We study the effect of radio-jet core shift, which is a dependence of the position of the jet radio core on the observational frequency. We derive a new method of measuring the jet magnetic field based on both the value of the shift and the observed radio flux, which complements the standard method that assumes equipartition. Using both methods, we re-analyse the blazar sample of Zamaninasab et al. We find that equipartition is satisfied only if the jet opening angle in the radio core region is close to the values found observationally, ≃0.1-0.2 divided by the bulk Lorentz factor, Γ j . Larger values, e.g., 1/Γ j , would imply magnetic fields much above equipartition. A small jet opening angle implies in turn the magnetization parameter of ≪ 1. We determine the jet magnetic flux taking into account this effect. We find that the transverseaveraged jet magnetic flux is fully compatible with the model of jet formation due to BH spin energy extraction and the accretion being a magnetically arrested disc (MAD). We calculate the jet average mass-flow rate corresponding to this model and find it consists of a substantial fraction of the mass accretion rate. This suggests the jet composition with a large fraction of baryons. We also calculate the average jet power, and find it moderately exceeds the accretion power,Ṁc 2 , reflecting BH spin energy extraction. We find our results for radio galaxies at low Eddington ratios are compatible with MADs but require a low radiative efficiency, as predicted by standard accretion models.
We apply the jet model developed in the preceding paper of Zdziarski et al. to the hardstate emission spectra of Cyg X-1. We augment the model for the analytical treatment of the particle evolution beyond the energy dissipation region, and allow for various forms of the acceleration rate. We calculate the resulting electron and emission spectra as functions of the jet height, along with the emission spectra integrated over the outflow. The model accounts well for the observed radio, infrared, and GeV fluxes of the source, although the available data do not provide unique constraints on the model free parameters. The contribution of the jet emission in the UV-to-X-ray range turns out to be in all the cases negligible compared to the radiative output of the accretion component. Nevertheless, we find out that it is possible to account for the observed flux of Cyg X-1 at MeV energies by synchrotron jet emission, in accord with the recent claims of the detection of strong linear polarization of the source in that range. However, this is possible only assuming a very efficient particle acceleration leading to the formation of flat electron spectra, and jet magnetic fields much above the equipartition level.
We use published data on the power and production efficiency of jets in blazars with double radio lobes in order to compare results obtained using different methods. In order to eliminate selection effects, we use cross-matched sub-samples containing only luminous blazars. We compare the three main existing methods, namely those based on the emission of radio lobes, on spectral fitting, and on radio core shift. We find the average jet power obtained for identical samples with the radio-lobe method is ∼10 times lower than that from the spectral fitting. In turn, the power from spectral fitting is compatible with that from core-shift modelling for plausible parameters of the latter. We also consider a phenomenological estimator based on the γ-ray luminosity. We examine uncertainties of those methods and discuss two alternative hypotheses. In one, the blazar-fit and core-shift methods are assumed to be correct, and the lower power from radio lobes is caused by intermittency of accretion. Long periods of quiescence cause the energy in the radio lobes, accumulated over the lifetime of the blazar, to be much less than that estimated based on the present luminous state. In addition, the power calculated using the radio lobes can be underestimated for intrinsically compact jets, in which the radio core flux can be over-subtracted. In our second hypothesis, the radio-lobe method is assumed to be correct, and the blazar-fit and core-shift powers are reduced due to the presence of ∼15 pairs per proton and a larger magnetization than usually assumed, respectively.
This is part one of our study of models of jets with distributed electron acceleration. We present here our assumptions, basic equations, and their solutions for the steady-state electron distribution. We assume the shape of the rate of electron acceleration and the dependencies of its normalization and the magnetic field strength on the height along the jet. Our focus is on the hard spectral state of black-hole binaries, for which we take into account that their typical radio spectra are flat. This appears to require a constant dissipation rate per unit logarithmic length and conservation of the magnetic energy flux. Our electron kinetic equation includes adiabatic and radiative losses and advection, and our photon radiative transfer equation includes synchrotron absorption and emission and Compton emission. Apart from the self-Compton process, we take into account Compton scattering of stellar and accretion photons and absorption of very-high energy gamma-rays by pair production on soft photons. We present a general solution of the kinetic equation with advection and radiative and adiabatic losses and an analytic solution in the case of dominant synchrotron losses in conical jets. In the following paper, we present detailed spectra resulting from our equations as applied to Cyg X-1.
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