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

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.

arXiv comment16 pages in pdflatex, 1 pdf figure, jcap latex style; paper was significantly revised, Sec. 3 was extended, some notations were improved; version published in JCAP

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• Chiral magnetic effect in the presence of an external axial-vector field
• General field theory and weak Euler-Lagrange equation for classical particle-field systems in plasma physics
• Permanent mean spin source of the chiral magnetic effect in neutron stars
• Magnetic helicity in rotating neutron stars
• Charged Dirac fermions with anomalous magnetic moment in the presence of the chiral magnetic effect and of a noncommutative phase space
• Reconnection of magnetic fields in neutron stars driven by the electron mass term in the triangle anomaly