Introducing PHAEDRA: a new spectral code for simulations of relativistic magnetospheres

TL;DR

PHAEDRA is a novel spectral code designed for simulating relativistic magnetospheres, offering high accuracy and low dissipation, demonstrated through various tests and an application to the aligned rotator problem.

Contribution

It introduces a new spectral scheme for force-free electrodynamics that improves accuracy and handles current sheets effectively.

Findings

Demonstrates convergence to analytic solutions

Achieves low numerical dissipation outside current sheets

Successfully models the aligned rotator with localized resistivity

Abstract

We describe a new scheme for evolving the equations of force-free electrodynamics, the vanishing-inertia limit of magnetohydrodynamics. This pseudospectral code uses global orthogonal basis function expansions to take accurate spatial derivatives, allowing the use of an unstaggered mesh and the complete force-free current density. The method has low numerical dissipation and diffusion outside of singular current sheets. We present a range of one- and two-dimensional tests, and demonstrate convergence to both smooth and discontinuous analytic solutions. As a first application, we revisit the aligned rotator problem, obtaining a steady solution with resistivity localised in the equatorial current sheet outside the light cylinder.