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A recent analysis of the mass-to-light ratio of galaxies, groups and clusters by Bahcall, Lubin and Dorman (1995) suggests that while the M/L ratio of galaxies increases with scale up to radii of R ~ 0.1-0.2h-1 Mpc, due to the large dark halos around galaxies (see Fig. 3; also Ostriker et al. 1974), this ratio appears to flatten and remain approximately constant for groups and rich clusters, to scales of ~ 1.5 Mpc, and possibly even to the larger scales of superclusters (Fig. 4). The flattening occurs at M/LB appeq 200-300h, corresponding to Omegam ~ 0.2. This observation suggests that most of the dark matter is associated with the dark halos of galaxies. Unlike previous expectations, this result implies that clusters do not contain a substantial amount of additional dark matter, other than that associated with (or torn-off from) the galaxy halos, and the hot intracluster medium. Bahcall et al. (1995) suggest that the relatively large M/LB ratio of clusters (~ 300h) results mainly from a high M/LB ration of elliptical/S0 galaxies. They show (Fig. 3) that ellipticals have an M/LB ratio that is approximately 3 to 4 times larger than typical spirals at the same radius [(M/LB)s ~ 100h and (M/LB)e ~ 400h within r ltapprox 200h-1 Kpc]. Since clusters are dominated by elliptical and S0 galaxies, a high M/LB ratio results.

Figure 3

Figure 3. Mass-to-light ratio of spiral and elliptical galaxies as a function of scale (Bahcall, Lubin and Dorman 1995). The large boxes indicate the typical (~ 1sigma) range of M/LB for bright ellipticals and spirals at their luminous (Holmberg) radii. (LB refers to total corrected blue luminosity; see text.) The best-fit M/LB propto R lines are shown.

Figure 4

Figure 4. Composite mass-to-light ratio of different systems - galaxies, groups, clusters, and superclusters - as a function of scale (Bahcall et al. 1995). The best-fit M/LB propto R lines for spirals and ellipticals (from Fig. 3) are shown. We present median values at different scales for the large samples of galaxies, groups and clusters, as well as specific values for some individual galaxies, X-ray groups, and superclusters. Typical 1sigma uncertainties and 1sigma scatter around median values are shown. Also presented, for comparison, are the M/LB (or equivalently Omega) determinations from the cosmic virial theorem, the least action method, and the range of various reported results from the Virgocentric infall and large-scale bulk flows (assuming mass traces light). The M/LB expected for Omega = 1 and Omega = 0.3 are indicated.

Unless the distribution of matter is very different from the distribution of light, with large amounts of dark matter in the "voids" or on very large scales, the above results suggest that the mass density in the universe may be low, Omegam ~ 0.2 (or Omegam ~ 0.3 for a small bias of b ~ 1.5, where the bias factor b relates the overdensity in galaxies to the overdensity in mass: b ident (Delta rho / rho)gal / (Delta rho / rho)m).

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