This paper studied the faint, diffuse extended X-ray emission associated with the radio lobes and the hot gas in the intracluster medium (ICM) environment for a sample of radio galaxies. We used shallow ($\sim 10$ ks) archival Chandra observations for 60 radio galaxies (7 FR I and 53 FR II) with $0.0222 \le z \le 1.785$ selected from the 298 extragalactic radio sources identified in the 3CR catalog. We used Bayesian statistics to look for any asymmetry in the extended X-ray emission between regions that contain the radio lobes and regions that contain the hot gas in the ICM. In the Chandra broadband ($0.5 - 7.0$ keV), which has the highest detected X-ray flux and the highest signal-to-noise ratio, we found that the non-thermal X-ray emission from the radio lobes dominates the thermal X-ray emission from the environment for $\sim 77\%$ of the sources in our sample. We also found that the relative amount of on-jet axis non-thermal emission from the radio lobes tends to increase with redshift compared to the off-jet axis thermal emission from the environment. This suggests that the dominant X-ray mechanism for the non-thermal X-ray emission in the radio lobes is due to the inverse Compton upscattering of cosmic microwave background (CMB) seed photons by relativistic electrons in the radio lobes, a process for which the observed flux is roughly redshift independent due to the increasing CMB energy density with increasing redshift.

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