The spectral simulations of axisymmetric force-free pulsar magnetosphere

TL;DR

This paper develops a spectral numerical method to simulate the time-dependent force-free pulsar magnetosphere, accurately reproducing known solutions and revealing detailed structures like the equatorial current sheet.

Contribution

It introduces a pseudo-spectral approach with an absorbing boundary and divergence-free magnetic field enforcement for force-free pulsar magnetosphere simulations.

Findings

Successfully reproduces Deutsch vacuum and Michel monopole solutions.

Resolves the equatorial current sheet effectively.

Steady-state spin-down luminosity matches previous estimates.

Abstract

A pseudo-spectral method with an absorbing outer boundary is used to solve a set of the time-dependent force-free equations. In the method, both electric and magnetic fields are expanded in terms of the vector spherical harmonic (VSH) functions in spherical geometry and the divergencelessness of magnetic field is analytically enforced by a projection method. Our simulations show that the Deutsch vacuum solution and the Michel monopole solution can be well reproduced by our pseudo-spectral code. Further the method is used to present the time-dependent simulation of the force-free pulsar magnetosphere for an aligned rotator. The simulations show that the current sheet in the equatorial plane can be resolved well, and the obtained spin-down luminosity in the steady state is in good agreement with the value given by Spitkovsky (2006).