Hadronic models of blazars require a change of the accretion paradigm

We study hadronic models of broad-band emission of jets in radio-loud active galactic nuclei, and their implications for the accretion in those sources. We show that the models that account for broad-band spectra of blazars emitting in the GeV range in the sample of Bottcher et al. have highly super-Eddington jet powers. Furthermore, the ratio of the jet power to the radiative luminosity of the accretion disc is similar to 3000 on average and can be as high as similar to 10(5). We then show that the measurements of the radio core shift for the sample imply low magnetic fluxes threading the black hole, which rules out the Blandford-Znajek mechanism to produce powerful jets. These results require that the accretion rate necessary to power the modelled jets is extremely high, and the average radiative accretion efficiency is similar to 4 x 10(-5). Thus, if the hadronic model is correct, the currently prevailing picture of accretion in AGNs needs to be significantly revised. Also, the obtained accretion mode cannot be dominant during the lifetimes of the sources, as the modelled very high accretion rates would result in too rapid growth of the central supermassive black holes. Finally, the extreme jet powers in the hadronic model are in conflict with the estimates of the jet power by other methods.