Substructure and dynamical state of 2092 rich clusters of galaxies derived from photometric data

Dynamical state of galaxy clusters is closely related to their observational properties in X-ray, optical and radio wavelengths. We develop a method to diagnose the substructure and dynamical state of galaxy clusters by using photometric data of Sloan Digital Sky Survey (SDSS). To trace mass distribution, the brightness distribution of member galaxies is smoothed by using a Gaussian kernel with a weight of their optical luminosities. After deriving the asymmetry, the ridge flatness and the normalized deviation of the smoothed optical map, we define a relaxation parameter, Gamma, to quantify dynamical state of clusters. This method is applied to a test sample of 98 clusters of 0.05<z\lesssim0.42 collected from literature with known dynamical states and can recognize dynamical state for relaxed (Gamma\ge0) and unrelaxed (Gamma<0) clusters with a success rate of 94%. We then calculate relaxation parameters of 2092 rich clusters previously identified from the SDSS, of which 28% clusters are dynamically relaxed with Gamma\ge0. We find that the dominance and absolute magnitude of the brightest cluster galaxy closely correlate with dynamical state of clusters. The emission power of radio halos is quantitatively related to cluster dynamical state, beside the known dependence on the X-ray luminosity.