Upper Limit on the Coronal Cosmic Ray Energy Budget in Seyfert Galaxies

The IceCube collaboration has reported possible detections of high-energy neutrinos from nearby Seyfert galaxies. While central hot coronae are proposed as the primary neutrino production site, the exact coronal cosmic-ray energy budget has been loosely constrained. In this study, we propose a new stringent upper bound on the coronal cosmic-ray energy budget of Seyfert galaxies, considering both accretion dynamics and observed properties of radio-quiet Seyfert galaxies. Notably, even under the calorimetric condition where cosmic rays lose all their energies, our limit indicates that the coronal neutrino flux of NGC~1068 is about an order of magnitude fainter than the observed levels. This discrepancy suggests the need for further theoretical and observational investigations on the IceCube signals from Seyfert galaxies.