A HYDRODYNAMICAL MODEL FOR THE EXPLOSION OF A NEUTRON-STAR JUST BELOW THE MINIMUM MASS

We continue our investigation of the instability of a neutron star at the minimum mass, constructing a hydrodynamical model to follow the evolution of the unstable star. We first perform a detailed analysis of the linear stability of equilibrium configurations near the minimum mass, by solving the radial eigenvalue problem for the fundamental mode. We adopt the Harrison-Wheeler equation of state for the microphysical model. We find that the minimum mass configuration M(mmc) = 0.196 M, is stable to small perturbations. The reason is that even if cold matter remains in beta-equilibrium, nuclear reactions are too slow to drive nuclei to complete statistical equilibrium. Stability to radial perturbations is lost only at a lower critical mass M(min) = 0.16 M., corresponding to approximately 0.8 M(mmc). Next we integrate the Lagrangian equations of Newtonian hydrodynamics to follow the dynamical evolution of the unstable star, perturbed initially by stripping matter from its surface. The star quickly adjusts on a dynamical time scale to a new bound equilibrium configuration of lower density. The instability then evolves through two stages. In the secular phase, nuclei in the perturbed layers in the crust undergo continuous beta-decays and eventually become unstable to spontaneous fission. Only when the transition is sufficiently advanced does rapid expansion occur. In this explosion phase, the outer layers expand first, as the instability originates in the star's crust where the beta-decaying nuclei reside. Following the loss of the external shells, the inner layers accelerate abruptly, attaining escape velocity after a few milliseconds. A weak shock forms close to the star's center and propagates outward. Meanwhile, beta-decays and spontaneous nuclear fissions heat the star to temperatures of 0.5-1 MeV. At the onset of the secular phase of expansion, following mass stripping, antineutrinos of energies approximately 10 MeV are emitted with a luminosity of approximately 10(49-51) ergs s-1. An antineutrino burst of L(nuBAR) = 10(51-52) ergs s-1 then signals the onset of the explosion. The luminosity later decays as the star expands and disperses matter to infinity. The total kinetic energy of the dispersed star reaches approximately 5 x 10(49) ergs. The ejected debris moves at a mean velocity approximately 1-6 x 10(4) km s-1. The entire process resembles a minisupernova event. We finally show that a simple dynamical model constructed using a 3-polytrope equation of state for hot dense matter reproduces the key dynamical features of the instability in the explosion phase. The hydrodynamical calculations in this paper essentially confirm the main results of our previous investigations carried out for simple homogeneous models.