Correlation of $γ$-ray and high-energy cosmic ray fluxes from the giant lobes of Centaurus A

Abstract: The spectral energy distribution of giant lobes shows one main peak detected by the Wilkinson Microwave Anisotropy Probe at low energy of $10^{-5}$ eV and a faint $\gamma$-ray flux imaged by Fermi Large Area Telescope at energy $\geq$ 100 MeV. On the other hand, Pierre Auger Observatory associated some ultra-high-energy cosmic rays with the direction of Centaurus A and IceCube reported 28 neutrino-induced events in a TeV - PeV energy range, although none of them related with this direction. In this work we describe the spectra for each of the lobes, the main peak with synchrotron radiation, and the high-energy emission with $pp$ interactions. Obtaining a good description of the main peak, we deduce the magnetic fields, electron densities and the age of the lobes. Describing successfully the $\gamma$-ray emission by pp interactions and considering as targets those thermal particles in the lobes with density in the range $10^{-10}$ to $10^{-4}\, {\rm cm}^{-3}$, we calculate the number of ultra-high-energy cosmic rays. Although $\gamma$-spectrum is well described with any density in the range, only when $10^{-4}\, {\rm cm}^{-3}$ is considered, the expected number of events is very similar to that observed by Pierre Auger Observatory, otherwise we obtain an excessive luminosity. In addition, correlating the $\gamma$-ray and neutrino fluxes through pp interactions we calculate the number of high-energy neutrinos expected in IceCube. Our analysis indicates that neutrinos above 1 TeV cannot be produced in the lobes of Centaurus A, which is consistent with the results recently published by IceCube Collaboration.