Three Mistakes in Pulsar Electrodynamics

TL;DR

This paper critically examines the foundational 1969 pulsar electrodynamics theory by Goldreich and Julian, identifying three mathematical mistakes and highlighting overlooked solutions, supported by magnetohydrodynamic experiments.

Contribution

It reveals three key errors in the classic pulsar electrodynamics theory and emphasizes the importance of a neglected solution, advancing understanding of pulsar physics.

Findings

Identified three mathematical mistakes in the Goldreich-Julian model

Highlighted the significance of a neglected solution to the frozen-in field equation

Presented magnetohydrodynamic experiments relevant to pulsar research

Abstract

In the paper Pulsar Electrodynamics, published in 1969, Goldreich and Julian propose some basic properties of pulsars, such as the oft-cited Goldreich-Julian density, light cylinder, open and closed magnetic field lines, corotation and so on. However, inspection of their mathematics reveals three mistakes: first, the relative velocity is irrelevantly replaced by the corotation velocity; second, a hypothesis in their theory is contradictory to Maxwell's equations; and third, their theory neglected a special solution of the frozen-in field equation which is of particular importance for pulsar research. We additionally describe the results of a series of magnetohydrodynamic experiments that may be beneficial to the understanding of pulsar electrodynamics.