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We present the velocity dispersion and dynamical mass estimates for 270galaxy clusters included in the first Planck Sunyaev-Zeldovich (SZ) sourcecatalogue, the PSZ1. Part of the results presented here were achieved during atwo-year observational program, the ITP, developed at the Roque de losMuchachos Observatory (La Palma, Spain). In the ITP we carried out a systematicoptical follow-up campaign of all the 212 unidentified PSZ1 sources in thenorthern sky that have a declination above $-15^\circ$ and are without knowncounterparts at the time of the publication of the catalogue. We present forthe first time the velocity dispersion and dynamical mass of 58 of these ITPPSZ1 clusters, plus 35 newly discovered clusters that are not associated withthe PSZ1 catalogue. Using Sloan Digital Sky Survey (SDSS) archival data, weextend this sample, including 212 already confirmed PSZ1 clusters in thenorthern sky. Using a subset of 207 of these galaxy clusters, we constrainedthe $M_{\rm SZ}$--$M_{\rm dyn}$ scaling relation, finding a mass bias of $(1-B)= 0.83\pm0.07$(stat)$\pm0.02$(sys). We show that this value is consistent withother results in the literature that were obtained with different methods(X-ray, dynamical masses, or weak-lensing mass proxies). This result cannotdissolve the tension between primordial cosmic microwave backgroundanisotropies and cluster number counts in the $\Omega_{\rm M}$--$\sigma_8$plane.

Velocity dispersion and dynamical mass for 270 galaxy clusters in the Planck PSZ1 catalogue