An assessment of the pulsar outer gap model. II: Implications for the   predicted $\gamma$-ray spectra
  One of the most important predictions of any gap model for pulsar magnetospheres is the predicted $\gamma$-ray spectra. In the outer gap model, the properties of the synchro-curvature radiation are sensitive to many parameters, whose realistic ranges have been studied in detail in an accompanying paper. There we demonstrated that the uncertainty in the radius of curvature, the magnetic field geometry, and the X-ray surface flux may affect by orders of magnitude the predicted flux and spectral peak in the $\gamma$-ray regime. Here, we present a systematic, numerical study of the impact of the different parameters on the particle dynamics along the gap and calculate the emitted synchro-curvature radiation along the trajectory. By integrating the emitted radiation along the gap and convolving it with a parametrized particle distribution, we discuss how the comparison with the wealth of {\em Fermi}-LAT data can be used to constrain the applicability of the model. The resulting spectra show very different energy peaks, fluxes and shapes, qualitatively matching the great variety of the observed {\em Fermi}-LAT pulsars. In particular, if we see a large fraction of photons emitted from the initial part of the trajectory, we show that the spectra will be flatter at the low-energy {\it Fermi}-LAT regime (100 MeV -- 1 GeV). This provides a solution for such observed flat spectra, while still maintain synchro-curvature radiation as the origin of these photons. 
Daniele Vigan\`o (1), Diego F. Torres (1,2), Kouichi Hirotani (3),   Mart\'in E. Pessah (4) ((1) ICE (IEEC/CSIC), Barcelona,...
astro-ph.HE