Stability of Spherical Nuclei in the Inner Crust of Neutron Stars

Abstract

Neutron stars are the densest objects in the Universe. In this paper, we consider the so-called inner crust—the layer where neutron-excess nuclei are immersed in the degenerate gas of electrons and a sea of quasi-free neutrons. It was generally believed that spherical nuclei become unstable with respect to quadrupole deformations at high densities, and here, we consider this instability. Within the perturbative approach, we show that spherical nuclei with equilibrium number density are, in fact, stable with respect to infinitesimal quadrupole deformation. This is due to the background of degenerate electrons and associated electrostatic potential, which maintain stability of spherical nuclei. However, if the number of atomic nuclei per unit volume is much less than the equilibrium value, instability can arise. To avoid confusion, we stress that our results are limited to infinitesimal deformations and do not guarantee strict thermodynamic stability of spherical nuclei. In particular, they do not exclude that substantially non-spherical nuclei (so-called pasta phase) represent a thermodynamic equilibrium state of the densest layers of the neutron star crust. Rather, our results point out that spherical nuclei can be metastable even if they are not energetically favourable, and the timescale of transformation of spherical nuclei to the pasta phases should be estimated subsequently.