Effective Resistivity in Relativistic Reconnection: A Prescription Based on Fully Kinetic Simulations

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 1 order of magnitude) than equivalent kinetic calculations. Reconnection-driven phenomena could be accordingly modeled in resistive MHD employing a nonuniform, “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, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>η</mml:mi> <mml:mi>eff</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mi>α</mml:mi> <mml:msub> <mml:mi>B</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo stretchy="false">∣</mml:mo> <mml:mi mathvariant="bold-italic">J</mml:mi> <mml:msup> <mml:mo stretchy="false">∣</mml:mo> <mml:mi>p</mml:mi> </mml:msup> <mml:mo>/</mml:mo> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mo stretchy="false">∣</mml:mo> <mml:mi mathvariant="bold-italic">J</mml:mi> <mml:msup> <mml:mo stretchy="false">∣</mml:mo> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mo>+</mml:mo> <mml:msup> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mi>e</mml:mi> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>t</mml:mi> </mml:msub> <mml:mi>c</mml:mi> </mml:mrow> </mml:mfenced> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:mfenced> </mml:math> , where B 0 is the reconnecting magnetic field strength, J is the current density, n t is the lab-frame total number density, e is the elementary charge, and c is the speed of light. The guide field dependence is encoded in α 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.