Axisymmetric force-free magnetosphere of a pulsar. I. The structure close to the magnetic axis

TL;DR

This paper analytically investigates the structure of a pulsar's force-free magnetosphere near the magnetic axis, deriving asymptotic series for flux and current functions, and incorporating the current sheet into the global model.

Contribution

It provides the first analytical solution for the pulsar magnetosphere near the magnetic axis, including the current sheet and plasma-producing gaps.

Findings

Derived asymptotic series for flux and current functions at infinity.

Found the flux function at the polar gap differs from the surface dipolar field.

Excluded backward particle flow, supporting the stationary cascade scenario.

Abstract

The stationary axisymmetric force-free magnetosphere of a pulsar is studied analytically. The pulsar equation is solved in the region close to the magnetic axis. Proceeding from linearization of the current function in the axial region, we find the axial magnetic flux function valid at any altitude above the neutron star. This function is used as a starting approximation to develop series for the non-linear pulsar equation in the polar region. Taking into account the quasi-monopolar character of the pulsar magnetic flux at infinity, we obtain unique asymptotic series for the flux and current functions. At infinity, both functions are close but not equivalent to those known for the case of a force-free monopole. The flux function at the top of the polar gap is found to differ from the dipolar one at the neutron star surface. With our results, the transverse current sheet closing the pulsar circuit at the neutron star surface is consistently incorporated into the global magnetospheric structure, the backward particle flow at small polar angles can be excluded and the stationary cascade scenario looks admissible. The present paper is the first step toward complete analytic description of the pulsar force-free magnetosphere allowing for the plasma-producing gaps and pulsar current circuit closure.