Constraining mass and shape of galaxy clusters through large scale structures

The mass estimation of galaxy clusters is a crucial point for modern cosmology, and can be obtained by several different techniques. In this work we discuss a new method to measure the mass of galaxy clusters connecting the gravitational potential of the cluster with the kinematical properties of its surroundings. We explore the dynamics of the structures located in the region outside virialized cluster, We identify groups of galaxies, as sheets or filaments, in the cluster outer region, and model how the cluster gravitational potential perturbs the motion of these structures from the Hubble fow. This identification is done in the redshift space where we look for overdensities with a filamentary shape. Then we use a radial mean velocity profile that has been found as a quite universal trend in simulations, and we fit the radial infall velocity profile of the overdensities found. The method has been tested on several cluster-size haloes from cosmological N-body simulations giving results in very good agreement with the true values of virial masses of the haloes and orientation of the sheets. We then applied the method to the Coma cluster and even in this case we found a good correspondence with previous. It is possible to notice a mass discrepancy between sheets with different alignments respect to the center of the cluster. This difference can be used to reproduce the shape of the cluster, and to demonstrate that the spherical symmetry is not always a valid assumption. In fact, if the cluster is not spherical, sheets oriented along different axes should feel a slightly different gravitational potential, and so give different masses as result of the analysis described before. Even this estimation has been tested on cosmological simulations and then applied to Coma, showing the actual non-sphericity of this cluster