Cluster surveys 341Figure 11.15. Constraints tomandfrom CMB anisotropies (Boomerang: De
Bernardiset al2000; Maxima: Hananyet al2000), distant Type Ia supernovae (Perlmutter
et al1999; Schmidtet al1998) and several methods based on galaxy clusters.
originated. Such a volume can be evaluated from the ratio of the luminosity of
the cluster galaxies,L, with thefield luminosity density,jf. Thus,
ρ 0 =Mcl/Vcl=(M/L)cl×jf, and m=(M/L)cl/(M/L)cr (11.28)where(M/L)cr=ρcr/jf.
Important effects which could bias this measurement are luminosity
segregation of the cluster versus the field, and differential evolution of the cluster
galaxies compared to the field. With enough spectrophotometric data, one can
reasonably control these issues. The CNOC survey (e.g. Carlberget al1996)
is the best study to date of cluster dynamics of an x-ray selected sample of 16
clustersat z. 0 .5. This study lead to a measurement of average mass-to-light
ratio(M/L)= 295 ± 54 hM L− 1 , as well as of the luminosity densityjfin the
field. Thus, Carlberget alobtain: m= 0. 24 ± 0. 05 ± 0 .09 (the second error
is the sytematic one).
Using the constraint onm derived in the previous section from the
application of the third method (universal dynamics), we note a remarkable
agreement fromcompleteley independent techniquesbased on galaxy clusters,
i.e.m 0 .2–0.5.
These bounds on the matter density parameter are shown in figure 11.15
together with measurements of (m,) from high redshift supernovae used
as standard candles (Perlmutteret al1999, Schmidtet al1998), and from
the recent landmark experiments—Boomerang (De Bernardiset al2000) and
Maxima (Hananyet al2000) which have measured CMB anisotropies on small