Conditions for jet break-out in NS mergers

Abstract

We consider conditions for jet break-out through ejecta following mergers of neutron stars and provide simple relations for the break out conditions. We demonstrate that: (i) break-out requires that the isotropic-equivalent jet energy $E_j$ exceeds the ejecta energy $E_{ej}$ by $E_j\ge E_{ej}/{\beta }_0$, where ${\beta }_0=V_{ej}/c$, $V_{ej}$ is the maximum velocity of the ejecta. If the central engine terminates before the break out, the shock approaches the edge of the ejecta slowly $\propto 1/t$; late break out occurs only if at the termination moment the head of the jet was relatively close to the edge. (ii) If there is a substantial delay between the ejecta's and the jet's launching, the requirement on the jet power increases. (iii) The forward shock driven by the jet is mildly strong, with Mach number $M\approx 5/4$ (increasing with time delay $t_d$); (iii) the delay time $t_d$ between the ejecta and the jet's launching is important for $t_d>t_0=(3/16)c{M}_{ej}{V}_{ej}/L_j=1.01\sec M_{ej,-2}{L}_{j,51}^{-1}\left({\beta }_{ej}/0.3\right)$, where $M_{ej}$ is ejecta mass, $L_j$ is the jet luminosity (isotropic equivalent). For small delays, $t_0$ is also an estimate of the break-out time.

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Cited by in corpus (2)

• Constraining the Jet Launching Time of GRB 170817A by Utilizing the Baryon Loading
• Broadband Emission from a Kilonova Ejecta-Pulsar Wind Nebula System: Late-Time X-ray Afterglow Rebrightening of GRB 170817A