Half-quantized Non-Abelian Vortices in Neutron ${}^3{P}_2$ Superfluids inside Magnetars

Abstract

We point out that half-quantized non-Abelian vortices exist as the minimum energy states in rotating neutron ${}^3{P}_2$ 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.

7 pages, 2 figures

References in corpus (4)

• Rapid Cooling of the Neutron Star in Cassiopeia A Triggered by Neutron Superfluidity in Dense Matter
• Discrete symmetries and 1/3-quantum vortices in condensates of F=2 cold atoms
• Quasi-Nambu-Goldstone Modes in Bose-Einstein Condensates
• Magnetic Properties of Quantized Vortices in Neutron ${}^3{P}_2$ Superfluids in Neutron Stars

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