Toward a Realistic Pulsar Magnetosphere

TL;DR

This paper investigates non-ideal pulsar magnetospheres with non-zero parallel electric fields, exploring their structures, dissipation, and implications for pulsar radiation, bridging the gap between vacuum and ideal force-free models.

Contribution

It introduces models of non-ideal pulsar magnetospheres with variable electric fields, providing a continuum between vacuum and force-free solutions and analyzing their dissipation and observational signatures.

Findings

Maximum dissipation is 20-40% of Poynting flux in aligned rotators.

Solutions with $J > ho c$ exhibit oscillations potentially observable.

Limiting solutions with $J= ho c$ relate to pulsar on/off states.

Abstract

We present the magnetic and electric field structures as well as the currents and charge densities of pulsar magnetospheres which do not obey the ideal condition, ${\bf E \cdot B =0}$. Since the acceleration of particles and the production of radiation requires the presence of an electric field component parallel to the magnetic field, ${\bf E}_\parallel$, the structure of non-Ideal pulsar magnetospheres is intimately related to the production of pulsar radiation. Therefore, knowledge of the structure of non-Ideal pulsar magnetospheres is important because their comparison (including models for the production of radiation) with observations will delineate the physics and the parameters underlying the pulsar radiation problem. We implement a variety of prescriptions that support nonzero values for ${\bf E}_\parallel$ and explore their effects on the structure of the resulting magnetospheres. We produce families of solutions that span the entire range between the vacuum and the (ideal) Force-Free Electrodynamic solutions. We also compute the amount of dissipation as a fraction of the Poynting flux for pulsars of different angles between the rotation and magnetic axes and conclude that this is at most 20-40% (depending on the non-ideal prescription) in the aligned rotator and 10% in the perpendicular one. We present also the limiting solutions with the property $J=\rho c$ and discuss their possible implication on the determination of the "on/off" states of the intermittent pulsars. Finally, we find that solutions with values of $J$ greater than those needed to null ${\bf E}_\parallel$ locally produce oscillations, potentially observable in the data.