Magnetic helicity evolution in a neutron star accounting for the Adler-Bell-Jackiw anomaly

TL;DR

This paper investigates how surface terms influence magnetic helicity evolution in neutron stars, revealing that quantum effects can dominate classical contributions under certain conditions, potentially explaining magnetar bursts.

Contribution

It introduces a new quantum surface term in magnetic helicity evolution equations for neutron stars, highlighting its significance compared to classical terms under rigid rotation.

Findings

Quantum surface term can dominate classical contributions in neutron stars.

Surface effects may lead to magnetic reconnection and bursts in magnetars.

Quantum effects are significant only under rigid rotation conditions.

Abstract

We analyze the role of the surface terms in the conservation law for the sum of the magnetic helicity density and the chiral imbalance of the charged particle densities. These terms are neglected in the Anomalous MagnetoHydroDynamics (AMHD), where infinite volume is considered typically. We discuss a finite volume system, such as a magnetized neutron star (NS), and study the contribution of the surface terms to the evolution of the magnetic helicity. Accounting for the fast washing out of the chiral imbalance in a nascent NS, we demonstrate that the surface terms contribution can potentially lead to the reconnection of magnetic field lines and subsequent gamma or X-ray bursts observed from magnetars. We derive the additional surface terms originated by the mean spin flux through a volume boundary arising due to macroscopic spin effects in electron-positron plasma. Then, comparing this quantum surface term with the classical one known in standard MHD, we find that the new quantum contribution prevails over classical term for the rigid NS rotation only.