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

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.

8 pages, 2 figures; accepted for publication in MNRAS

References in corpus (5)

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• Toward a Realistic Pulsar Magnetosphere
• The Extended Pulsar Magnetosphere
• A Particle Simulation for the Pulsar Magnetosphere: Relationship of Polar Cap, Slot Gap, and Outer Gap
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Cited by in corpus (6)

• Theory of pulsar magnetosphere and wind
• On the Global Structure of Pulsar Force-free Magnetosphere
• Similarity Inner Solutions for the Pulsar Equation
• Axisymmetric force-free magnetosphere of a pulsar. II. Transition from the self-consistent two-fluid model
• Formation of filament-like structures in the pulsar magnetosphere and the short-term variability of pulsar emission
• Two-fluid model of the pulsar magnetosphere represented as an axisymmetric force-free dipole