  The time evolution of high-energy synchrotron radiation generated in a
relativistic pair plasma energized by reconnection of strong magnetic fields is
investigated with two- and three-dimensional (2D and 3D) particle-in-cell (PIC)
simulations. The simulations in this 2D/3D comparison study are conducted with
the radiative PIC code OSIRIS, which self-consistently accounts for the
synchrotron radiation reaction on the emitting particles, and enables us to
explore the effects of synchrotron cooling. Magnetic reconnection causes
compression of the plasma and magnetic field deep inside magnetic islands
(plasmoids), leading to an enhancement of the flaring emission, which may help
explain some astrophysical gamma-ray flare observations. Although radiative
cooling weakens the emission from plasmoid cores, it facilitates additional
compression there, further amplifying the magnetic field $B$ and plasma
density~$n$, and thus partially mitigating this effect. Novel simulation
diagnostics utilizing 2D histograms in the $n\mbox{-}B$ space are developed and
used to visualize and quantify the effects of compression. The $n\mbox{-}B$
histograms are observed to be bounded by relatively sharp power-law boundaries
marking clear limits on compression. Theoretical explanations for some of these
compression limits are developed, rooted in radiative resistivity or 3D kinking
instabilities. Systematic parameter-space studies with respect to guide
magnetic field, system size, and upstream magnetization are conducted and
suggest that stronger compression, brighter high-energy radiation, and perhaps
significant quantum electrodynamic (QED) effects such as pair production, may
occur in environments with larger reconnection-region sizes and higher
magnetization, particularly when magnetic field strengths approach the critical
(Schwinger) field, as found in magnetar magnetospheres.
