Beyond ideal MHD: towards a more realistic modelling of relativistic astrophysical plasmas

Many astrophysical processes involving magnetic fields and quasi-stationary processes are well described when assuming the fluid as a perfect conductor. For these systems, the ideal-magnetohydrodynamics (MHD) description captures the dynamics effectively and a number of well-tested techniques exist for its numerical solution. Yet, there are several astrophysical processes involving magnetic fields which are highly dynamical and for which resistive effects can play an important role. The numerical modelling of such non-ideal MHD flows is significantly more challenging as the resistivity is expected to change of several orders of magnitude across the flow and the equations are then either of hyperbolic-parabolic nature or hyperbolic with stiff terms. We here present a novel approach for the solution of these relativistic resistive MHD equations exploiting the properties of implicit-explicit (IMEX) Runge-Kutta methods. By examining a number of tests, we illustrate the accuracy of our approach under a variety of conditions and highlight its robustness when compared with alternative methods, such as the Strang splitting. Most importantly, we show that our approach allows one to treat, within a unified framework, those regions of the flow which are both fluid-pressure dominated (such as in the interior of compact objects) and instead magnetic-pressure dominated (such as in their magnetospheres). In view of this, the approach presented here could find a number of applications and serve as a first step towards a more realistic modelling of relativistic astrophysical plasmas.