The IceCube Collaboration has recently reported compelling evidence of high-energy neutrino emission from NGC 1068, and also mild excesses for NGC 4151 and CGCG420-015, local Seyfert galaxies. This has increased the interest along neutrino emission from hot-corona surrounding the super massive black holes of Seyfert Galaxies. In this paper, we revisit phenomenological constraints on the neutrino emission from hot-coronae of Seyfert galaxies, using an assumption of sub-equipartition between cosmic-rays and magnetic energy densities. We show that not only these sources are consistent with such an assumption but also that the data point towards low values for the ratio between thermal and magnetic pressure, the so called beta plasma parameters inside Seyfert galaxies. We exploit this finding to constrain the Seyfert diffuse neutrino flux and we obtain that, in order not to overproduce neutrinos, not all the sources can be efficient neutrino emitters. In our approach (along with previous findings), Seyfert galaxies provide a negligible contribution to the diffuse neutrino spectrum above ∼ 100 TeV, allowing space for other astrophysical sources. However, future data from high-energy neutrino telescopes will be crucial to shed more light onto the contribution of this source class to the cosmic neutrino background.
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