# Critical Conditions for Core-Collapse Supernovae Academic Article

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### abstract

• The explosion of a core-collapse supernova can be approximated by the breakdown of steady-state solutions for accretion onto a proto-neutron star (PNS). We analytically show that as the neutrino luminosity exceeds a critical value ${L}_{c}$, the neutrinosphere pressure exceeds the hydrostatic limit even for an optimal shock radius $R$. This yields ${L}_{c}\ensuremath{\propto}{M}^{2}{\mathcal{T}}^{2}$ (with logarithmic corrections) and $R\ensuremath{\propto}M/\mathcal{T}$, in agreement with numerical results, where $M$ and $\mathcal{T}$ are the PNS mass and neutrino temperature, respectively. The near-critical flow can be approximated as a ballistic shell on top of an isothermal layer.

• June 1, 2012