Novel scheme for simulating the force-free equations: Boundary conditions and the evolution of solutions towards stationarity

Abstract

Force-Free Electrodynamics (FFE) describes a particular regime of magnetically dominated relativistic plasmas, which arises on several astrophysical scenarios of interest such as pulsars or active galactic nuclei. In this article, we present a full 3D numerical implementation of the FFE evolution around a Kerr black hole. The novelty of our approach is three-folded: i) We use the "multi-block" technique [1] to represent a domain with S 2 × R + topology within a stable finite-differences scheme. ii) We employ as evolution equations those arising from a covariant hyperbolization of the FFE system [2]. iii) We implement stable and constraint-preserving boundary conditions to represent an outer region given by a uniform magnetic field aligned or misaligned respect to the symmetry axis.We find stationary jet solutions which reach equilibrium -through boundary conditions-with the outer numerical surface. This is so, even when the outer boundary is located very close to the central region (i.e. rout ∼ 10M ). These numerical solutions reproduce most of the known results for analogue astrophysical settings. *

Magnetosphere of an orbiting neutron star

“…II-C and Appendix), so we recommend the interest readers to refer there for further details. In order to handle CS, for which the force-free approximation breaks down, we use a standard approach in which the electric field is effectively dissipated to maintain the condition that the plasma is magnetically dominated (i.e., B 2 − E 2 > 0), as discussed in [33] (see also [44]).…”

“…The code used here to evolve the equations of forcefree electrodynamics was first described in [33]; and later extended in [34], where a careful treatment to handle the boundary conditions on the NS surface was presented, in contrast to the matching procedure used in previous GRFF simulations 2 . Since then, our code has been further tested and employed in other astrophysical scenarios [35,36], as well.…”

Striped Blandford/Znajek jets from advection of small-scale magnetic field

“…In fact, Blandford & Znajek (1977) examine a paraboloidal field line configuration with Ω F ∈ [0.27Ω BH , 0.5Ω BH ]. In stationary, axisymmetric force-free electrodynamics, a field line angular velocity Ω F may be defined employing the relations given in section 2.2 (Blandford & Znajek 1977;Carrasco & Reula 2017):…”

Astrophysical jets from boosted compact objects

“…We are interested on modeling the magnetosphere of a compact object (BH or NS) that travels across a uniform magnetic field by solving the equations of force-free electrodynamics. The code used here was first described in [21] for black holes and later extended in [22], by developing appropriate boundary conditions for the perfectly conducting surface of a neutron star. Since we adopt the reference frame of the central object, its motion relative to the uniform magnetic field will be accomplished through suitable boundary conditions at the external surface of the domain.…”

“…Although a detailed description of our numerical implementation can be found on previous works [21,22], we shall start this section by briefly summarizing its basic features along with information about the metric and the set of evolution equations employed. Then, we shall describe initial data and boundary conditions for the two scenarios we want to study.…”