Multi-frequency synchrotron self-Compton models of the brightness temperature problem in compact extra-galactic radio sources

Flux variations in quasars and BL Lac objects over a time scale of a day or less suggest an extremely high brightness temperature in these sources, which cannot be explained by conventional synchrotron theory. This work addresses the issue of extreme brightness temperature by applying synchrotron theory to unconventional electron distributions. We consider a scenario in which relativistic electrons are continuously injected into the emission region. In the first approximation, we assume the electrons are monoenergetic for simplicity. This approximation is insufficient when modelling the spectrum of S5~0716+714, we therefore modified the electron injection spectrum to one which is a double power law in energy. This retains the low radio frequency spectral characteristics of monoenergetic electrons, which extends to higher frequencies as a power law. To complete the study of the intrinsic properties of synchrotron emission from monoenergetic electrons, we also examine their circular polarisation. We find that (1) electron distribution with low energy cut-off is able to generate high brightness temperature, and (2) the flat synchrotron spectrum produced by such distribution is in good agreement with that of the observed, and (3) in contrast to a power-law distribution, circular polarisation of synchrotron emission from monoenergetic electrons does not change sign