340 Highlights in modern observational cosmology
Figure 11.14.Constraints in the plane of the cosmological parametersm−σ 8 derived
from the observed evolution of the cluster abundance in the RDCS sample (Borganiet
al2001). Contours are 1σ,2σand 3σC.L. The three parameters(A,α,β)describe
the uncertainties in converting cluster masses into temperatures (T ∼ M^2 /^3 /β), and
temperatures into x-ray luminosities (LX ∼ Tα( 1 +z)A). The two values for each
parameter bracket the range which is allowed from current x-ray observations of distant
clusters.
(1) b−fgasmethod,
(2) Oort method (M/L)and
(3) universal dynamics.11.4.3.1 b−fgasmethod (Whiteet al1993)
A reasonable assumption is that clusters are large enough that they should host a
‘fair sample’ of the matter in the universe (e.g. there is no special segregation of
baryons over the dark matter). In addition, x-ray observations clearly show that
most of the baryons in clusters reside in the hot intracluster gas. The gas-to-total-
mass ratio,fgas, can be measured using x-ray or SZ observations. The fraction of
baryons,b=ρB/ρcr, is well constrained by the primordial nucleosynthesis
theory and the measurement of deuterium abundance from high-zabsorption
systems. If we knowfgasandb, then we simply have:m=b/fgas.
Deuterium measurements in recent years have settled on the value (Burles
and Tytler 1998)bh^2 = 0. 02 ± 0 .002. Ettori and Fabian (1999) have used 36
x-ray clusters to estimate a mean value〈fgas〉= 0. 059 h−^3 /^2 with a 90% range of
fgas=(0.036–0.087)h−^3 /^2. Hence,
m=B/fgas 0. 34 h−^1 /^2 0. 4 ± 0. 2 (forH 0 = 65 ), (11.27)where the error represents an approximate range reflecting the scatter infgas.
11.4.3.2 Oort method (M/L)
The mean density of the universe is equal to the mass of a large galaxy cluster
divided by the equivalent comoving volume in the field from which that mass