An Alternative Numerical Method for the Stationary Pulsar Magnetosphere

TL;DR

This paper introduces a new numerical approach to model stationary pulsar magnetospheres without relying on artificial current sheets, providing more physically consistent solutions that include jet-like structures.

Contribution

The authors propose an alternative numerical method that decomposes the pulsar equation into Ampere's law and the force-free condition, avoiding the need for a current sheet.

Findings

Generated a magnetosphere model without a current sheet similar to CKF near the star

Discovered force-free condition breakdown near the light cylinder due to dissipation

Produced a jet-like structure at large distances along the pole

Abstract

Stationary pulsar magnetospheres in the force-free system are governed by the pulsar equation. In 1999, Contopoulos, Kazanas, and Fendt (hereafter CKF) numerically solved the pulsar equation and obtained a pulsar magnetosphere model called the CKF solution that has both closed and open magnetic field lines. The CKF solution is a successful solution, but it contains a poloidal current sheet that flows along the last open field line. This current sheet is artificially added to make the current system closed. In this paper, we suggest an alternative method to solve the pulsar equation and construct pulsar magnetosphere models without a current sheet. In our method, the pulsar equation is decomposed into Ampere's law and the force-free condition. We numerically solve these equations simultaneously with a fixed poloidal current. As a result, we obtain a pulsar magnetosphere model without a current sheet, which is similar to the CKF solution near the neutron star and has a jet-like structure at a distance along the pole. In addition, we discuss physical properties of the model and find that the force-free condition breaks down in a vicinity of the light cylinder due to dissipation that is included implicitly in the numerical method.