Anderson-Bogoliubov phonon in inner crust of neutron stars: Dipole excitation in spherical Wigner-Seitz cell

TL;DR

This study investigates how the Anderson-Bogoliubov phonon behaves in the inner crust of neutron stars, revealing that it does not penetrate clusters and may weakly couple with lattice phonons, affecting neutron star properties.

Contribution

It provides a microscopic analysis of the AB phonon in the presence of clusters using Hartree-Fock-Bogoliubov and RPA methods, highlighting its suppression inside clusters and similarity to pygmy resonances.

Findings

AB phonon mode emerges systematically in the model.

Phonon amplitude is suppressed inside clusters.

Behavior resembles pygmy dipole resonance at high neutron densities.

Abstract

Background: The Anderson-Bogoliubov (AB) phonon, called also the superfluid phonon, has attracted attentions since it may influence the thermal conductivity and other properties of inner crust of neutron stars. However, there are limited number of microscopic studies of the AB phonon where the presence of clusters is explicitly taken into account.\\ Purpose: We intend to clarify how the presence of clusters affects the AB phonon in order to obtain microscopic information relevant to the coupling between the AB phonon and the lattice phonon. \\ Methods: The Hartree-Fock-Bogoliubov model and the quasiparticle random-phase approximation formulated in a spherical Wigner-Seitz cell are adopted to describe neutron superfluidity and associated collective excitations. We perform systematic numerical calculations for dipole excitation by varying the neutron chemical potential and the number of protons in a cell. \\ Results:The model predicts systematic emergence of the dipole AB phonon mode, which however exhibits strong suppression of phonon amplitude inside the cluster. We find also that the phonon amplitude around the cluster surface varies as the neutron density. At higher neutron densities the AB phonon mode exhibits behaviour similar to the pygmy dipole resonance in neutron-rich nuclei.\\ Conclusions: The dipole AB phonon mode does not penetrate into the clusters. This suggests that the coupling between the AB phonon and the lattice phonon may be weak.