Maximum brightness temperature for an incoherent synchrotron radio source

We discuss here a limit on the maximum brightness temperature achievable for an incoherent synchrotron radio source. This limit, commonly referred to in the literature as an inverse Compton limit, prescribes that the brightness temperature for an incoherent synchrotron radio source may not exceed ~10^{12} K, a fact known from observations. However one gets a somewhat tighter limit on the brightness temperatures, T_{b}~10^{11.5} K, independent of the inverse Compton effects, if one employs the condition of equipartition of energy in magnetic fields and relativistic particles in a synchrotron radio source. Pros and cons of the two brightness temperature limits are discussed.