We present analysis results for a nearby galaxy cluster Abell 1631 at $z~=~0.046$ using the X-ray observatory Suzaku. This cluster is categorized as a low X-ray surface brightness cluster. To study the dynamical state of the cluster, we conduct four-pointed Suzaku observations and investigate physical properties of the Mpc-scale hot gas associated with the A1631 cluster for the first time. Unlike relaxed clusters, the X-ray image shows no strong peak at the center and an irregular morphology. We perform spectral analysis and investigate the radial profiles of the gas temperature, density, and entropy out to approximately 1.5~Mpc in the east, north, west, and south directions by combining with the XMM-Newton data archive. The measured gas density in the central region is relatively low (${rm a~few} times~10^{-4}~{rm cm^{-3}}$) at the given temperature ($sim2.9~{rm keV}$) compared with X-ray-selected clusters. The entropy profile and value within the central region ($r<0.1~r_{200}$) are found to be flatter and higher ($gtrsim400~ {rm keV~cm}^2$). The observed bolometric luminosity is approximately three times lower than that expected from the luminosity-temperature relation in previous studies for relaxed clusters. These features are also observed in another low surface brightness cluster, Abell 76. The spatial distributions of galaxies and the hot gas appear to be different. The X-ray luminosity is relatively lower than that expected from the velocity dispersion. A post-merger scenario may explain the observed results.
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