Neutronization of matter in a stellar core and convection during gravitational collapse

Abstract

The roles of neutrinos and convective instability in collapsing supernovae are considered. Spherically symmetrical computations of the collapse using the Boltzmann equation for the neutrinos lead to the formation of the condition of convective instability, ${\left( {\frac{{\partial P}}{{\partial s}}} \right)_{\rho {Y_l}}}\frac{{ds}}{{dr}} + {\left( {\frac{{\partial P}}{{\partial {Y_L}}}} \right)_{\rho s}}\frac{{d{Y_L}}}{{dr}}$ < 0, in a narrow region of matter accretion above the neutrinosphere. If instability arises in this region, the three-dimensional solution will represent a correction to the spherically symmetrical solution for the gravitational collapse. The mean neutrino energies change only negligibly in the narrow region of accretion. Nuclear statistical equilibrium is usually assumed in the hot proto-neutron stellar core, to simplify the computations of the collapse. Neutronization with the participation of free neutrons is most efficient. However, the decay of nuclei into nucleons is hindered during the collapse, because the density grows too rapidly compared to the growth in the temperature, and an appreciable fraction of the energy is carried away by neutrinos. The entropy of the matter per nucleon is modest at the stellar center. All the energy is in degenerate electrons during the collapse. If the large energy of these degenerate electrons is taken into account, neutrons are efficiently formed, even in cool matter with reduced Y _e (the difference between the numbers of electrons and positrons per nucleon). This process brings about an increase in the optical depth to neutrinos, the appearance of free neutrons, and an increase in the entropy per nucleon at the center. The convectively unstable region at the center increases. The development of large-scale convection is illustrated using a multi-dimensional gas-dynamical model for the evolution of a stationary, unstable state (without taking into account neutrino transport). The time for the development of convective instability (several milliseconds) does not exceed the time for the existence of the unstable region at the center (10ms). The realization of this type of instability is fundamentally different from a spherically symmetrical model. The flux of neutrinos changes and the mean energy of the neutrinos is increased, which has important implications for the detection of neutrinos from supernovae. For these same reasons, the energy absorped in the supernova envelope also changes in the transition to such a multi-dimensional model.