On the Axisymmetric Force‐free Pulsar Magnetosphere

We investigate the axisymmetric magnetosphere of an aligned rotating magneticdipole surrounded by an ideal force-free plasma. We concentrate on the magneticfield structure around the point of intersection of the separatrix between theopen and closed field-line regions and the equatorial plane. We first study thecase where this intersection point is located at the Light Cylinder. We findthat in this case the separatrix equilibrium condition implies that all thepoloidal current must return to the pulsar in the open-field region, i.e., thatthere should be no finite current carried by the separatrix/equator currentsheet. We then perform an asymptotic analysis of the pulsar equation near theintersection point and find a unique self-similar solution; however, a LightSurface inevitably emerges right outside the Light Cylinder. We then perform asimilar analysis for the situation where the intersection point lies somewhereinside the Light Cylinder, in which case a finite current flowing along theseparatrix and the equator is allowed. We find a very simple behavior in thiscase, characterized by a 90-degree angle between the separatrix and the equatorand by finite vertical field in the closed-field region. Finally, we discussthe implications of our results for global numerical studies of pulsarmagnetospheres.Comment: 31 pages, including 5 figure