High brightness temperatures and circular polarisation in extra-galactic radio sources

Context.Some rapidly variable extra-galactic radio sources show very high brightness temperatures $T_{\rm B}>10^{12}$ K and high degrees of circular polarisation (${\sim}1\%$). Standard synchrotron models that assume a power-law electron distribution cannot produce such high temperatures and have much lower degrees of intrinsic circular polarisation. Aims.We examine the synchrotron and inverse Compton radiation from a monoenergetic electron distribution and discuss the constraints placed upon it by radio, optical and hard X-ray/gamma-ray observations. Methods.The standard expressions of synchrotron theory are used. Observational 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 and maximum frequency of synchrotron emission, together with a parameter governing the strength of the inverse Compton radiation. Results.The model gives brightness temperatures $T_{\rm B}\sim10^{13}$ to $10^{14}\,$K for moderate (${\lesssim}10$) Doppler boosting factors together with 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. If the energy density in relativistic particles is comparable to or greater than the magnetic energy density, we show that 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. Magnetically dominated sources can also fulfil these requirements at the cost of a slightly lower limit on the brightness temperature. Conclusions.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