Determination of the Analytical Solutions of the Radio Emission Geometry and Polar Cap Structure of Pulsars Having Perturbed Dipole

Abstract We model an analytical solution to generate the shape of the polar cap structure and discuss the geometrical distortion due to the presence of both longitudinal plasma current flow across the polar cap regime, i.e., polar cap current perturbation, and pulsar rotation, i.e., rotational perturbation. An analytical solution to the parameter space associated with the radio emission geometrical coordinate is produced by using the first- and second-order power series expansion method for the rotationally perturbed dipole case. In general, polar caps show a quasi-elliptical shape, but in the presence of higher-order plasma current our results show that they can be converted into an elliptical structure with a monotonically reduced dimension. Our results show that the rotational effect also leads to a contraction of the dimensions of the polar cap for a given range of the obliquity parameters. We have found that the last open field line constant, as a fraction of the light cylinder radius, decreases in the presence of nonzero plasma current discharge. We also demonstrate that under certain conditions introducing a higher-order plasma current (e.g., with a scale factor ζ p = J / J GJ close to 1 in the closed field line region) can lead to a structure resembling a cosmic-combed magnetosphere.