Pulsar Magnetosphere Revisited: Emission Geometry and the Synthesis of the Vacuum-Dipole and the Rotating-Magnetosphere Models

Abstract

We reconsider the vacuum-dipole model (VDM) and the corotating-magnetosphere model (CMM) for pulsar electrodynamics. Both the VDM and the CMM are fatally flawed as stand-alone models. The former model is used for deriving certain pulsar parameters, such as the surface magnetic field strength and characteristic age, but it lacks the plasma required to emit the observed radiation. The latter model introduces important concepts, such as the Goldreich-Julian charge density and corotation electric field, which form the basis for more detailed models, but it neglects the inductive electric field. When this field is included, the model is unstable to growth of large-amplitude electric oscillations when subject to a temporal perturbation. Furthermore, the predicted highly-relativistic magnetospheric plasma given by the two models is inconsistent with results obtained from observations with the Double Pulsar system. We therefore propose a way of synthesizing the VDM and the CMM for obliquely rotating pulsars. We first modify the VDM to a "minimal" model by assuming that the parallel component of the inductive electric field is screened by charges. We define a class of synthesized models as a linear combination of a fraction y times the minimal model and 1 - y times the CMM. We suggest that the synthesized model provides a basis for understanding the abrupt changes in the magnetospheres of some pulsars, which can alter their slowing down rates. The synthesized model also implies that the velocity of the magnetospheric plasma depends on y and the position of the emission point, which is determined numerically based on the obliquity and viewing angles for emission heights close to stellar surface in dipolar magnetic field structure. We also explore the field structure by including higher order terms in the ratio of the radius to the light-cylinder radius in the magnetic field and explore the implications of these additional terms.