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Astron. Astrophys. 331, 493-505 (1998)

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1. Introduction

One of the fundamental questions of modern cosmology is how the gravitationally bound systems in our Universe have formed. Some clues about the answer to this question may be provided by studying their intrinsic properties, such as size, internal kinetic energy, and luminosity, as well as the relations between these properties.

Elliptical galaxies are, e.g., known to populate a two dimensional manifold in the (R, [FORMULA] ,L)-space, referred to as the "fundamental plane" (FP hereafter; Djorgovski & Davis 1987, Dressler et al. 1987); this relation between R, [FORMULA] and L has been interpreted as arising from the virial equilibrium of these systems. In virial equilibrium, there is a relation between R, [FORMULA] , and M (instead of L). In order to understand the FP as arising from the virial relation, a non-constant mass-to-light ratio is required for the ellipticals, viz. M /L [FORMULA] (e.g. Pahre et al. 1995).

The deviation from a constant M /L ratio could be the result of differences in the stellar population among ellipticals (e.g. Renzini & Ciotti 1993), or of a partly dissipative formation process (Capelato et al. 1995). The tilt of the FP relative to a constant M /L is also observed in the infra-red, where metallicity effects are much reduced with respect to the optical (Pahre et al. 1995). This may suggest that such a tilt is due to deviations from homology in ellipticals as apparent in the correlations between light-profile shape and [FORMULA] or [FORMULA] (as described by, e.g. Caon et al. 1993 or Graham et al. 1996).

It has been shown through simulations that mergers of non-homologous systems can produce a FP which slightly deviates from the expectation from the virial condition (Capelato et al. 1995). The fact that dwarf ellipticals do not follow the same relation as regular ellipticals (Bender et al. 1993) may then indicate a different formation process for the two classes or, more simply, that interactions have a different impact for large and small galaxies (Levine 1996).

The FP is also important as a distance indicator, since [FORMULA] is a distance-independent quantity, while L and R both depend on the distance with different scaling laws. Before the FP was established, the relation between [FORMULA] and L found by Faber & Jackson (1976) was used as a secondary distance indicator for ellipticals (similar to the relation discovered by Tully & Fisher (1977) for spiral galaxies).

Schaeffer et al. (1993)(hereafter S93) concluded on the basis of a sample of 16 galaxy clusters that these systems also populate a FP. They used a compilation by West, Dekel & Oemler (1989) of photometric data, and velocity dispersions for Abell clusters from Struble & Rood (1991). Schaeffer et al. also concluded that apparently there is a similar FP for all bound systems, which they supposed to span 9 orders of magnitudes in luminosity! This result was interpreted in the context of the hierarchical structure formation scenario, as an indication that globular clusters, galaxies and galaxy clusters have similar formation processes. The dispersion in the FP should then reflect the dispersion in the formation epoch.

There are several reasons for re-examining the existence and properties of a possible FP of clusters. First, the cluster sample used by S93 is rather heterogeneous: velocity dispersions and interloper corrections have not been derived in the same way for all clusters, and photometric data come from about 20 different sources. Moreover, S93 use as characteristic scale the de Vaucouleurs radius; however, as shown in Adami et al. (1998)(hereafter Paper VII) the de Vaucouleurs profile gives a poor fit to the observed density profile of galaxy clusters. Indeed, we show in Paper VII that this profile is too cusped within the central 100 kpc. For these reasons, the potentially important result of S93 needs confirmation. In the present paper, we re-examine the evidence for a FP for galaxy clusters, using the large data-sample from the ESO Nearby Abell Cluster Survey (ENACS, see Katgert et al. 1996, hereafter Paper I, Mazure et al. 1996, hereafter Paper II, Biviano et al. 1997, Paper III, and Katgert et al. 1997, Paper V), in combination with the Cosmos Galaxy Catalogue. As discussed in Paper V, our Cosmos data contain parts of the well-calibrated Edinburgh-Durham Southern Galaxy Catalogue (EDSGC, Heydon-Dumbleton et al. 1989), as well as somewhat less well calibrated parts of the Cosmos catalogue outside the EDSGC (courtesy of H. McGillivray). Although in Paper V we found evidence for a difference in the quality of the photometric calibration between the two kinds of Cosmos data, there was no evidence for systematic magnitude offsets between the two parts of the Cosmos Catalogue. So, for the present discussion we can regard the ENACS and Cosmos datasets to be both homogeneous.

In Sect. 2 we give a short description of the sample of clusters that we used in the present analysis, and of the two catalogues. In Sect. 3 we discuss the methods with which we determined the core-radii, R, the velocity dispersion, [FORMULA] , and the total cluster luminosities, L. In Sect. 4 we derive the parameters that describe the FP of galaxy clusters and in Sect. 5 we compare our results to other determinations of the FP of galaxy clusters and early-type galaxies.

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© European Southern Observatory (ESO) 1998

Online publication: February 16, 1998