Relativistic reconnection with effective resistivity: I. Dynamics and reconnection rate

Relativistic magnetic reconnection is one of the most fundamental mechanisms considered responsible for the acceleration of relativistic particles in astrophysical jets and magnetospheres of compact objects. Understanding the properties of the dissipation of magnetic fields and the formation of non-ideal electric fields is of paramount importance to quantify the efficiency of reconnection at energizing charged particles. Recent results from particle-in-cell (PIC) simulations suggest that the fundamental properties of how magnetic fields dissipate in a current sheet might be captured by an "effective resistivity" formulation, which would locally enhance the amount of magnetic energy dissipated and favor the onset of fast reconnection. Our goal is to assess this ansatz quantitatively by comparing fluid models of magnetic reconnection with a non-constant magnetic diffusivity and fully-kinetic models. We perform 2D resistive relativistic magnetohydrodynamic (ResRMHD) simulations of magnetic reconnection combined to PIC simulations using the same initial conditions (namely a Harris current sheet). We explore the impact of crucial parameters such as the plasma magnetization, its mass density, the grid resolution, and the characteristic plasma skin depth. Our ResRMHD models with effective resistivity can quantitatively reproduce the dynamics of fully-kinetic models of relativistic magnetic reconnection. In particular, they lead to reconnection rates consistent with PIC simulations, while for constant-resistivity fluid models the reconnection dynamics is generally 10 times slower. Even at modest resolutions the adoption of an effective resistivity can qualitatively capture the properties of kinetic reconnection models and produce reconnection rates compatible with collisionless models, i.e. of the order of $\sim10^{-1}$.