Estimation of the muon energy spectrum emitted by high energy gamma rays from the Crab nebula

The vertical integral spectrum of TeV muons produced by the UHE gamma rays incident on Earth from the direction of the Crab nebula is calculated. The analytical estimate of the muon spectrum is made using the standard cascade equation for muons and the latest photopion production cross section obtained from the At to the DESY ep collider experiment. The derived integral muon energy spectrum generated by the photoproduced pions is compared with the estimated muon energy spectra from the direct production of muon pairs and photoproduced pions of charmed particle decay. The present analytical estimates have been compared with the earlier simulation estimate of Halzen and co-workers along with the analytical results of Drees and co-workers. The present results show a little bit flatter muon energy spectrum when compared to the earlier simulation result, The muon energy spectrum has also been estimated from photopions using the simulation formulation of Halzen and Stanev with latest parametrization and has been found fairly comparable with the present result.