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.

The Elasticity of the Neutron Star Mantle: The Improved Compressible Liquid Drop Model for Cylindrical Phases

“…[6]. A similar result was obtained by the authors in [54], according to which the spherical nuclei in the crust are stable with respect to infinitesimal quadrupole deformations, and thus transition from the crust to the mantle is not associated with the absolute instability of spherical nuclei.…”

Is there pasta in neutron stars?

“…Quite generically, the liquid-drop approach [6,7] predicts that spherical nuclei are no longer energetically favored above u ∼ 0.2 (see also Refs. [8,9] and references therein). Beyond this point, different types of structures are expected to appear independently of the adopted nuclear parametrization [7]: cylinders ("spaghetti") for u ≲ 0.35, slabs ("lasagna") for u ≲ 0.65, inverted cylinders ("buccatini") for u ≲ 0.8 and bubbles ("Swiss cheese") for higher filling fractions.…”