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2. Omegam - The Matter Density

Table 1 presents a summary of several different techniques for measuring the matter density of the Universe. These techniques have been developed over a wide range of scales, from galaxy (~ 100-200 kpc), through cluster (Mpc), on up to more global scales (redshifts of a few). Excellent, recent reviews on determinations of Omega can be found in Dekel, Burstein & White (1997) and Bahcall, Lubin & Dorman 1995 and references therein. The first part of the table lists Omegam determinations that are independent of OmegaLambda; the second part lists Omegam determinations that are not independent of OmegaLambda; and the third part of the table lists OmegaLambda determinations. In addition to listing the physical basis of the method, types of object under study, and values of Omegam plus an estimated uncertainty, Table 1 makes explicit some of the assumptions that underlie each of these techniques. Although in many cases, 95% confidence limits are quoted, these estimates must ultimately be evaluated in the context of the validity of their underlying assumptions. It is non-trivial to assign a quantitative uncertainty in many cases, but in fact systematic effects may be the dominant source of uncertainty. Several of these assumptions and uncertainties are discussed further below. They include, for example, diverse assumptions about mass tracing light, mass-to-light ratios being constant, clusters being representative of the Universe, clumping of X-ray gas, non-evolution of type Ia supernovae, and the non-evolution of elliptical galaxies. For methods that operate over very large scales (gravitational lensing and type Ia supernovae), assumptions about OmegaLambda or Omegatotal are currently required to place limits on Omegam.

Table 1. SUMMARY OF Omegam and OmegaLambda DETERMINATIONS

Sample Method Scale Assumptions Omegam Error

OmegaLambda Independent Methods

Galaxies dyn. M/L ratio 100 kpc galaxies representative ~ 0.1
M/L constant
Clusters dyn. M/L ratio < few Mpc clusters representative ~ 0.2
M/L constant
Clusters X-ray M/L ratio < few Mpc hydrostatic eqm ~ 0.2
Clusters baryon fraction clusters representative 0.3-0.5
no clumping
Clusters morphology model dept. > 0.3
Local Group Least action principle 1 Mpc LG representative ~ 0.15
no external torques
model uniqueness
Galaxies Virial Theorem 1-300 Mpc mass-indept. biasing 0.2-0.4
(pairwise velocities) point masses
Galaxies Peculiar velocities 100 Mpc biasing > 0.3 95%

Sample Method Scale Assumptions Omegam Error

OmegaLambda Dependent Methods

Type Ia SNae Hubble diagram z < 0.5 OmegaLambda = 0 0.88 90%
no evolution effects
Omegatot = 1 > 0.49 95%
Lensed QSO's lensing statistics global OmegaLambda = 0 > 0.15 90%
dark matter distrib.
slow galaxy evolution
dust small effect
6 lenses strong lensing global OmegaLambda = 0 low Omega
model dependent
CMB multipole analysis global CDM 0.3-1.5

Sample Method Scale Assumptions OmegaLambda Error

Type Ia SNae z < 0.5 Omegatot = 1 < 0.51 95%
Lensed QSO's lensing statistics global Omegatot = 1 < 0.66 95%
6 lenses strong lensing global Omegatot = 1 < 0.9 95%
H0 t0 age discrepancy 100 Mpc H0 > 65 > 0.5 66%
t0 > 13 Gyr

Since lower values of the matter density tend to be measured on smaller spatial scales, it has given rise to the suspicion that the true, global value of Omega0 must be measured on scales beyond even those of large clusters, i.e., scales of greater than ~ 100 Mpc (e.g., Dekel 1994). In that way, one might reconcile the low values of Omegam inferred locally with a spatially flat Universe. However, recent studies (Bahcall, Lubin & Dorman 1995) suggest that the M / L ratios of galaxies do not continue to grow beyond a scale size of about ~ 200 kpc (corresponding to the sizes of large halos of individual galaxies). In their Jeans analysis of the dynamics of 16 rich clusters, Carlberg et al. (1997) also see no further trend with scale. Hence, currently the observational evidence does not indicate that measurements of Omegam on cluster size scales are biased to lower values than the true global value.

A brief description of several techniques for measuring the matter density is given below. These methods are discussed in the context of both their strengths and weaknesses, paying particular attention to the underlying assumptions. An excellent and more complete review on this topic is given by Dekel, Burstein & White (1997); also see Trimble (1987).

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