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

We continue our investigation of the instability of a neutron star at the minimum mass, constructing a hydrodynamical model to follow the ev olution of the unstable star. We first perform a detailed analysis of the linear stability of equilibrium configurations near the minimum ma ss, 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 matt er remains in beta-equilibrium, nuclear reactions are too slow to driv e nuclei to complete statistical equilibrium. Stability to radial pert urbations is lost only at a lower critical mass M(min) = 0.16 M., corr esponding to approximately 0.8 M(mmc). Next we integrate the Lagrangia n equations of Newtonian hydrodynamics to follow the dynamical evoluti on of the unstable star, perturbed initially by stripping matter from its surface. The star quickly adjusts on a dynamical time scale to a n ew bound equilibrium configuration of lower density. The instability t hen evolves through two stages. In the secular phase, nuclei in the pe rturbed layers in the crust undergo continuous beta-decays and eventua lly become unstable to spontaneous fission. Only when the transition i s 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, at taining escape velocity after a few milliseconds. A weak shock forms c lose to the star's center and propagates outward. Meanwhile, beta-deca ys and spontaneous nuclear fissions heat the star to temperatures of 0 .5-1 MeV. At the onset of the secular phase of expansion, following ma ss stripping, antineutrinos of energies approximately 10 MeV are emitt ed with a luminosity of approximately 10(49-51) ergs s-1. An antineutr ino burst of L(nuBAR) = 10(51-52) ergs s-1 then signals the onset of t he explosion. The luminosity later decays as the star expands and disp erses matter to infinity. The total kinetic energy of the dispersed st ar 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 r esembles a minisupernova event. We finally show that a simple dynamica l model constructed using a 3-polytrope equation of state for hot dens e matter reproduces the key dynamical features of the instability in t he explosion phase. The hydrodynamical calculations in this paper esse ntially confirm the main results of our previous investigations carrie d out for simple homogeneous models.