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The second catalogue of Planck Sunyaev-Zeldovich (SZ) sources, hereafterPSZ2, represents the largest galaxy cluster sample selected by means of theirSZ signature in a full-sky survey. Using telescopes at the Canary Islandobservatories, we conducted the long-term observational program 128-MULTIPLE-16/15B (hereafter LP15), a large and complete optical follow-upcampaign of all the unidentified PSZ2 sources in the northern sky, withdeclinations above $-15^\circ$ and no correspondence in the first Planckcatalogue PSZ1. This paper is the third and last in the series of LP15 results,after Streblyanska et al. (2019) and Aguado-Barahona et al. (2019), andpresents all the spectroscopic observations of the full program. We complementthese LP15 spectroscopic results with Sloan Digital Sky Survey (SDSS) archivaldata and other observations from a previous program (ITP13-08), and present acatalog of 388 clusters and groups of galaxies including estimates of theirvelocity dispersion. The majority of them (356) are the optical counterpart ofa PSZ2 source. A subset of 297 of those clusters is used to construct the$M_{\rm SZ}-M_{\rm dyn}$ scaling relation, based on the estimated SZ mass fromPlanck measurements and our dynamical mass estimates. We discuss and correctfor different statistical and physical biases in the estimation of the masses,such as the Eddington bias when estimating $M_{SZ}$ and the aperture and thenumber of galaxies used to calculate $M_{dyn}$. The SZ-to-dynamical mass ratiofor those 297 PSZ2 clusters is $(1-B) = 0.80\pm0.04$ (stat) $\pm 0.05$ (sys),with only marginal evidence for a possible mass dependence of this factor. Ourvalue is consistent with previous results in the literature, but presents asignificantly smaller uncertainty due to the use of the largest sample size forthis type of studies.

astronomy and astrophysics

Velocity dispersion and dynamical masses for 388 Galaxy Clusters and  groups. Calibrating the $M_{\rm SZ}$--$M_{\rm dyn}$ scaling relation for the  PSZ2 sample