A two‐dimensional electrodynamical model is used to study particle acceleration in the outer magnetosphere of a pulsar. The charge depletion from the Goldreich–Julian charge density causes a large electric field along the magnetic field lines. The charge particles are accelerated by the electric field and emit γ‐rays via the curvature process. Some of the emitted γ‐rays may collide with X‐ray photons to make new pairs, which are accelerated again on the different field lines and emit γ‐rays. We simulate the pair creation cascade in the meridional plane using the pair creation mean‐free path, in which the X‐ray photon number density is proportional to the inverse square of the radial distance. With the space charge density determined by the pair creation simulation, we solve the electric structure of the outer gap in the meridional plane and calculate the curvature spectrum. We investigate in detail the relation between the spectrum and total current, which is carried by the particles produced in the gap and/or injected at the boundaries of the gap. We demonstrate that the hardness of the spectrum is strongly controlled by the current carriers. Especially, the spectrum sharply softens if we assume a larger particle injection at the outer boundary of the outer gap. This is because the mean‐free path of the pair creation of the inwardly propagating γ‐ray photons is much shorter than the light radius, so many pairs are produced in the gap to quench the outer gap. Because the two‐dimensional model can link both gap width along the magnetic field line and trans‐field thickness with the spectral cut‐off energy and flux, we can diagnose both the current through the gap and the inclination angle between the rotational and magnetic axes. We apply the theory to the Vela pulsar. By comparing the results with the Energetic Gamma Ray Experiment Telescope (EGRET) data, we rule out any cases that have a large particle injection at the outer boundary. We also suggest the inclination angle of αinc≥ 65°. The present model predicts the outer gap starting from near the conventional null charge surface for the Vela pulsar.

We investigate the electrodynamics of an outer gap in the meridional plane of the aligned-rotator. The charge depletion from the Goldreich-Julian charge density causes a large electric field along the magnetic field line. The electrons or the positrons are accelerated by the field-aligned electric field and radiate the $\gamma$-rays tangentially to the local magnetic field line. Some of such $\gamma$-rays collide with $X$-rays to materialize as the electron-positron pairs on different field lines from the field line on which they were emitted. As a result, the electric field structure is expected to change across the field lines. Including these trans-field effects, we solve the formation of the electric field self-consistently with the curvature radiation and the pair creation processes. The $\gamma$-ray emission and the pair creation are treated by use of Monte Carlo technique. We demonstrate that the distribution of the electric field along the field lines is affected by both the gap geometry and the external currents coming into the gap through the boundaries. In the electrodynamical model, it has been known that the solution disappears if the current density carried by the electron-positron pairs produced in the gap exceeds a critical value. We show that the critical current density is significantly increased when the trans-field structure is taken into account. We also find that the location of the inner boundary of the gap shifts toward the stellar surface from the conventional null surface as the current density increases. The reason for the shift is derived from the stability condition of the inner boundary. We also argue that the ideal-MHD condition holds outside of the gap only when the low energy particles coexist with the high energy particles migrating from the gap.Comment: 28 pages, 8 figures. Accepted for publication in MNRA

We investigate the γ -ray emission from an outer-gap accelerator, which is located in the outer magnetosphere of a pulsar. The charge depletion from the GoldreichJulian density causes a large electric field along the magnetic field lines. The electric field accelerates electrons and positrons to high energies. We solve the formation of the electric field self-consistently with the radiation and the pair creation processes in one-dimensional geometry along the magnetic field lines, and calculate the curvature spectrum for comparison with the observations. We find that, because the particles escape from the accelerating region with Lorentz factors as large as 10⁷.⁵, curvature radiation from outside of the gap, in which there is no electric field, still makes an important contribution to the spectrum. Including the outside emission, the model spectra are improved between 100 MeV and 1 GeV for the Vela-type pulsars. Since field line curvature close to the light cylinder affects the spectrum at several hundred MeV, there is a possibility to diagnose the field structure by using the spectrum in these bands. The difference found in the γ -ray spectra of the two pulsars, PSR B083345 (Vela) and B170644, is deduced from the dimensionless electric current running through the gap. The extension to three-dimensional modelling with self-consistent electrodynamics is necessary to understand the difference in the observed flux between the two pulsars

No abstract

No abstract