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3.3. Beyond the Virial Theorem

With some hundreds velocities available, more detailed models became possible. A new heresy came around, the "binary model" of Valtonen & Byrd [143], [144], somewhat anticipated in the works of Gainullina [51], and Wesson et al. [152], [153]. Valtonen & Byrd suggested that Coma could be dymanically dominated by a tightly bound couple of galaxies (NGC 4874 - NGC 4889). Their model, while reducing the global dark-matter discrepancy for the cluster, nevertheless implied a very large M/L ratio for the two central dominant galaxies (~ 2000). During the last 40 years, Zwicky's heresy had become common sense; trying to reject the dark-matter hypothesis had become the new heresy! This model was rejected 10 years later, when The & White [133] showed that Valtonen & Byrd's model was inconsistent with the sigmav-profile at the centre of Coma.

Other groups followed more traditional approaches. Most (Kent & Gunn, Millington & Peach [97], The & White [130], Merritt [94]) came to the conclusions that the best-fit model is also the simplest, i.e. light traces mass, and galaxy orbits are isotropic throughout the cluster (Fuchs & Materne [49] disagreed, but their fitting method was found [97] to be very sensitive to the assumed form of the density profile). While "simplest is best" provided an adequate description of the cluster dynamics, other models could not be excluded, and the mass-to-light ratio of Coma was shown to be uncertain by a factor four (from 50 to 200 Msun / Lsun, see Bailey). Merritt first showed that the shape of the galaxy velocity distribution at different radii contains information on the orbital anisotropy. His attempt of fitting the velocity distribution of galaxies in Coma was unsuccesful though, because of the skewness of the velocity distribution (see Fig. 5). It took 9 years to understand that the skewness was caused by the contaimination of the SW group galaxy velocities (Colless & Dunn).

Figure 5

Figure 5. The observed line-of-sight distribution of the Coma galaxy velocities (in km/s) with three theoretical models superposed - from Merritt.

The X-ray observations of Gursky et al. [63] and Meekins et al. [92] showed the existence of a hot IC gas component in Coma. The mass of this new component was estimated by Gursky et al. to be quite below the total cluster mass, but far from negligible.

Figure 6

Figure 6. The mass (in solar mass units) of the various components of the Coma cluster, as a function of the clustercentric distance, in arcminutes, according to the model of Gerbal et al. (log-log plot).

The newly discovered IC gas mass component was taken into account in the so-called "Multi-Mass Model" of Capelato, Gerbal et al. [23], [24], [34], [55], where they also considered a spectrum of galaxy masses. Capelato et al. [24] suggested the existence of a virialized core surrounded by a still collapsing halo. Gerbal et al. [55] were possibly the first to show that the IC gas contribution to the total mass increases with the clustercentric distance (see Fig. 6).

The basic uncertainty in the X-ray based mass estimation is the ignorance of the detailed gas temperature profile. From the HEAO 1 A-2 and OSO 8 observations in the 2-60 keV band, Henriksen & Mushotzky [67] deduced a steep gas temperature decrease with clustercentric distance. As a consequence, they revised the total cluster mass estimate downward by a factor four. Cowie et al. [29] reached a similar conclusion, by using additional data from the Einstein IPC.

Figure 7

Figure 7. 2D chi2 contours (at 68, 90 and 90 % confidence level) for the Iron abundance (with respect solar) vs. gas temperature (keV), for two pointings of EXOSAT - from Hughes et al.

The & White [131] criticized these results, showing that such a steep temperature decrease would require galaxies in the outer part of the cluster to be on nearly circular orbits. Based on X-ray data, Hughes et al. [72], [73], [74] showed that the X-ray temperature does decrease off-centre (see Fig. 7), but not as steeply as in Henriksen et al.'s model (which was shown to be internally inconsistent).

By combining the information from the optical and the X-ray data, Hughes et al. constrained the total mass of Coma within 1 Mpc to 3.9-7.2 × 1014 Msun (1.1-3.0 × 1015 Msun within 5 Mpc), and the mass-to-light ratio to 90-250 Msun / Lsun. Hughes also found that the ratio of the gas mass to the total mass increases with the distance from the cluster centre, thus confirming the early suggestion of Gerbal et al., and anticipating Watt et al. [149].

Following works have not substantially modified our knowledge of the total mass and mass-to-light ratio of Coma (current estimates are M ~ 2 × 1015 Msun and M / L ~ 160 Msun / Lsun, see Fusco-Femiano & Hughes [50], Makino [89], and Hughes' contribution in these proceedings). The new measures of the IC gas temperature (see Briel and Honda in these proceedings) should allow to reach even better accuracies.

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