Clusters of galaxies are fascinating objects because their observations can in principle allow one to constrain the parameters of the standard cosmological model. In particular, they are widely used as indicators of the mean matter density of the universe. Galaxy clusters have been shown to harbour very large quantities of dark matter since the pioneering work of Zwicky (1933), but its exact quantity, its spatial distribution and above all its very nature are still awaiting answers.
Clusters are the most massive objects for which both the luminous baryonic mass (consisting of the X-ray emitting intracluster gas and the visible part of galaxies) and the total gravitating mass can be estimated. Most often, the assumption of isothermal hydrostatic equilibrium (IHE) of the intra-cluster gas within the dark matter potential well is adopted to derive the total mass of clusters from X-ray observations, although many clusters exhibit obvious substructures, both in the galaxy distribution and in the X-ray emission morphology.
Beyond the classical ratio, clusters are at the center of new cosmological tests of the mean density, which are different in spirit and which are more global. Partly because of this new perspective, general observational properties of clusters have been investigated in detail in recent years. These studies were triggered by analytical arguments as well as numerical simulations which indicated that clusters might have similar properties in their structure. A first means of determining the mean density from clusters is to use their abundance as well as their relative evolution with redshift (Oukbir & Blanchard 1992; Bartlett 1997). A further important property of clusters is that their baryon fraction is expected to be identical (White et al. 1993), reflecting the universal baryonic content of the universe. As primordial nucleosynthesis calculations provide very strong constraints on the value of the baryonic density parameter , determining the baryonic fraction in galaxy clusters allows to derive the matter density parameter . This surmise, when applied to a set of clusters, leads to a high mean baryon fraction , of the order of % (David et al. 1995, hereafter D95; White & Fabian 1995; Cirimele et al. 1997; Evrard 1997). Consequently, the critical value is disfavored (as the primordial nucleosynthesis is indicative of , one obtains ). White et al. (1993) have reviewed this critical issue in the case of the Coma cluster.
Some caution is necessary though, since there exists an appreciable dispersion in the range of published baryon fractions. This scatter may be due to intrinsic dispersion in baryon fractions of different clusters. If real, it is important to understand the origin of such a scatter. However, Evrard (1997) did not find any convincing evidence for a significant variation in the baryon fraction from cluster to cluster. Such a result is in contrast with Loewenstein & Mushotzky (1996) and D95. These latter authors, from their study of ROSAT PSPC observations of a sample of groups and clusters of galaxies, have found a correlation between the gas fraction and the gas temperature, breaking the simplest self-similar picture (the different conclusion of Evrard could be due to the limited range of temperatures he used). A possible explanation for such variations, if real, could in principle be the development of a segregation between baryons and dark matter occurring during the cluster collapse, operating more efficiently in massive clusters. However, this mechanism has been shown by White et al. (1993) to be insufficient to significantly enhance the baryon fraction and it is therefore unlikely that such a phenomenon could lead to a substantial scatter in baryon fractions. Another possibility is that in poor clusters and groups, a part of the gas has been swept away in the shallow dark matter potential well by galactic winds, being thus less concentrated than in massive clusters. This scenario would also be consistent with the claim that the gas to stellar mass ratio increases monotonically with the temperature of the cluster (David et al. 1990, hereafter D90). Finally, a further possibility is that mass estimates are not accurate and that a systematic bias exists with temperature. In any case, D95 derived this correlation from a very reduced set of objects (7 clusters and 4 groups) and it would deserve further investigation based on a larger sample.
As a consequence, it was one of our aims to address these questions with improved statistics. Moreover, in the baryon problem, the reliability of mass estimates is rather crucial and assumptions such as equilibrium and isothermality may introduce systematic differences in the results that we wish to examine in detail. The validity of mass estimates has been questioned by Balland & Blanchard (1997). We have therefore taken the opportunity of this study to perform a comparison between the standard mass estimate based on the IHE -model and an alternative method derived from scaling arguments and numerical simulations including gas physics (see Sect. 3.3), hereafter called the scaling law model (SLM).
In this paper, we present an analysis of a sample of 26 galaxy clusters and 7 groups taken from the literature. We required that optical data were available for our objects and searched for a precise information on the galaxy spatial distribution and luminosity function, on the X-ray temperature and on the gas density profile, in order to be able to build up the density and mass profiles for galaxies, gas and dark matter. This allows to compute properly the baryon fraction rather than only the gas fraction as is often done. This is especially important for low mass objects, in which the stellar component is generally believed to be relatively more important. Our sample comprises clusters with temperatures from 1 to 14 keV, and therefore allows us to investigate several interesting quantities beyond gas and baryon fractions, like the mass to light ratio and the ratio of galaxy baryonic mass to gas mass (possibly providing important constraints on galaxy formation), over a wide range of temperatures. All the data used here come from the literature, with the exception of Abell 665, for which we have analysed an archival ROSAT image to obtain the gas density profile. In fact, this cluster has already been studied from Einstein data by two teams (Durret et al. 1994; Hughes & Tanaka 1992), finding in each case a surprisingly very high gas fraction (respectively 50% and 33%). We will see this cluster provides a striking example of the scatter in different mass determinations.
The sample is presented in Sect. 2. The methods to compute the various quantities for each cluster in the sample is presented in Sect. 3 and the results are presented in Sect. 4. In Sect. 5, we examine the trend with temperature for several quantities.
In all the present study, we assumed a and cosmology.
© European Southern Observatory (ESO) 2000
Online publication: October 2, 2000