Emission Patterns and Light Curves of Gamma-Rays in the Pulsar Magnetosphere with a Current-Induced Magnetic Field

We study the emission patterns and light curves of gamma-rays in the pulsar magnetosphere with a current-induced magnetic field perturbation. Based on the solution of a static dipole with the magnetic field induced by some currents (perturbation field), we derive the solutions of a static as well as a retarded dipole with the perturbation field in the Cartesian coordinates. The static (retarded) magnetic field can be expressed as the sum of pure static (retarded) dipolar magnetic field and the static (retarded) perturbation field. We use the solution of the retarded magnetic field to investigate the influence of the perturbation field on the emission patterns and light curves, and we apply the perturbed solutions to calculate the gamma-ray light curves for the case of the Vela pulsar. We find out that the perturbation field induced by the currents will change the emission patterns and then light curves of gamma-rays, especially for a larger perturbation field. Our results indicate that the perturbation field created by the outward-flowing (inward-flowing) electrons (positrons) can decrease the rotation effect on the magnetosphere and makes emission pattern appear to be more smooth relative to that of the pure retarded dipole, but the perturbation field created by the outward-flowing (inward-flowing) positrons (electrons) can make the emission pattern less smooth.