The inverse Compton catastrophe and high brightness temperature radio   sources
  The occurrence of the inverse Compton catastrophe when the synchrotron brightness temperature exceeds a threshold value, usually estimated to be 10^{12} K, appears to be in contradiction with observation because: (i) the threshold is substantially exceeded by several intra-day variable radio sources, but the inverse Compton emission is not observed, (ii) powerful, extra-galactic radio sources of known angular size do not appear to congregate close to the predicted maximum brightness temperature. We re-examine the parameter space available to synchrotron sources using a population of monoenergetic electrons, in order to see whether the revised threshold temperature is consistent with the data. The electron distribution and the population of each generation of scattered photons are computed using spatially averaged equations. We confirm our previous finding that intrinsic brightness temperatures T_{\rm B}~10^{14} K can occur without catastrophic cooling. We show that substantially higher temperatures cannot be achieved either in transitory solutions or in solutions that balance losses with a powerful acceleration mechanism. Depending on the observing frequency, we find strong cooling can set in at a range of threshold temperatures and the imposition of the additional constraint of equipartition between particle and magnetic field energy is not warranted by the data. Postulating a monoenergetic electron distribution, which approximates one that is truncated below a certain Lorentz factor, \gamma_{min}, alleviates several theoretical difficulties associated with the inverse Compton catastrophe, including those mentioned above. 
Olivia Tsang, J. G. Kirk