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The shape of cD envelopes is most easily understood by a simple two component model of a galaxy potential on top of a more extended cluster potential indicating that envelopes surrounding cD galaxies are structurally independent of the underlying galaxy. Figure 7 shows one attempt to model the envelope of A2670 (Schombert 1988). The major limitations to this method are an unresolved cluster core value, rh, and lack of velocity dispersion data on cD envelopes. However, adequate models are produced from typical cluster core radii and velocity dispersions, lending support to the idea that cD envelopes are a "'sea" of stars bound not to the underlying galaxy, but to the cluster potential as a whole. The underlying galaxy is simply at rest with respect to the cluster's potential and benefits from its unique position with the adhesion of the surrounding cluster light as a cD envelope. This argues that we should decouple the properties of cD envelopes from the underlying galaxy. The discovery of cD envelopes either independent of an underlying galaxy (cluster light) or with non-concentric isophotes (such as the starpile in A545, Struble 1988) supports this idea.

Figure 7

Figure 7. A two component cD envelope model for A2670. Various values of halo radius and velocity dispersion, as well as halo M / L and power-law slope beta, are shown.

Since cD envelopes are cluster-sized entities, it would not be surprising to find correlations between envelope properties, such as occurrence and luminosity. and global cluster properties, such as cluster morphological type. However, Figure 8 shows that, this is not as pronounced as expected. Both the occurrence and luminosity of cD envelopes are shown with respect to cluster Rood-Sastry type (a pleasure of the dynamical state of the cluster, where cD and B type cluster are assumed to be highly evolved and L/F/I clusters are irregular and in a pre-collapse state) and Bautz-Morgan type (a measure of the dominance of the BCM, also reflecting the dynamical state of a cluster). Although there is a tendency for more and brighter cD envelopes to occur in advanced cluster types, there are still significant numbers of envelopes in unevolved clusters with comparable brightnesses.

Figure 8

Figure 8. Rood-Sastry and Bautz-Morgan cluster type versus cD envelope ocurrence and luminosity. Although a majority and the brightest cD envelopes ocurr in the evolved cluster types, a significant number exist in unevolved clusters.

Comparing the physical properties of clusters to cD envelopes is even less edifying: the correlations are weak to non-existent. In Figures 9 and 10, the cD envelope luminosity is plotted against two cluster properties, richness and total X-ray luminosity. If the stripping of cluster galaxies by the mean tidal field is the source of light for cD envelopes, then one would expect a direct correspondence between number of cluster members and envelope luminosity. Figure 9 shows there is a relationship (a correlation coefficient of 0.72), similar to the Lenv propto N2 trend predicted by Malumuth and Richstone (1984), although weak. An equivalent weak relation exist between X-ray and envelope luminosity as shown in Figure 10.

Figure 9

Figure 9. Cluster richness versus cD envelope luminosity.

Figure 10

Figure 10. X-ray luminosity versus cD envelope luminosity.

Additional evidence as to the origin of cD envelopes comes from inspection of their broadband colors (i.e. a measure of the dominant stellar population). Although color information at the surface brightnesses typical for cD envelopes is extremely difficult, requiring long integrations with CCD's that have excellent flattening characteristics. I have examined several cD galaxies with various filter schemes and have concluded that no color gradients are visible through the transition from galaxy to envelope light, and the mean colors are the same as an old elliptical-like population. This is somewhat surprising in view of the fact that Bothun and Schombert (1990) found evidence for truncated galaxies in the present-day cD clusters. Even if most of these truncated galaxies are ellipticals, one would expect, from the color-magnitude relation for galaxies (B - V = 0.9 for low luminosity ellipticals) plus any blue disk material stripped from spiral, a minimal change of 0.1 to 0.2 B - V gradients.

It is difficult to draw a strong conclusion of dynamical origin to cD envelopes while lacking clear cluster correlations. Combined with the stellar population information, I believe that the formation of cD envelopes was an early process, from one of two scenarios : (1) the envelopes have their origin in tidal stripping of protogalactic material of subcluster members or (2) as Merritt suggests, the envelope is a remnant of the special location of the BCM; all galaxies initially had large envelopes, but were stripped by the cluster mean tidal field except the BCM's. This latter view is attractive since then the parallel evolution of mergers for the BCM's interior and stripping for envelopes both reflect, to some degree the richness and mass concentration of the initial subcluster and, thus, are partially reflecting in present-day global cluster correlations. However, this scenario would also predict that all BCM's should be cD's and does not explain where all the excess material from early tidal stripping is today (e.g., not in the form of stars). In addition, Bothun and Schombert (1990) have shown strong evidence of ongoing dynamical friction and tidal stripping in present day clusters. The amount of material available may be insufficient to form cD envelopes, which would further support an earlier epoch for envelope formation.

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