The brightness temperature problem in extreme IDV quasars: a model for PKS 0405-385

I re-examine the brightness temperature problem in PKS 0405-385 which is an extreme intra-day variable radio quasar with an inferred brightness temperature of $\sim 5 \times 10^{14}$ K at 5 GHz, well above the Compton catastrophe limit of $\sim 10^{11}$ K reached when the synchrotron photon energy density exceeds the energy density of the magnetic field. If one takes into account the uncertainty in the distance to the ionized clouds responsible for interstellar scintillation causing rapid intra-day variability in PKS 0405-385 it is possible that the brightness temperature could be as low as $\sim 10^{13}$ K at 5 GHz, or even lower. The radio spectrum can be fitted by optically thin emission from mono-energetic electrons, or an electron spectrum with a low-energy cut-off such that the critical frequency of the lowest energy electrons is above the radio frequencies of interest. If one observes optically thin emission along a long narrow emission region, the average energy density in the emission region can be many orders of magnitude lower than calculated from the observed intensity if one assumed a spherical emission region. I discuss the physical conditions in the emission region and find that the Compton catastrophe can then be avoided using a reasonable Doppler factor. I also show that MeV to 100 GeV gamma-ray emission at observable flux levels should be expected from extreme intra-day variable sources such as PKS 0405-385.