CORE-COLLAPSE SUPERNOVA EXPLOSIONS: AN ANALYTICAL ONE-DIMENSIONAL ANALYSIS
Core-collapse supernova (Type II, for example, Cassiopeia A) implosion and the subsequent supernova explosion due to core bounce were studied analytically by solving the continuity, Euler, Poisson and energy equations by taking the star as an “ideal gas system”. Outward shock propagation and inward accretion shock due to the supernova implosion were calculated by solving the continuity and momentum equations for the shell layer outside of the core with the Kirkwood-Bethe hypothesis. The collapse time of the core-mass of having radius of a 3000km to a protoneutron star with radius of 108km is calculated to be approximately 1.2s. The heat transport during the evolution turns out to depend on the macroscopic parameters such as gravitational potential, the mass and the collapsing and expanding velocity of the supernova which indicates that the heat transfer from/to a system is determined by the evolution process for an ideal gas system, and vice versa. In detail, the heat escaped from the star during the collapse is about and the heat absorption during the expansion after the bounce is about which are comparable to the values obtained by detailed computation.
heat transport, explosion, implosion, supernova, ideal gas system.