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.
