Effects of finite sizes of atomic nuclei on shear modulus and torsional oscillations in neutron stars

TL;DR

This paper investigates how the finite sizes of spherical nuclei affect the shear modulus and torsional oscillation frequencies in neutron star crusts, revealing that finite-size effects lower oscillation frequencies, especially at higher frequencies and for certain neutron star models.

Contribution

It introduces the finite-size effect of spherical nuclei into shear modulus calculations and analyzes its impact on crustal torsional oscillation frequencies in neutron stars.

Findings

Finite-size effects decrease shear modulus and oscillation frequencies.

Effects are more significant for higher azimuthal quantum numbers.

Finite-size effects are especially important above 100 Hz frequencies.

Abstract

The shear modulus of neutron star matter is one of the important properties for determining torsional oscillations in neutron stars. We take into account the effects of finite sizes of spherical nuclei on the shear modulus and examine the frequencies of crustal torsional oscillations. The shear modulus decreases owing to the finite-size effect, which in turn decreases the frequencies of torsional oscillations. In particular, the finite-size effect becomes more crucial for oscillations with a larger azimuthal quantum number and for neutron star models with a weaker density dependence of nuclear symmetry energy. In practice, when one identifies the quasi-periodic oscillations from a neutron star, where the magnetic effect is negligible, with crustal torsional oscillations, the finite-size effect can be more significant at frequencies higher than $\sim 100$ Hz.