There is convincing quantitative evidence that all of the extragalactic radio sources radiate by the commonly accepted incoherent synchrotron process. This evidence includes:
The shapes of the spectra of the extended (transparent) sources are power law or dual power law and their detailed shapes are in agreement with synchrotron models where the relativistic particles both gain and lose energy.
In the compact sources, the spectral peak occurs at shorter wavelengths in the smaller sources, as predicted by the synchrotron model, and the measured angular sizes are in good agreement with those estimated from the observed self-absorption cutoff wavelength.
The maximum observed brightness temperature is ~ 1012, as is expected from an incoherent synchrotron source which is "cooled" by inverse Compton scattering.
The variations in intensity and polarization and their dependence on wavelength and time are in qualitative agreement with those expected from an expanding cloud of relativistic particles.
The source of energy, the so-called "central engine," is thought to be the associated quasar or AGN. The observed correlation between 21-cm observations of HI and the strength of the nuclear radio source supports the concept that the radio source is fueled by the accretion of gas onto a massive collapsed object, possibly a black hole.
Energy from the central engine appears to be transported to the outer lobes via a highly collimated beam of relativistic particles, but there has been little progress in understanding how the potential energy of the condensed object is converted into an apparently stable particle beam. Near the core, VLBI measurements, as well as observations of rapid flux density variations and the absence of inverse Compton scattered X-rays, are interpreted as the result of Doppler beaming by a highly relativistic outflow from the nucleus with Lorentz factors typically in the range of 5 to 10. But the evidence for bulk relativistic motion in the extended jets is ambiguous.