Exploring the spectral properties of radio relics I: Integrated spectral index and Mach number

TL;DR

This study investigates the discrepancy between radio and X-ray derived Mach numbers in galaxy cluster radio relics, revealing that differences arise from the observables' sensitivity to different parts of the shock Mach number distribution and relic orientation effects.

Contribution

The paper demonstrates that radio and X-ray Mach number estimates probe different aspects of shock distributions, explaining the observed discrepancies in galaxy cluster relics.

Findings

Radio observations are sensitive to high Mach number regions.

X-ray measurements reflect the average Mach number.

X-ray Mach number varies with relic orientation.

Abstract

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.