TITLE: Core-Collapse Supernovae: A Phase-Diagram Analysis of the Shock Revival Mechanism
ABSTRACT: As massive stars end their life, the iron core collapses forming a hydrodynamic shock wave in the inner region. This shock stalls few hundred milliseconds later rather than propagating directly to the envelope. The "delayed neutrino mechanism" is believed to play a crucial role in re-energizing the shock until it reaches the star's envelope and causes a supernova explosion. We show that the propagation of the shock can be analyzed through a series of quasi-stationary approximations. Those approximations are then used to explore the evolution of the system in phase-space fashion, shown to provide qualitative and quantitative insights into the initiation of expansion and its nature. The prospects for an explosion can be assessed with analogy to a linear damped/anti-damped oscillator. This yields a criterion for the critical neutrino luminosity needed to reach an explosion and is found to be in good agreement with simulations. Moreover, the mass accretion rate of the star plays a crucial role in the dynamics leading to an explosion. We find a critical mass accretion rate, below which explosion will occur after several oscillations, and above which it will commence in a non-oscillatory fashion.