This thesis has been dedicated to the study of Galaxy Clusters as Cosmological
tools. The work is divided into two main parts; the first is purely observational,
whereas the second is dedicated to the preparation of tools for cosmological
analyses.
The observational section has been developed within the frame of the optical
validation program Sunyaev-Zeldovich (SZ) sources, observed by the Planck
satellite in the northern hemisphere, and included in the PSZ1 catalogue. The
212 targets were observed during a two-year International Time Project (ITP)
at the Roque de Los Muchachos Observatory (ORM) facilities on La Palma
Island.
During the observational programme, each target underwent a validation
process in two phases: photometric and spectroscopic. In the first phase, we
performed imaging in g0, r 0 and i0-bands at INT/WFC and WHT/ACAM. We
obtained a deep photometry for the majority of the targets, reaching a magnitude
in r 0-band of about 23.2 and 23.8 for WFC/INT and ACAM/WHT,
respectively. This allowed us to estimate their photometric redshift up to
zphot  0:8 cluster richness. In the second phase, we performed the spectroscopy
of the photometrically-confirmed clusters. We used TNG/DOLORES
and GTC/OSIRIS spectrographs in order to observe clusters at zphot  0:4 and
zphot > 0:4, respectively. The aim of the spectroscopic follow-up is to confirm
clusters and to characterise their physical properties, such as velocity dispersion
and mass. We used the Multi-Object Spectroscopy (MOS) technique in order
to observe as many cluster members as possible. Due to the large sample of
SZ effect sources, we were able to use, on average, only one mask per cluster,
so we retrieved a median number of cluster members of Ngal  14. Due to
this low number of galaxy members we could not use sophisticated membership
techniques. Therefore, we assigned the cluster membership according to the
galaxy radial velocity and distance from the cluster centre. At the end of the
follow-up programme we were able to validate for the first time a total of 88
new galaxy clusters.
The second part of this thesis is focused in the cosmology, with the main
aim of estimating the mass bias parameter (1􀀀b) through the characterisation
of the scaling relation between the cluster masses calculated from dynamical
and SZ proxies. The Planck Collaboration demonstrated that the mass bias is
crucial to determine the cosmological parameters
m and 8 by using the cluster
number counts formalism. The Planck Collaboration showed that the latter are
in tension with the parameters derived from CMB primary anisotropies, and
that, by varying the mass bias parameter, this tension could be alleviated.
Since the (1􀀀b) should be a measure of the bias of the SZ mass estimation,
it is extremely important to understand the possible biases in the dynamical
mass estimate. It is impossible to obtain an accurate dynamical mass estimate
if the velocity dispersion is biased. The nature of the biases may be statistical
or physical, and in this thesis we studied both kinds of biases by using
hydrodynamic simulations.
We tested three velocity dispersion estimators, namely biweight, gapper and
standard deviation, and observed that they present a statistical bias in the low
galaxy numbers regime. In order to correct this effect, we designed a receipt to
obtain unbiased velocity dispersions in the whole Ngal regime.
Physical biases are mainly related to the cluster members sampling. For
instance, due to the velocity dispersion radial profile a 5% bias is introduced
when clusters are sampled in their cores only. We also observed that the velocity
dispersion estimate obtained by using only the most massive galaxy members
is biased by about 2%. However, the most important source of bias is the
interlopers contamination, which overestimates the velocity dispersion by about
10%.
Furthermore, we demonstrated that even an unbiased velocity dispersion
could lead to a biased estimate of the cluster mass. We defined new mass
estimator, which takes into account this statistical effect.
In order to perform the cosmological analysis, we selected all clusters within
the ITP sample with reliable velocity dispersion estimation (more than 7 members
and no multiple detections). On the other hand, in order to improve the
statistical significance of our study, we applied the cluster identification procedure
to the PSZ1 clusters within the SDSS footprint as well. This way, we built
a sample of 207 galaxy clusters. This sample is the largest catalogue of clusters
for which both the SZ and dynamic masses have been estimated. Based on it
and after applying all corrections, we found that the mass bias parameters is
(1 􀀀 B) = 0:78  0:02.
The compatibility of this result with the one obtained by the Planck Collaboration
ensures that we are not able to alleviate the tension on the cosmological
parameters. However, we were able to reduce the uncertainty on the mass bias
down to  2% for the first time, based on velocity dispersion mass estimators.
Therefore, although the parameter estimates will not vary, our result will allow
us to reduce the uncertainty on the combination of
m and 8 by about a factor 2 with respect to previous studies. Other solutions are discussed.