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 } \geq 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 } ) { cM _ { 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 .