Gamma-rays from millisecond pulsar population within the central stellar cluster in the Galactic Center

It was proposed that the central dense stellar cluster in the Galactic Center, containing the mass of $\sim$4 times larger than that of the central black hole, had been formed as a result of a merging of several massive globular clusters. These globular clusters are expected to provide a large number of millisecond pulsars (MSPs) within the central parsec of the Galactic Center. We propose that the GeV $\gamma$-ray emission observed from the Galactic Center is in fact a cumulative effect of the emission from several globular clusters captured by the Galactic Center black hole. Moreover, the millisecond pulsars in globular clusters accelerate leptons in their wind zones to energies of the order of a few tens of TeV injecting them into the dense infrared and optical radiation region present within the central parsec. We calculate the expected TeV $\gamma$-ray emission produced by these leptons by the Inverse Compton Scattering process in the soft radiation field. It is shown that this emission can be responsible for the multi-TeV $\gamma$-rays observed by the Cherenkov telescopes from the Galactic Center for reasonable densities of the soft radiation, diffusion models for the propagation of leptons, their injection parameters (fluxes and spectral proprieties). If the energy conversion efficiency from the pulsars to the relativistic leptons is of the order of 10%, then about a thousand of MSPs have to be present in the central cluster in the Galactic Center.