Outer-magnetospheric model for Vela-like pulsars:formation of sub-GeV spectrum

We investigate the $\gamma$-ray emission from a outer-gap accelerator, which is located in the outer-magnetosphere of a pulsar. The charge depletion from the Goldreich-Julian 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 curvature spectrum to compare with the observations. We find that because the particles escape from the accelerating region with large Lorentz factors as $10^{7.5}$, curvature radiation from the outside of the gap, in which there is no electric field, still has a 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 the field line curvature close to the light cylinder affects the spectrum in several hundred MeV, there is a possibility to diagnose the field structure by using the spectrum in these bands. The difference found in the $\gamma$-ray spectra of the twin pulsars, PSR B0833-45 (Vela) and B1706-44, is deduced from the dimensionless electric current running through the gap. The extension to the three-dimensional modeling with self-consistent electrodynamics is necessary to understand the difference in the observed flux between the twin pulsars