Spectral features in gamma-rays expected from millisecond pulsars

In the advent of next generation gamma-ray missions, we present general properties of spectral features of high-energy emission above $1\MeV$ expected for a class of millisecond, low magnetic field ($\sim 10^9\G$) pulsars. We extend polar-cap model calculations of Rudak & Dyks (1999) by including inverse Compton scattering events in ambient field of thermal X-ray photons and by allowing for two models of particle acceleration. In the range between $1\MeV$ and a few hundred GeV the main spectral component is due to curvature radiation of primary particles. Synchrotron component due to secondary pairs becomes dominant only below $1\MeV$. The slope of the curvature radiation spectrum in the energy range from $100\MeV$ to $10\GeV$ strongly depends on the model of longitudinal acceleration, whereas below $\sim 100\MeV$ all slopes converge to a unique value of 4/3 (in a $\nu {\cal F}_\nu$ convention). The thermal soft X-ray photons, which come either from the polar cap or from the surface, are Compton upscattered to a domain of the VHE and form a separate spectral component peaking at $\sim 1\TeV$. We discuss observability of millisecond pulsars by future high energy instruments and present two rankings relevant for GLAST and MAGIC. We point to the pulsar J0437-4715 as a promising candidate for observations.