Magnetic reconnection with a 0.1 rate: Effective resistivity in general relativistic magnetohydrodynamics

TL;DR

The paper addresses fast relativistic magnetic reconnection in collisionless astrophysical plasmas by introducing an effective resistivity $\eta = |\mathbf{E}^*|/(n e c)$ in relativistic resistive MHD, linked to charge-starved X-points. This approach reproduces the fast kinetic-rate reconnection ($\beta_{\rm rec} \gtrsim 0.1$) seen in PIC simulations, both in local Harris sheets and in global black-hole magnetospheres, without relying on nonlocal derivatives or grid-scale resistivity. Across varying guide fields, the non-uniform resistivity yields reconnection rates consistent with kinetic models, whereas a uniform resistivity underpredicts the rate and requires substantially higher resolution. Consequently, this resistivity model enables scalable GRRMHD simulations of magnetospheric and jet dynamics while capturing collisionless reconnection physics, with implications for rapid flaring in neutron-star and black-hole systems.

Abstract

Relativistic magnetic reconnection is thought to power various multi-wavelength emission signatures from neutron stars and black holes. Relativistic resistive magnetohydrodynamics (RRMHD) offers the simplest model of reconnection. However, a small uniform resistivity underestimates the reconnection rate compared to first-principles kinetic models. By employing an effective resistivity based on kinetic models - which connects the reconnection electric field to the charge-starved current density - we show that RRMHD can reproduce the increased reconnection rate of kinetic models, both in local current sheets and in global black hole magnetospheres.

Figures (12)

• Figure 1: Charge starvation in a PIC simulation of a reconnecting Harris sheet. Positrons (first panel) and electrons (second panel) counter stream at near the speed of light. The Lorentz invariant $(J^\mu J_\mu)_{\rm tot}$ of the total current (third panel) remains spacelike ($<0$) in the current sheet showing that the current is supplied by counter streaming electrons and positrons. White lines and arrows show magnetic field lines linearly spaced in values of the out-of-plane vector potential. The third panel is normalized by $(n_0 e c)^2$ with upstream total number density $n_0$. The upstream skin depth $d_{e,0} = \sqrt{mc^2/4\pi n_0 e^2}$ is indicated by the vertical white line.
• Figure 2: First panel: Time evolution of the reconnection rate $\beta_{\rm{rec}}$ for RRMHD with uniform $\eta$ (blue), non-uniform $\eta$ (purple), and PIC (orange), showing that the non-uniform $\eta$ case matches the PIC reconnection rate $\gtrsim 0.1$, while the uniform $\eta$ case shows the typical rate of RRMHD $\sim 0.03$. Second panel: Time evolution of the four velocity of the outflow out of the X-point (taken as the maximum in the domain), which becomes Alfvénic as steady state is reached. The value expected for an Alfvénic outflow ($\Gamma_{\rm A}\beta_{\rm A} = \sqrt{\sigma}$) is indicated by the black dashed line.
• Figure 3: Comparison between PIC (left) and RRMHD with non-uniform $\eta$ (right) for $|\bm{E}^*|/B_0$ (top), $\rho/\rho_0$ (middle), and total out-of-plane electric field as a proxy for the reconnection rate $\beta_{\rm rec} \sim E_z / B_0$ (bottom). The X-points show a peak in $|\bm{E}^*|$ and drop in $\rho$, resulting in a fast $\beta_{\rm rec} \gtrsim 0.1$, both in RRMHD and PIC. White lines show contours of the out-of-plane vector potential with arrows indicating the direction of the in-plane magnetic field.
• Figure 4: Zoom-in of non-ideal electric field component $\eta |J_z|/B_0$ (left) and density $\rho/\rho_0$ (right) in X-points for PIC (top), RRMHD with non-uniform $\eta$ (middle), and uniform $\eta$ (bottom). For uniform $\eta$, X-points are thinner and plasmoids are smaller. White lines show contours of the out-of-plane vector potential with arrows indicating the direction of the in-plane magnetic field.
• Figure 5: Left: The magnitude of the physical component of the reconnection electric field $(r/r_g)^2 {E}^{\hat{\phi}}/ {B}_0$ in the tetrad frame, indicating a reconnection rate $\beta_{\rm rec}\gtrsim 0.1$ for non-uniform $\eta$ (top half), and $\beta_{\rm rec} \sim 0.03$ for uniform $\eta$ (bottom half), where the white line divides the non-uniform and uniform case along the equator. Right: The localization of the non-ideal electric field $(r/r_g^2) \eta \sqrt{J_{i} J^{i}}/{B}_0 \sim \beta_{\rm rec}$ is shown in a zoom in of the reconnection layer (top for non-uniform $\eta$, bottom for uniform $\eta$) as indicated by the silver rectangle on the left. White lines show contours of the out-of-plane vector potential, with arrows indicating the direction of the in-plane magnetic field. Both quantities are compensated by a factor $(r/r_g)^2$ to account for the decay of the monopolar upstream magnetic field component ${B}^{\hat{r}} \propto (r_g/r)^2$.