We consider conditions for jet breakout through ejecta following mergers of neutron stars and provide simple relations for the breakout conditions. We demonstrate that: (i) break-out requires that the isotropic-equivalent jet energy Ej exceeds the ejecta energy Eej by Ej ≥ Eej/βej, where βej = Vej/c, Vej is the maximum velocity of the ejecta. If the central engine terminates before the breakout, the shock approaches the edge of the ejecta slowly ∝ 1/t; late breakout 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 ≈ 5/4 (increasing with time delay td); (iii) the delay time td between the ejecta and the jet’s launching is important for $t_\mathrm{ d} \gt t_0= ({3 }/{16}) {c M_{\mathrm{ ej}} V_{\mathrm{ ej}}}/{L_\mathrm{ j}} = 1.01 {\rm \mathrm{ s}} M_{\mathrm{ ej}, -2} L_{\mathrm{ j}, 51} ^{-1} \left({\beta _{\mathrm{ ej}}} /{0.3} \right)$, where Mej is ejecta mass, Lj is the jet luminosity (isotropic equivalent). For small delays, t0 is also an estimate of the break-out time.
This content will become publicly available on June 28, 2023
- Publication Date:
- NSF-PAR ID:
- 10353390
- Journal Name:
- The Astrophysical Journal Letters
- Volume:
- 933
- Issue:
- 1
- Page Range or eLocation-ID:
- L2
- ISSN:
- 2041-8205
- Sponsoring Org:
- National Science Foundation
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