  In this paper we compile the analysis of ~ 200 synchrotron flare events from
~ 90 distinct objects/events for which the distance is well established, and
hence the peak luminosity can be accurately estimated. For each event we
measure this peak and compare it to the rise and decay timescales, as fit by
exponential functions, which allows us in turn to estimate a minimum brightness
temperature for all the events. The astrophysical objects from which the flares
originate vary from flare stars to supermassive black holes in active galactic
nuclei, and include both repeating phenomena and single cataclysmic events
(such as supernovae and gamma ray burst afterglows). The measured timescales
vary from minutes to longer than years, and the peak radio luminosities range
over 22 orders of magnitude. Despite very different underlying phenomena,
including relativistic and non-relativistic regimes, and highly collimated
versus isotropic phenomena, we find a broad correlation between peak radio
luminosity and rise/decay timescales, approximately of the form L ~ t^5. This
rather unexpectedly demonstrates that the estimated minimum brightness
temperature, when based upon variability timescales, and with no attempt to
correct for relativistic boosting, is a strongly rising function of source
luminosity. It furthermore demonstrates that variability timescales could be
used as an early diagnostic of source class in future radio transient surveys.
As an illustration of radio transients parameter space, we compare the
synchrotron events with coherent bursts at higher brightness temperatures to
illustrate which regions of radio transient parameter space have been explored.
