Half-quantized Non-Abelian Vortices in Neutron $^3P_2$ Superfluids inside Magnetars

TL;DR

This paper demonstrates the existence of half-quantized non-Abelian vortices in neutron $^3P_2$ superfluids within magnetar cores, revealing their unique properties, formation mechanisms, and associated spontaneous magnetization effects.

Contribution

It identifies and characterizes half-quantized non-Abelian vortices in neutron superfluids under strong magnetic fields, a novel finding in astrophysical superfluid vortex physics.

Findings

Half-quantized non-Abelian vortices exist in magnetar cores.

Vortices form a tangled network due to non-commutative interactions.

Vortex cores exhibit strong anti-ferromagnetic magnetization.

Abstract

We point out that half-quantized non-Abelian vortices exist as the minimum energy states in rotating neutron $^3P_2$ superfluids in the inner cores of magnetars with magnetic field greater than $3 \times 10^{15}$ Gauss, while they do not in ordinary neutron stars with smaller magnetic fields. One integer vortex is split into two half-quantized vortices. The number of vortices is about $10^{19}$ and they are separated at about $\mu$m in a vortex lattice for typical parameters, while the vortex core size is about 10-100 fm. They are non-Abelian vortices characterized by non-Abelian first homotopy group, and consequently when two vortices corresponding to non-commutative elements collide, a rung vortex must be created between them, implying the formation of an entangled vortex network inside the cores of magnetars. We find the spontaneous magnetization in the vortex core showing anti-ferromagnetism whose typical magnitude is about $10^{8-9}$ Gauss that is ten times larger than that of integer vortices, when external magnetic fields are present along the vortex line.