Non-corotating models for pulsar magnetospheres

Abstract: We reconsider pulsar electrodynamics for an obliquely rotating pulsar, and propose a way of synthesizing the vacuum dipole model (VDM) and the rotating magnetosphere model (RMM). We first modify the VDM by assuming that the parallel component of the inductive electric field is screened by charges. We refer to the resulting model as the minimal model. We calculate the screening charge density in the minimal model and compare it with the (Goldreich-Julian) charge density in the RMM. We identify the plasma velocity in the minimal model as the electric drift velocity due to the perpendicular component of the inductive electric field. We define a class of synthesized models as a linear combination of a fraction $y$ times the minimal model and $1-y$ times the RMM. These models require a gap (with $E_\parallel\ne0$) between the corotating stellar surface and the non-corotating magnetosphere. We present illustrative plots of the charge density, of the location of nulls (where the charge density is zero) and of the three components of the plasma velocity as a function of the angles ($\theta,\psi$) relative to the rotation axis, for specific values of the obliquity $\alpha$ and the parameter $y$. We discuss the question "Can any pulsar magnetosphere be corotating?" critically, pointing out difficulties associated with setting up corotation in the polar cap region. We speculate that the corotating plasma may flow across the last closed field line from the closed-field region. We suggest that abrupt changes in the spin-down rate in some pulsars may be due to jumps between the RMM and the minimal model.