The thermal, chemical, and kinematic properties of the potentially multi-phase circum/inter-galactic medium at the virial radii of galaxy clusters remain largely uncertain. We present an X-ray study of Abell 2246 and GMBCG J255.34805+64.23661 (z=0.23 and 0.45), two foreground clusters of the UV-bright QSO HS 1700+6416, based on 240 ks Chandra/ACIS-I observations. We detect enhanced diffuse X-ray emission to the projected distances beyond r_{200} radii of these two clusters. The large-scale X-ray emission is consistent with being azimuthally symmetric at the projected radii of the QSO (0.36 and 0.8 times the radii of the two clusters). Assuming a spherical symmetry, we obtain the de-projected temperature and density profiles of the X-ray-emitting gas. Excluding the cool cores that are detected, we find that the mean temperature of the hot gas is about 4.0 keV for Abell 2246 and 5.5 keV for GMBCG J255.34805+64.23661, although there are indications for temperature drop at large radii. From these results, we can estimate the density and pressure distributions of the hot gas along the QSO sightline. We further infer the radial entropy profile of Abell 2246 and compare it with the one expected from purely gravitational hierarchical structure formation. This comparison shows that the ICM in the outer region of the clusters is likely in a clumpy and multi-phased state. These results, together with the upcoming HST/COS observations of the QSO sightline, will enable a comprehensive investigation of the multi-phase medium associated with the clusters.
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