Filling fractions for the formation of nuclear pasta in neutron stars: semiclassical vs liquid-drop predictions

TL;DR

This paper compares semiclassical and liquid-drop models for nuclear pasta formation in neutron stars, finding quasi-universal filling fractions around 0.13-0.15 and linking them to nuclear curvature effects.

Contribution

It demonstrates that pasta formation filling fractions are quasi-universal and explains their values using a simplified stability criterion based on nuclear curvature.

Findings

Pasta appears at filling fractions around 0.13-0.15.

Filling fractions are quasi-universal across different models.

Nuclear curvature correction explains the transition filling fractions.

Abstract

Historically, a sequence of nuclear pasta shapes was predicted to appear in the deepest region of the inner crust of a neutron star within the compressible liquid-drop picture, when the filling fraction $u$ exceeds some threshold values. However, later calculations showed that these values depend on the details of the liquid-drop model. Here we investigate the existence of pasta in neutron stars within the semiclassical extended Thomas-Fermi approach using various generalized Skyrme functionals. The filling fractions for the different transitions are found to be quasi-universal, unlike the pasta density ranges governed by the symmetry energy at relevant densities. In particular, pasta emerge at $u_\mathrm{sp}\approx0.13-0.15$. By applying a simplified stability criterion within the liquid-drop framework, we show that these values of $u_\mathrm{sp}$ can be explained by the nuclear curvature correction. In this way, the abundance of pasta can be easily estimated. This criterion can also be used to optimize the search of pasta within the more realistic extended Thomas-Fermi approach.