Axion electrodynamics and magnetohydrodynamics

TL;DR

This paper develops formulations of axion-electrodynamics and magnetohydrodynamics in a cosmological setting, exploring their couplings, instabilities, and implications for dark matter and magnetic field evolution.

Contribution

It introduces new formulations for axion-electrodynamics and MHD with general scalar couplings, highlighting the role of $eta$-dynamo and the conditions for dark matter preservation.

Findings

The $eta$-dynamo term arises naturally from helical coupling.

Successful nonlinear formulations are possible with $()$-coupling, preserving dark matter properties.

Gravitational and magnetic instabilities of axion MHD are analyzed.

Abstract

We formulate axion-electrodynamics and magnetohydrodynamics (MHD) in the cosmological context assuming weak gravity. The two formulations are made for a general scalar field with general $f(\phi)$-coupling, and an axion as a massive scalar field with $\phi^2$-coupling, with the helical electromagnetic field. The $\alpha$-dynamo term appears naturally from the helical coupling in the MHD formulation. In the presence of the electromagnetic coupling, however, the Schr\"odinger and hydrodynamic formulations of the coherently oscillating axion are {\it not} available for the conventional $\phi$ coupling; instead, $\phi^2$ coupling allows successful formulations preserving the dark matter nature of the axion to nonlinear order. In the MHD formulation, direct couplings between the scalar and electromagnetic fields appear only for non-ideal MHD. We study gravitational and magnetic instabilities of the scalar field and axion MHDs.