To investigate the 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. 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. We found: (1) The distorted and non-distorted clusters occupy well-defined loci in the L-T plane, demonstrating 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. (2) Ellipticity and Off-center show no evolutionary effects between high and low redshift cluster subsets, while there may be a hint of weak evolutions for the Concentration and Asymmetry, in such a way that high-z clusters show more distorted morphology. (3) 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 period of time.
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