We present the first results of a pilot X-ray study of 37 rich galaxy clusters at $0.1<z<1.1$ in the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) field. Diffuse X-ray emissions from these clusters were serendipitously detected in the XMM-Newton fields of view. We systematically analyze X-ray images of 37 clusters and emission spectra of a subsample of 17 clusters with high photon statistics by using the XMM-Newton archive data. The frequency distribution of the offset between the X-ray centroid or peak and the position of the brightest cluster galaxy was derived for the optical cluster sample. The fraction of relaxed clusters estimated from the X-ray peak offsets in 17 clusters is $29pm11(pm13)$%, which is smaller than that of the X-ray cluster samples such as HIFLUGCS. Since the optical cluster search is immune to the physical state of X-ray-emitting gas, it is likely to cover a larger range of the cluster morphology. We also derived the luminosity-temperature relation and found that the slope is marginally shallower than those of X-ray-selected samples and consistent with the self-similar model prediction of 2. Accordingly, our results show that the X-ray properties of the optical clusters are marginally different from those observed in the X-ray samples. The implication of the results and future prospects are briefly discussed.
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