Modulated gamma-ray emission from compact millisecond pulsar binary systems

Context. A significant number of the millisecond pulsars (MSPs) have been discovered within binary systems. Tens of these MSPs emit γ-rays that are modulated with the pulsar period since this emission is produced in the inner pulsar magnetosphere. In several such binary systems, the masses of the companion stars have been derived allowing two classes of objects to be distinguished, which are called the black widow and the redback binaries. Pulsars in these binary systems are expected to produce winds that create conditions for acceleration of electrons, when colliding with stellar winds. These electrons should interact with the anisotropic radiation from the companion stars producing γ-ray emission modulated with the orbital period of the binary system, similar to what is observed in the massive TeV γ-ray binary systems. Aims. We consider the interaction of a MSP wind with a very inhomogeneous stellar wind from the companion star within binary systems of the black widow and redback types. Our aim is to determine the features of γ-ray emission produced in the collision region of the winds from a few typical MSP binary systems. Methods. It is expected that the pulsar wind should mix efficiently with the inhomogeneous stellar wind. The mixed winds move outside the binary with relatively low velocity. Electrons accelerated in such mixed, turbulent winds can interact with the magnetic field and strong radiation from the companion star, producing not only synchrotron radiation but also γ-rays in the inverse Compton process, fluxes of which are expected to be modulated on the periods of the binary systems. Applying numerical methods, we calculated the GeV-TeV gamma-ray spectra and the light curves expected from some MSP binary systems. Results. Gamma-ray emission, produced within the binary systems, is compared with the sensitivities of the present and future gamma-ray telescopes. It is concluded that energetic MSP binary systems create a new class of TeV γ-ray sources that could be detectable by the future Cherenkov arrays (e.g., CTA) and possibly also by the extensive campains with the present arrays (HESS, MAGIC, VERITAS). However, γ-ray emission from the MSP binary systems is predicted to have different features than those observed in the case of massive TeV gamma-ray binaries such as LS I 303 61 or LS 5039. The maximum in the TeV γ-ray orbital light curve should appear when the MSP is behind the companion star. This is in contrast to the observations of the orbital light curves from the massive TeV γ-ray binaries (LS I 303 61 or LS 5039). Moreover, the GeV and orbital TeV γ-ray light curves should be positively correlated unlike the case of massive TeV γ-ray binaries. Conclusions. We conclude that TeV γ-ray emission, modulated on the orbital period of MSP binary systems, should be detected by the future CTA. Moreover, some MSP binary systems of the Redback type might also show GeV γ-ray emission modulated on the binary periods on the level detectable by Fermi-LAT