# Stability of a force-free Hall equilibrium and release of magnetic energy

## TL;DR

This paper analyzes the stability of a force-free Hall equilibrium, revealing that Hall instability can lead to magnetic energy release through current sheet formation, with implications for neutron stars and stellar coronae.

## Contribution

It provides a stability analysis showing that Hall drift does not prevent instability and describes how magnetic energy is released via current sheets.

## Key findings

- Hall instability growth rates scale with magnetic field strength and diffusivity.
- Unstable modes develop into current sheets at nonlinear stages.
- Magnetic energy is released in spikes, each emitting several percent of total energy.

## Abstract

Conservation of magnetic helicity by the Hall drift does not prevent Hall instability of helical fields. This conclusion follows from stability analysis of a force-free spatially-periodic Hall equilibrium. The growth rates of the instability scale as $\sigma \propto B^{3/4}\eta^{1/4}$ with the field strength $B$ and magnetic diffusivity $\eta$ and can be large compared to the rate of resistive decay of the background field. The instability deviates the magnetic field from the force-free configuration. The unstable eigenmodes include a fine spatial structure which evolves into current sheets at the nonlinear stage of the instability. The instability catalyses the resistive release of magnetic energy. The energy is released in a sequence of spikes, every spike emits several percent of the total energy. A numerically defined scaling for the energy released in a single spike permits an extrapolation to astrophysically relevant values of the Hall number. The instability can be relevant to magnetic energy release in a neutron star crust and, possibly, in stellar coronae.