High brightness temperatures and circular polarisation in extra-galactic   radio sources
  Some rapidly variable extra-galactic radio sources show very high brightness temperatures T_B>10^{12}K and high degrees of circular polarisation (1%). Standard synchrotron models that assume a power-law electron distribution cannot produce such high temperatures and have much lower degrees of intrinsic circular polarisation. We examine the synchrotron and inverse Compton radiation from a monoenergetic electron distribution using standard synchrotron theory. Constraints on the source parameters are found by formulating the results as functions of the source size, Doppler boosting factor, optical depth to synchrotron self-absorption, maximum frequency of synchrotron emission, and the strength of the inverse Compton radiation. The model gives brightness temperatures T_B=10^{13}K to 10^{14}K for moderate (<10) Doppler boosting factors and intrinsic degrees of circular polarisation at the percent level. It predicts a spectrum I_\nu\propto\nu^{1/3} between the radio and the infra-red as well as emission in the MeV to GeV range. We find the conditions under which electrons do not cool within the source, enabling the GHz emission to emerge without absorption and the potentially catastrophic energy losses by inverse Compton scattering to be avoided. We suggest that sources such as PKS 1519 -273, PKS 0405 -385 and J 1819 +3845 can be understood within this scenario without invoking high Doppler boosting factors, coherent emission mechanisms, or the dominance of proton synchrotron radiation. 
J. G. Kirk, O. Tsang