We use the weak gravitational lensing effect to study the mass distribution and dynamical state of a sample of 24 X-ray luminous clusters of galaxies (0.05 < z < 0.31) observed with the FORS1 instrument mounted on the VLT-Antu (Unit Telescope 1) under homogeneous sky conditions and subarsecond image quality. The galaxy shapes were measured in the combined V, I, R image after deconvolution with a locally determined point-spread-function, while the two-dimensional mass distributions of the clusters were computed using an algorithm based on the maximum entropy method. By comparing the mass and light distributions of the clusters in our sample, we find that their mass centers, for the majority of the clusters, is consistent with the positions of optical centers. We find that some clusters present significant mass substructures which generally have optical counterparts. At least in one cluster (Abell 1451), we detect a mass substructure without an obvious luminous counterpart. The radial profile of the shear of the clusters was fitted using circular and elliptical isothermal elliptical distributions, which allowed the finding of a strong correlation between the orientation of the major-axis of the matter distribution and the corresponding major-axes of the brightest cluster galaxy light-profiles. Estimates of how close to dynamical relaxation are these clusters were obtained through comparison of our weaklensing mass measurements with the x-ray and velocity dispersion determinations available in the literature. We find that clusters with intra-cluster gas colder than 8 keV show a good agreement between the different mass determinations, but clusters with gas hotter than 8 keV present discrepant mass values. The clusters diagnosed to be out of equilibrium are Abell 1451, 2163 and 2744, all of them having hints of substructure. Abell 2744 presents the largest discrepancy between its X-ray and weak-lensing temperature determinations, which can be interpreted as being due to the interaction between the two kinematical components along the line of sight found by Girardi & Mezzeti (2001).
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