The variability time-scales and brightness temperatures of radio flares from stars to supermassive black holes

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.