Hiroki Nagakura, Yu Yamamoto, Shoichi Yamada
We develop a new semi-dynamical method to study shock revival by neutrino heating in core-collapse supernovae. Our new approach is an extension of the steady state approach with the light bulb approximation, which has been widely used in the supernova community for the investigation of the criteria for successful supernova explosions. In this approach we get rid of the steady-state condition and take into account deviations from it instead. We have in mind the scenario that not the critical luminosity but the critical fluctuations generated by hydrodynamical instabilities such as SASI and neutrino-driven convection in the post-shock region determines the onset of shock revival. We validate our new approach by some test calculations, confirming that it indeed captures the essential evolution of shock wave qualitatively. We then apply the method in various conditions to find that there is a critical fluctuation for shock revival. The critical fluctuation can be well fit by the following formula: fcrit=0.8*(Min/1.4M)*{1-(rsh/10^8cm)}, in which f denotes the normalized amplitude of pressure perturbation. We also find that the critical fluctuation decreases with the shock radius, whereas it increases with the mass of the central core. We discuss the possible implications of our results for 3D effects on shock revival, which is currently controversial in the supernova community.
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http://arxiv.org/abs/1209.0596
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