Multiband Emission up to PeV Energy from the Crab Nebula in a Spatially Dependent Lepto-hadronic Model

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Abstract
Multiband emissions from radio to ultra-high-energy gamma-rays in the Crab Nebula have been detected. To explain the observed results, nonthermal photon production in the Crab Nebula is carefully studied in a spatially dependent lepto-hadronic model. In our model, the dynamical evolution of the pulsar wind nebula (PWN) is simulated in a spherically symmetric system. Both electrons and protons are accelerated at the termination shock. The relevant particle propagation equations, as well as the photon evolving equation, are simultaneously solved. For the Crab Nebula, our results reveal that the observed multiband photon spectra can be reproduced with reasonable model parameters. In particular, the photons with energy ≳200 TeV are mainly contributed to by the hadronic component via proton–proton interaction. The contribution of the hadronic component depends on both proton spectral index α p and number density n H of the medium within the PWN. Additionally, high-energy neutrino fluxes are predicted with variable proton spectral indices. The predicted fluxes are not only far below the sensitivities of current neutrino observatories but also beneath the atmospheric neutrino background with energy less than ∼40 TeV. Moreover, the calculated radial profiles of surface brightness and spectral index are presented.

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