Velocity dispersion vs cluster mass: a new scaling law with The Three Hundred clusters

The Planck Collaboration has shown that the number of clusters as a function of their mass and redshift is an extremely powerful tool for cosmological analyses. However, the true cluster mass is not directly measurable. Among the possible approaches, clusters mass could be related to different observables via self similar scaling law. These observables are related to the baryonic components of which a cluster is composed. However, the theoretical relations that allow the use of these proxies often are affected by observational and physical biases, which impacts on the determination of the cluster mass. Fortunately, cosmological simulations are an extremely powerful tool to assess these problems. We present our calibration of the scaling relation between mass and velocity dispersion of galaxy members from the study of the simulated clusters of \THP{} project with mass above $10^{13} M_\odot$. In order to investigate the presence of a redshift dependence, we analyzed 16 different redshifts between $z = 0$ and $z = 2$. Finally, we investigated the impact of different AGN feedback models.