http://arxiv.org/abs/1507.08314
We derive an integral condition for core-collapse supernova explosions and use it to construct a new diagnostic of explodability. The fundamental challenge in core-collapse supernova theory is to explain how a stalled accretion shock revives to explode a star. In this manuscript, we assume that shock revival is initiated by the delayed-neutrino mechanism and derive an integral condition for shock expansion, $v_s > 0$. Assuming that $v_s > 0$ corresponds to explosion, we recast this integral condition as a dimensionless condition for explosion, $\Psi > 0$. Using 1D simulations, we confirm that $\Psi = 0$ during the stalled phase and $\Psi > 0$ during explosion. Having validated the integral condition, we use it to derive a useful explosion diagnostic. First, for a given set of parameters, we find the family of solutions to the steady-state equations, parameterized by shock radius $R_s$, yielding $\Psi(R_s)$. For any particular solution, $\Psi(R_s)$ may be negative, zero, or positive, and, since $\Psi \propto v_s$, this corresponds to a solution with a receding, stationary, or expanding shock, respectively. Within this family, there is always a solution with a minimum $\Psi$, $\Psi_{\rm min}$. When $\Psi_{\rm min} < 0$, there always exists a stalled accretion shock solution, but when $\Psi_{\rm min} > 0$, all solutions have $v_s > 0$. Therefore, $\Psi_{\rm min} = 0$ defines a critical hypersurface for explosion, and we show that the critical neutrino luminosity curve proposed by Burrows \& Goshy (1993) is a projection of this more general critical condition. Finally, we propose and verify with 1D simulations that $\Psi_{\rm min}$ is a reliable and accurate explosion diagnostic.
J. Murphy and J. Dolence
Fri, 31 Jul 15
21/59
Comments: 15 pages and 10 figures; submitted. Figure 7 is the money plot and eqs. 17 & 18 are the money equations. We humbly welcome your comments
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