# Fast Magnetic Reconnection: Secondary Tearing Instability and Role of the Hall Term

## TL;DR

This paper investigates the ideal tearing instability in Hall-MHD simulations, revealing that the Hall term significantly accelerates magnetic reconnection and energy release in thin current sheets, explaining explosive astrophysical phenomena.

## Contribution

It introduces detailed simulations of the Hall-MHD tearing instability, highlighting the role of the Hall term in enhancing reconnection rates and explosive energy release.

## Key findings

- Hall term increases reconnection rate up to ten times compared to linear phase.
- Secondary current sheets naturally evolve to ideal aspect ratios at high Lundquist numbers.
- Reconnection occurs on super-Alfvénic timescales, explaining explosive astrophysical events.

## Abstract

Magnetic reconnection provides the primary source for explosive energy release, plasma heating and particle acceleration in many astrophysical environments. The last years witnessed a revival of interest in the MHD tearing instability as a driver for efficient reconnection. It has been established that, provided the current sheet aspect ratio becomes small enough ($a/L \sim S^{-1/3}$ for a given Lundquist number $S\gg 1$), reconnection occurs on ideal Alfv\'en timescales and becomes independent on $S$. Here we investigate, by means of two-dimensional simulations, the \emph{ideal} tearing instability in the Hall-MHD regime, which is appropriate when the width of the resistive layer $\delta$ becomes comparable to the ion inertial length $d_i$. Moreover, we study in detail the spontaneous development and reconnection of secondary current sheets, which for high $S$ naturally adjust to the ideal aspect ratio and hence their evolution proceeds very rapidly. For moderate low $S$, the aspect ratio tends to the Sweet-Parker scaling ($a/L \sim S^{-1/2}$), in order to fulfill the condition $\delta \ll a$ necessary for the onset of a tearing instability. When the Hall term is included, the reconnection rate of this secondary nonlinear phase is enhanced and, depending on the ratio $d_i/\delta$, can be twice with respect to the pure MHD case, and up to ten times larger than the linear phase. Therefore, the evolution of the tearing instability in thin current sheets in the Hall-MHD regime naturally leads to an explosive disruption of the reconnecting site and to energy release on super-Alfv\'enic timescales, as required to explain astrophysical observations.