  We present a multiwavelength analysis of 29 merging galaxy clusters that
exhibit radio relics. For each merging system, we perform a weak-lensing
analysis on Subaru optical imaging. We generate high-resolution mass maps of
the dark matter distributions, which are critical for discerning the merging
constituents. Combining the weak-lensing detections with X-ray emission, radio
emission, and galaxy redshifts, we discuss the formation of radio relics from
the past collision. For each subcluster, we obtain mass estimates by fitting a
multi-component NFW model with and without a concentration-mass relation.
Comparing the two mass estimate techniques, we find that the concentration-mass
relation underestimates (overestimates) the mass relative to fitting both
parameters for high- (low-) mass subclusters. We compare the mass estimates of
each subcluster to their velocity dispersion measurements and find that they
preferentially lie below the expected velocity dispersion scaling relation,
especially at the low-mass end (~$10^{14}\ M_\odot$). We show that the majority
of the clusters that exhibit radio relics are in major mergers with a mass
ratio below 1:4. We investigate the position of the mass peak relative to the
galaxy luminosity peak, number density peak, and BCG locations and find that
the BCG tends to better trace the mass peak position. Finally, we update a
golden sample of 8 galaxy clusters that have the simplest geometries and can
provide the cleanest picture of the past merger, which we recommend for further
investigation to constrain the nature of dark matter and the acceleration
process that leads to radio relics.
