Cluster mass estimation through Fair Galaxies
  We analyse a catalogue of simulated clusters within the theoretical framework
of the Spherical Collapse Model (SCM), and demonstrate that the relation
between the infall velocity of member galaxies and the cluster matter
overdensity can be used to estimate the mass profile of clusters, even though
we do not know the full dynamics of all the member galaxies. In fact, we are
able to identify a limited subset of member galaxies, the 'fair galaxies',
which are suitable for this purpose. The fair galaxies are identified within a
particular region of the galaxy distribution in the redshift (line-of-sight
velocity versus sky-plane distance from the cluster centre). This 'fair region'
is unambiguously defined through statistical and geometrical assumptions based
on the SCM. These results are used to develop a new technique for estimating
the mass profiles of observed clusters and subsequently their masses. We tested
our technique on a sample of simulated clusters; the mass profiles estimates
are proved to be efficient from 1 up to 7 virialization radii, within a typical
uncertainty factor of 1.5, for more than 90 per cent of the clusters
considered. Moreover, as an example, we used our technique to estimate the mass
profiles and the masses of some observed clusters of the Cluster Infall Regions
in the Sloan Digital Sky Survey catalogue. The technique is shown to be
reliable also when it is applied to sparse populated clusters. These
characteristics make our technique suitable to be used in clusters of large
observational catalogues.
