2013ApJ...765..124L

We study the phase-averaged spectra and luminosities of γ-ray emissions from young, isolated pulsars within a revised outer gap model. In the revised version of the outer gap, there are two possible cases for the outer gaps: the fractional size of the outer gap is estimated through the photon-photon pair process in the first case (Case I), and is limited by the critical field lines in the second case (Case II). The fractional size is described by Case I if the fractional size at the null charge surface in Case I is smaller than that in Case II, and vice versa. Such an outer gap can extend from the inner boundary, whose radial distance to the neutron star is less than that of the null charge surface to the light cylinder for a γ-ray pulsar with a given magnetic inclination. When the shape of the outer gap is determined, assuming that high-energy emission at an averaged radius of the field line in the center of the outer gap, with a Gaussian distribution of the parallel electric field along the gap height, represents typical emission, the phase-averaged γ-ray spectrum for a given pulsar can be estimated in the revised model with three model parameters. We apply the model to explain the phase-averaged spectra of the Vela (Case I) and Geminga (Case II) pulsars. We also use the model to fit the phase-averaged spectra of 54 young, isolated γ-ray pulsars, and then calculate the γ-ray luminosities and compare them with the observed data from Fermi-LAT.