Studying the dynamical properties of 20 nearby galaxy clusters

Using SDSS-DR7, we construct a sample of 42382 galaxies with redshifts in the region of 20 galaxy clusters. Using two successive iterative methods, the adaptive kernel method and the spherical infall model, we obtained 3396 galaxies as members belonging to the studied sample. The 2D projected map for the distribution of the clusters members is introduced using the 2D adaptive kernel method to determine the cluster centres. The cumulative surface number density profile for each cluster is fitted well with the generalized King model. The core radii of the cluster samples are found to vary from 0.18Mpch-1 (A1459) to 0.47Mpch-1 (A2670) with a mean value of 0.295Mpch-1. The infall velocity profile is determined using two different models: Yahil approximation and Praton model. Yahil approximation is matched with the distribution of galaxies only on the outskirts (infall regions) of many clusters of the sample, while it is not matched with the distribution within the inner core of the clusters. Both Yahil approximation and Praton model are matched together in the infall region for about nine clusters in the sample but they are completely unmatched for the clusters characterized by a high central density. For these clusters, Yahil approximation is not matched with the distribution of galaxies, while Praton model can describe well the infall pattern of such clusters. The integrated velocity dispersion profile shows that there are different behaviours within the cluster's virialized region, while it exhibits a flattened-out behaviour outside the virialized region up to the turnaround radius. Under the assumption that the mass follows galaxy distribution, we determine the mass and mass profile by two independent mass estimators; projected mass and virial mass methods. The virial mass profile is corrected by applying the surface pressure term which reduces the virial mass by about 14 per cent. The projected mass profile is larger than the corrected virial mass profile for nearly all clusters by about 28 per cent. The virial mass agrees with the NFW mass and Praton mass at rv. The virial mass profile within 1.5Mpch-1 is fitted with the NFW mass profile. The concentration parameter ranges from 1.3 to 39.17, and has a mean value of 12.98.