Magnetic dissipation in short gamma-ray-burst jets. I. Resistive relativistic MHD evolution in a model environment

Short gamma-ray bursts originate when relativistic jets emerge from the remnants of binary neutron star (BNS) mergers, as observed in the first multi-messenger event GW170817 - GRB 170817A, which coincided with a gravitational wave signal. Both the jet and the remnant are believed to be magnetized, and the presence of magnetic fields is known to influence the jet propagation across the surrounding post-merger environment. In the magnetic interplay between the jet and the environment itself, effects due to a finite plasma conductivity may be important, especially in the first phases of jet propagation. We aim to investigate these effects, from jet launching to its final breakout from the post-merger environment. We used the PLUTO numerical code to perform 2D axisymmetric and full 3D resistive relativistic magnetohydrodynamic (MHD) simulations, employing spherical coordinates with spatial radial stretching. We considered and compared different models for physical resistivity, which must be small but still dominating over the intrinsic numerical dissipation (which yields unwanted smearing of structures in any ideal MHD code). Stiff terms in the current density are treated with IMplicit-EXplicit Runge Kutta algorithms for time-stepping. A Synge-like gas (Taub equation of state) is also considered. All simulations were performed using an axisymmetric analytical model for both the jet propagation environment and the jet injection ; we leave the case of jet propagation in a realistic environment (i.e., imported from an actual BNS merger simulation) to a future study. As expected no qualitative differences are detected due to the effect of a finite conductivity but significant quantitative differences in the jet structure and induced turbulence are clearly seen in 2D axisymmetric simulations, and we also compare different resistivity models. We see the formation of regions with a resistive electric field parallel to the magnetic field, and nonthermal particle acceleration may be enhanced there. The level of dissipated Ohmic power is also dependent on the various recipes for resistivity. Most of the differences arise before the breakout from the inner environment, whereas once the jet enters the external weakly magnetized environment region these differences are preserved during further propagation despite the lower grid refinement. Finally, we show and discuss the 3D evolution of the jet within the same environment in order to highlight the emergence of nonaxisymmetric features.