Since the appearance of the widely used model proposed by Press and
Schechter (1974), much theoretical work was devoted to the study of the
mass function of cosmic structures. In fact, the mass function can provide
constraints on the cosmological model of the large scale structure of the
Universe. Groups of galaxies may represent an example of cosmic structures
quite suitable for this analysis. In fact they have been observed by many
authors and many catalogues of data are now available. Moreover, the
estimation of the mass of each group is not too uncertain since many redshifts
of group members are available in new catalogues.
The first estimate of cosmological parameters using groups of galaxies is
due to Gott and Turner (1977) who used their group catalogue (Turner and
Gott 1976) to estimate the index n of the power spectrum of primordial
density fluctuations. Now a much richer and more accurate amount of
data is available so that the estimation of the group mass function and
the comparison with theoretical models can be performed on more solid
observational grounds.
I consider five different group catalogues available in the literature:
Geller and Huchra (1983); Tully (1987b ); Vennik (1984); Ramella, Geller
and Huchra (1989) and Maia, da Costa and Latham (1989). The features
of each catalogue are analysed in detail and particular attention is paid to
the effect of observational biases. Several mass estimators proposed in the
literature are considered and the dependence of the derived mass function
on the estimator used is tested. In the literature it is commonly assumed
that groups have reached a stationary dynamical equilibrium so that the
conditions required by the virial theorem hold. This assumption is tested
for the groups of each catalogue using a general method whose main features
are described. Finally the set of all five group catalogues is tested in
order to determine whether they give homogeneous distributions not only
for the mass but also for all the main physical parameters of galaxy groups.
The main results I obtained can be outlined in the following points: • In each catalogue all mass estimators yield nearly the same mass
distribution, so that all considered mass estimators seem to be homogeneous.
• In each catalogue the groups are likely to be in a phase characterized
by strong dynamical evolution and only a small fraction of the observed
groups ( f'V 103) have reached the virial equilibrium; hence, I
have tried to correct the mass of each group in order to account for
the non-virialized dynamical state.
• The set of five catalogues analysed is not homogeneous not only with
respect to the mass distribution but also with respect to the distributions
of all main physical parameters of groups.
• The group catalogue property mainly responsible for the detected inhomogeneity
seems to be the group identification algorithm, although
other features of catalogues may play a non-negligible role.
• The analysis to groups within 20 M pc from us is also considered in
order to reduce the observational bias that seems to affect all the catalogues;
the main results, concerning the inhomogeneity of catalogues,
the stability against various mass estimators and the dynamical state
of groups, do not change; hence, it seems that the presence of observational
bias does not significantly affect the results obtained.
These results suggest the need of a new definition for groups of galaxies
and consequently the introduction of a new identification algorithm that
could possibly overcome the inhomogeneity shown by present catalogues.
A useful tool to test new identification algorithms can be provided by numerical
simulations of galaxy clustering.
The mass distribution functions that I have obtained from the various
catalogues can be profitably compared with theoretical predictions (e.g.
Press and Shechter, 197 4) in order to extract valuable constraints on the
cosmological models of the formation and development of the large scale
structure of the universe.
