The Correlation between the Total Magnetic Flux and the Total Jet Power

Magnetic field threading a black hole ergosphere is believed to play the key role in both driving the powerful relativistic jets observed in active galactic nuclei and extracting the rotational energy from a black hole via Blandford-Znajek process. The magnitude of magnetic field and the magnetic flux in the vicinity of a central black hole is predicted by theoretical models. On the other hand, the magnetic field in a jet can be estimated through measurements of either the core shift effect or the brightness temperature. In both cases the obtained magnetic field is in the radiating domain, so its direct application to the calculation of the magnetic flux needs some theoretical assumptions. In this paper we address the issue of estimating the magnetic flux contained in a jet using the measurements of a core shift effect and of a brightness temperature for the jets, directed almost at the observer. The accurate account for the jet transversal structure allow us to express the magnetic flux through the observed values and an unknown rotation rate of magnetic surfaces. If we assume the sources are in a magnetically arrested disk state, the lower limit for the rotation rate can be obtained. On the other hand, the flux estimate may be tested against the total jet power predicted by the electromagnetic energy extraction model. The resultant expression for power depends logarithmically weakly on an unknown rotation rate. We show that the total jet power estimated through the magnetic flux is in good agreement with the observed power. We also obtain the extremely slow rotation rates, which may be an indication that the majority of the sources considered are not in the magnetically arrested disk state.