2010ApJ...715.1318T

We discuss outer gap closure mechanism in the trans-field direction with the magnetic pair-creation process near the stellar surface. The gap closure by the magnetic pair creation is possible if some fraction of the pairs are produced with an outgoing momentum. By assuming that multiple magnetic field will affect the local field near the stellar surface, we show a specific magnetic field geometry near the stellar surface resulting in the outflow of the pairs. Together with the fact that the electric field is weak below null charge surface, the characteristic curvature photon energy emitted by incoming particles, which were accelerated in the outer gap, decreases drastically to ∼100 MeV near the stellar surface. We estimate the height measured from the last-open field line, above which 100 MeV photons are converted into pairs by the magnetic pair creation. We also show the resultant multiplicity due to the magnetic pair-creation process could acquire {M_{e^±}∼10^4–105}. In this model, the fractional outer gap size is proportional to P^–1/2. The predicted γ-ray luminosity (L_γ) and the characteristic curvature photon energy (E_c) emitted from the outer gap are proportional to B ² P ^–5/2 and B ^3/4 P^–1, respectively. This model also predicts that L_γ and E_care related to the spin-down power (L_sd) or the spin-down age of pulsars (τ) as L_γ{vprop} L ^5/8_sd or L_γ{vprop} τ^–5/4 and E_c{vprop} L ^1/4_sd or E_c {vprop} τ^–1/2, respectively.