Phase-averaged gamma-ray spectra from rotation-powered millisecond pulsars

Abstract

{\it Fermi}-LAT has detected pulsed gamma-ray emissions with high confidences from more than 40 millisecond pulsars (MSPs). Here we study the phase-averaged gamma-ray properties of MSPs by using revised version of a self-consistent outer gap model. In this model, a strong multipole magnetic field near the stellar surface for a MSP is assumed and such a field will be close to the surface magnetic fields ($\sim 10^{11}- 10^{12}$ G) of young ulsars; the outer gap of a MSP is controlled by photon-photon pair production process, where the effects of magnetic inclination angle ($\alpha$) and magnetic geometry have been taken into account, therefore the fractional size of the outer gap is a function of not only pulsar's period and magnetic field strength but also magnetic inclination angle and radial distance to the neutron star, the inner boundary of the outer gap can be estimated by the pair production process of the gamma-ray photons which are produced by the back-flowing particles through the null charge surface; inside the outer gap, a Gaussian distribution of the parallel electric field along the trans-field thickness is assumed, and the gamma-ray emission is represented by the emission from the average radial distance along the central field lines of the outer gap. Using this model, the phase-averaged gamma-ray spectra are calculated and compared with the observed spectra of 37 MSPs given by the second {\it Fermi}-LAT catalog of gamma-ray pulsars, our results show that the {\it Fermi}-LAT results can be well explained by this model. The thermal X-ray emission properties from MSPs are also investigated.