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
  The second catalogue of Planck Sunyaev-Zeldovich (SZ) sources, hereafter
PSZ2, represents the largest galaxy cluster sample selected by means of their
SZ signature in a full-sky survey. Using telescopes at the Canary Island
observatories, we conducted the long-term observational program 128-
MULTIPLE-16/15B (hereafter LP15), a large and complete optical follow-up
campaign of all the unidentified PSZ2 sources in the northern sky, with
declinations above $-15^\circ$ and no correspondence in the first Planck
catalogue 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), and
presents all the spectroscopic observations of the full program. We complement
these LP15 spectroscopic results with Sloan Digital Sky Survey (SDSS) archival
data and other observations from a previous program (ITP13-08), and present a
catalog of 388 clusters and groups of galaxies including estimates of their
velocity dispersion. The majority of them (356) are the optical counterpart of
a 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 from
Planck measurements and our dynamical mass estimates. We discuss and correct
for different statistical and physical biases in the estimation of the masses,
such as the Eddington bias when estimating $M_{SZ}$ and the aperture and the
number of galaxies used to calculate $M_{dyn}$. The SZ-to-dynamical mass ratio
for 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. Our
value is consistent with previous results in the literature, but presents a
significantly smaller uncertainty due to the use of the largest sample size for
this type of studies.
