breakout well after the engine shuts off. A latebreakout can explain the observed delay between gravitational waves and gammarays in GW 170817. We show that for the entire parameter space of jetparameters surveyed here (covering energies $\sim 10^{48}-10^{51}$ ergs andopening angles $\theta_j \sim 0.07-0.4$) the thermal energy deposited into theejecta by the jet propagation is less than that produced by r-process heatingon second timescales by a factor of $\gtrsim 10$. Shock heating is thusenergetically subdominant in setting the luminosity of thermally poweredtransients coincident with neutron star mergers (kilonovae). For typical shortGRB jet parameters, our conclusion is stronger: there is little thermal energyin the cocoon, much less than what is needed to explain the early bluecomponent of the kilonova in GW 170817.

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