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Numerical modelling of gamma-ray emission produced by electrons originating from the magnetospheres of millisecond pulsars in globular clusters

Globular clusters are source of gamma-ray radiation. At GeV energies, their emission is attributed to magnetospheric activity of millisecond pulsars residing in the clusters. Inverse Compton scattering of ambient photon fields on relativistic particles diffusing through cluster environment is thought to be the source of GeV-TeV emission of globular clusters. Using pair starved polar cap model gamma-ray emission from synthetic millisecond pulsar was modelled. In addition to pulsar emission characteristics, the synthetic pulsar model yielded spectra of electrons escaping pulsar magnetosphere. To simulate gamma-ray emission of globular cluster, both products of synthetic millisecond pulsar modelling were used. Gamma-ray spectra of synthetic millisecond pulsars residing in the cluster were summed to produce the magnetospheric component of cluster emission. Electrons ejected by these pulsars were injected into synthetic globular cluster environment. Their diffusion and interaction, both, with cluster magnetic field and ambient photon fields, were performed with Bednarek & Sitarek (2007) model yielding ICS component of cluster emission. The sum of the magnetospheric and ICS components gives the synthetic gamma-ray spectrum of globular cluster. The synthetic cluster spectrum stretches from GeV to TeV energies. Detailed modelling was preformed for two globular clusters: Ter 5 and 47 Tuc. Simulations are able to reproduce (within errors) the shape and the flux level of the GeV part of the spectrum observed for both clusters with the Fermi/LAT instrument. The synthetic flux level obtained in the TeV part of the clusters' spectrum is in agreement with a H.E.S.S. upper limit determined for 47 Tuc, and with emission level recently detected for Ter 5 with H.E.S.S. telescope. The synthetic globular cluster model, however, is not able to reproduce the exact shape of the TeV spectrum observed for Ter 5.