# Domain walls in neutron $^{3}P_{2}$ superfluids in neutron stars

## TL;DR

This paper investigates the structure and stability of domain walls in neutron $^{3}P_{2}$ superfluids within neutron stars using Ginzburg-Landau theory, revealing their potential role in astrophysical phenomena like star glitches.

## Contribution

It provides a detailed analysis of domain wall configurations, their localized modes, and stability in neutron star superfluids, introducing new insights into their astrophysical implications.

## Key findings

- Localized Nambu-Goldstone mode near domain walls in UN phase
- Restoration of U(1) symmetry near certain domain walls in D2-BN phase
- Energy release from domain wall deconstruction can explain star glitches

## Abstract

We work out domain walls in neutron $^{3}P_{2}$ superfluids realized in the core of neutron stars. Adopting the Ginzburg-Landau (GL) theory as a bosonic low-energy effective theory, we consider configurations of domain walls interpolating ground states, i.e., the uniaxial nematic (UN), D$_{2}$-biaxial nematic (D$_{2}$-BN), and D$_{4}$-biaxial nematic (D$_{4}$-BN) phases in the presence of zero, small and large magnetic fields, respectively. We solve the Euler-Lagrange equation from the GL free energy density, and calculate surface energy densities of the domain walls. We find that one extra Nambu-Goldstone mode is localized in the vicinity of a domain wall in the UN phase while a U(1) symmetry restores in the vicinity of one type of domain wall in the D$_{2}$-BN phase and all domain walls in the D$_{4}$-BN phase. Considering a pile of domain walls in the neutron stars, we find that the most stable configurations are domain walls perpendicular to the magnetic fields piled up in the direction along the magnetic fields in the D$_{2}$-BN and D$_{4}$-BN phases. We estimate the energy released from the deconstruction of the domain walls in the edge of a neutron star, and show that it can reach an astrophysical scale such as glitches in neutron stars.