An oblique pulsar magnetosphere with a plasma conductivity

TL;DR

This paper models oblique pulsar magnetospheres with varying plasma conductivities using a spectral method, revealing a smooth transition from vacuum to force-free solutions and confirming the sin^2 alpha dependence of spin-down luminosity.

Contribution

It introduces a pseudo-spectral approach to simulate pulsar magnetospheres with finite conductivity, extending previous force-free models to more realistic plasma conditions.

Findings

Transition from vacuum to force-free solutions demonstrated.

Confirmed sin^2 alpha dependence of spin-down luminosity.

Developed a spectral method for solving Maxwell equations in spherical geometry.

Abstract

An oblique pulsar magnetosphere with a plasma conductivity is studied by using a pseudo-spectral method. In the pseudo-spectral method, the time-dependent Maxwell equations are solved, 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. The pulsar magnetospheres in infinite (i. e., force-free approximation) and finite conductivities are simulated and a family of solutions that smoothly transition from the Deutsch vacuum solution to the force-free solution are obtained. The $\sin^2\alpha$ dependence of the spin-down luminosity on the magnetic inclination angle $\alpha$ in which the full electric current density are taken into account is retrieved in the force-free regime.