Aims. To investigate the possible relationships between dynamical status and other important characteristics of galaxy clusters, we conducted a study of X-ray cluster morphology using a sample of 101 clusters at redshift z ∼ 0.05-1 taken from the Chandra archive. Methods. The X-ray morphology is quantitatively characterized by a series of objectively measured simple statistics of the X-ray surface brightness distribution, which are designed to be robust against variations of image quality caused by various exposure times and various cluster redshifts. Using these measures, we quantitatively investigated the relationships between the cluster X-ray morphology and various other cluster characteristics. Results. We found: (1) Our measures are robust against various image quality effects introduced by exposure time difference, and various cluster redshifts. (2) The distorted and non-distorted clusters occupy well-defined loci in the L - T plane, demonstrating that the measurements of the global luminosity and temperature for distorted clusters should be interpreted with caution, or alternatively, a rigorous morphological characterization is necessary when we use a sample of clusters with heterogeneous morphological characteristics to investigate the L - T or other related scaling relations. (3) Ellipticity and Offcenterness show no evolutionary effects between high and low redshift cluster subsets, while there may be a hint of weak evolution for Concentration and Asymmetry, such that high-z clusters show more distorted morphology. (4) No correlation is found between X-ray morphology and X-ray luminosity or X-ray morphology and X-ray temperature of clusters, implying that interaction of clusters may not enhance or decrease the luminosity or temperature of clusters for extended periods of time. (5) Clusters are scattered and occupy various places in the plane composed of two X-ray morphological measures, showing a wide variety of characteristics. (6) Relatively strong correlations in Asymmetry-Concentration and Offcenter-Concentration plots indicate that low concentration clusters generally show a high degree of asymmetry or skewness, illustrating the fact that there are not many highly-extended smooth symmetric clusters. Similarly, a correlation between Asymmetry and Ellipticity may imply that there are not many highly-elongated but otherwise smooth symmetric clusters.
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