Stars with a core mass greater than about 30 M⊙ become dynamically unstable due to electron-positron pair production when their central temperature reaches 1.5-2.0 x 109 0K.The collapse and subsequent explosion of stars with core masses of 45, 52, and 60 M⊙ is calculated.The range of the final velocity of expansion (3,400 – 8,500 km/sec) and of the mass ejected (1 – 40 M⊙) is comparable to that observed for type II supernovae.
An implicit scheme of hydrodynamic difference equations (stable for large time steps) used for the calculation of the evolution is described.
For fast evolution the turbulence caused by convective instability does not produce the zero entropy gradient and perfect mixing found for slower evolution.A dynamical model of the convection is derived from the equations of motion and then incorporated into the difference equations.
