An effective Lagrangian description of supernova-core bounce

Abstract

In standard hydrodynamical supernova computations many variables are needed to describe the time evolution of the stellar core. A numerical grid of points is usually constructed to attain the desirable accuracy. This fact limits the codes to run in the biggest and fastest computers. A new semi-analytical approach for the problem of the dynamical evolution of the collapse, bounce and explosion of a supernova core is proposed. The relevant coordinates of the dynamical problem are chosen to define an effective Lagrangian. The Lagrangian variables are the radii of the shells, seen now as collective coordinates, which describe the global aspects of the process. An effective Lagrangian with these properties for any number of shells is presented. The equations of motion are obtained from this Lagrangian and then integrated numerically. The potentiality of the method is exemplified for the extreme case in which only two shells are used to describe the stellar core. Even in this instance, it is possible to discuss the circumstances for the occurrence of supernova explosion.