Galactic gamma-ray background as a constraint on millisecond pulsars

A large number of millisecond pulsars are believed to exist in the Galaxy. Their magnetic fields are generally 2-4 orders of magnitude smaller than those of the normal pulsars. These pulsars are thought to have been resurrected from the run-down old pulsars. We apply the mechanism proposed by Scharlemann et al. (1978) for particle acceleration along open field lines in the magnetospheres of these pulsars and find that particles can become highly relativistic. We then calculate the gamma-ray flux of curvature radiation from the accelerated particles. Since the number of millisecond pulsars in the Galaxy is quite uncertain, we survey the literature to get some estimates of the number of millisecond pulsars in the plane of the Galaxy and in the globular clusters. We use these numbers to work out the integrated high-energy gamma-ray flux from millisecond pulsars in the Galaxy as a function of the Galactic latitude and longitude. We discuss the results in the light of the COS B observations of the background gamma-radiation, which is the resultant diffuse emission when the contribution of the known point sources has been subtracted from the total emission, and the flux calculated by Strong et al. from the interaction of H I and H-2 with cosmic rays and inverse Compton emission. We are able to place useful constraints on the number of millisecond pulsars in the disk and in the globular clusters.