  We show that an upper limit of ~ 10^{12} K on the peak brightness temperature
for an incoherent synchrotron radio source, commonly referred to in the
literature as an inverse Compton limit, may not really be due to inverse
Compton effects. We show that a somewhat tighter limit T_{eq} ~ 10^{11} is
actually obtained for the condition of equipartition of energy between
radiating particles and magnetic fields which happens to be a configuration of
minimum energy for a self-absorbed synchrotron radio source. An order of
magnitude change in brightness temperature from T_{eq} in either direction
would require departures from equipartition of about eight orders of magnitude,
implying a change in total energy of the system up to ~ 10^{4} times the
equipartition value. Constraints of such extreme energy variations imply that
brightness temperatures may not depart much from T_{eq}. This is supported by
the fact that at the spectral turnover, brightness temperatures much lower than
~ 10^{11} K are also not seen in VLBI observations. Higher brightness
temperatures in particular, would require in the source not only many orders of
magnitude higher additional energy for the relativistic particles but also many
order of magnitude weaker magnetic fields. Diamagnetic effects do not allow
such extreme conditions, keeping the brightness temperatures close to the
equipartition value, which is well below the limit where inverse Compton
effects become important.
