  Radio relics are the manifestation of electrons presumably being shock
(re-)accelerated to high energies in the outskirts of galaxy clusters. However,
estimates of the shocks' strength yield different results when measured with
radio or X-ray observations. In general, Mach numbers obtained from radio
observations are larger than the corresponding X-ray measurements. In this
work, we investigate this Mach number discrepancy. For this purpose, we used
the cosmological code ENZO to simulate a sample of galaxy clusters that host
bright radio relics. For each relic, we computed the radio Mach number from the
integrated radio spectrum and the X-ray Mach number from the X-ray surface
brightness and temperature jumps. Our analysis suggests that the differences in
the Mach number estimates follow from the way in which different observables
are related to different parts of the underlying Mach number distribution:
radio observations are more sensistive to the high Mach numbers present only in
a small fraction of a shock's surface, while X-ray measurements reflect the
average of the Mach number distribution. Moreover, X-ray measurements are very
sensitive to the relic's orientation. If the same relic is observed from
different sides, the measured X-ray Mach number varies significantly. On the
other hand, the radio measurements are more robust, as they are unaffected by
the relic's orientation.
