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

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, ${\eta }_{\mathrm{e}\mathrm{f}\mathrm{f}}=\alpha B_0{\mathbf{\mid }\mathbf{J}\mathbf{\mid }}^p\mathrm{/}(\mathrm{\mid }\mathbf{J}{\mathrm{\mid }}^{p+1}+{\left(e{n}_{t}c\right)}^{p+1})$, where $B_0$ is the reconnecting magnetic field strength, $\mathbf{J}$ 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.