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tokens: 3.5 }. We are interested in calculating the amount of mass ejected by the accelerating shock wave. First, we find the depth x esc ( E; n ), defined as the shock position at which the peak material velocity, just behind the shock is where the prefactor accounts for the velocity in the immediate downstream of a strong shock, and the acceleration factor C f ≈ 2 long after shock passage. All matter exterior to x esc eventually accelerates to beyond v esc and becomes unbound. The ejected mass is given by where we used equation ( 6 ) in the last approximation, valid when x esc ≪ R ⋆ . Fig. 3 shows the material velocity profile as the shock propagates through the star, for an explosion energy of E / E bind = 0.018. This figure demonstrates the definition of x s – the depth at which material velocity first becomes sonic (red curve), and x esc – where the post-shock material velocity is eventually accelerated to v esc (purple curve). Figure 3. The material velocity profile at different times after an explosion with energy E / E bind = 0.018 set at the centre of an n = 3/2 polytrope. The dashed green line is the speed of sound in the undisturbed star, and the horizontal solid blue line is the threshold post-shock velocity that results in mass ejection, as described in the text. Highlighted in blue is the velocity profile at the end of the Sedov–Taylor phase, when the shock first becomes weak. The pulse is then subsonic throughout most of the star, until it transitions to a strong shock, shown in red , when the material velocity becomes sonic. Finally, in purple we show the velocity profile when the ejection criterion is first met, at depth x esc ≈ 10 −2 R ⋆ measured from the stellar edge. Fig. 4 provides a complementary view on the results of the numerical simulations, showing the velocity evolution throughout the stellar interior, demonstrating the analytical picture portrayed in Fig. 2 . During the spherical phases, the shock and material velocities decrease while density remains roughly the same. Later on, the pulse continues to decelerate since the ambient temperature drops in the outer layers of the star, while the (subsonic) material velocity behind the shock increases. At some point, the material velocities approach the local sound speed, and the shock begins to accelerate, transitioning to a strong shock. The material outside the layer at which v sh = v esc / C f is being ejected by the explosion. Figure 4. Shock and material velocity as a function of unperturbed density, for a simulation of an explosion of energy E / E bind = 2.9 × 10 −3 set in an n = 3 polytrope. The numerical results in this figure mirror the analytic picture in Fig. 2 . Peak material velocity is plotted in black, and the unperturbed sound speed in blue. The shock velocity (in red) was calculated from the material velocity and the local Mach number with respect to the material lying just ahead of the shock. Finally, the horizontal dashed line is the threshold shock velocity