Effective resistivity in relativistic reconnection: a prescription based on fully kinetic simulations

TL;DR

This paper derives an empirical effective resistivity prescription from kinetic simulations of relativistic magnetic reconnection, enabling improved modeling of reconnection rates in resistive MHD simulations using only single-fluid quantities.

Contribution

It introduces a new empirical formula for effective resistivity based on PIC simulation data, applicable to relativistic pair-plasma reconnection with guide fields.

Findings

The resistivity prescription accurately reproduces nonideal electric field structures.

It captures the guide field dependence through fitted parameters.

The approach enhances resistive MHD modeling of reconnection phenomena.

Abstract

A variety of high-energy astrophysical phenomena are powered by the release -- via magnetic reconnection -- of the energy stored in oppositely directed fields. Single-fluid resistive magnetohydrodynamic (MHD) simulations with uniform resistivity yield dissipation rates that are much lower (by nearly one order of magnitude) than equivalent kinetic calculations. Reconnection-driven phenomena could be accordingly modeled in resistive MHD employing a non-uniform, ``effective'' resistivity informed by kinetic calculations. In this work, we analyze a suite of fully kinetic particle-in-cell (PIC) simulations of relativistic pair-plasma reconnection -- where the magnetic energy is greater than the rest mass energy -- for different strengths of the guide field orthogonal to the alternating component. We extract an empirical prescription for the effective resistivity, $\eta_{\mathrm{eff}} = \alpha B_0 \mathbf{|J|}^p / \left(|\mathbf{J}|^{p+1}+\left(e n_t c\right)^{p+1}\right)$, where $B_0$ is the reconnecting magnetic field strength, $\bf J$ is the current density, $n_t$ the lab-frame total number density, $e$ the elementary charge, and $c$ the speed of light. The guide field dependence is encoded in $\alpha$ and $p$, which we fit to PIC data. This resistivity formulation -- which relies only on single-fluid MHD quantities -- successfully reproduces the spatial structure and strength of nonideal electric fields, and thus provides a promising strategy for enhancing the reconnection rate in resistive MHD simulations.