Astron. Astrophys. 361, 429-443 (2000)

2. The sample

We looked in the literature for objects studied thoroughly enough to allow us to compute the baryonic mass in galaxies, the mass in gas and in dark matter at any radius. This is quite not a refinement, since both the baryon fraction and the galaxy to gas mass ratio can vary very rapidly with radius, as will be seen in the next section. We therefore needed detailed information, which drastically reduced the possible number of objects that could be included in the sample. When a same object was studied by several teams, we applied straightforward selection criteria: for spatial X-ray data, for instance, we systematically prefer ROSAT observations, because of its improved spatial resolution and sensitivity, whereas for X-ray temperatures, Ginga and ASCA satellites were preferred to Einstein MPC, most temperatures of which come from the catalogue of David et al. (1993). Recently, it has been noted that cluster luminosities and temperatures might change noticeably when the central cooling flow emission is removed (Markevitch 1998; Arnaud & Evrard 1999). It is not clear which temperatures are to be used (especially when using a mass-temperature relationship derived from numerical simulations). In order to keep our sample as homogeneous as possible, we did not use cooling flow-corrected temperatures which are not always available. Furthermore Markevitch (1998) found that temperatures corrected for central emission are in the mean 3% larger, which will be of weak consequence in our average quantities. However, our treatment of the uncertainties on temperatures leads to large error bars when a large dispersion in measured temperatures exists (see Table 1), as for instance in the presence of a strong cooling flow.

In some cases, optical data may be very uncertain because of projection effects and magnitude limitations, especially for groups whose galaxy membership is sometimes tricky to establish. However, we tried to identify objects for which data are reasonably reliable and we derived mean dynamical quantities for this sub-sample as well. Finally, it must be emphasized that the X-ray limiting radius at which baryon fractions are estimated is a crucial parameter, since both the galactic mass derived from a King profile and the X-ray gas mass given by the Hubble-King model diverge respectively for and (the definition is given in Sect. 3), requiring that they be truncated. It is also important that the baryon fractions of different clusters be computed at an equivalent scale in order to test the scaling hypothesis and if statistical conclusions are to be brought out from them, i.e. that we use the radius containing the same overdensity, while information is actually available only up to the X-ray limiting radius which primarily depends on the characteristics of the observations (detector sensitivity, integration time...).

X-ray and optical data are summarised in Tables 1 and 2, using a Hubble constant . Notes on clusters which required a special treatment due to an incompleteness of data can be found at the end. Optical luminosities are given in the blue band. When the blue luminosity was not available, we used the following colors, corresponding to standard values for elliptical galaxies: B-V = 0.97, V-F = 0.76, r-F = 0.58 (Schneider et al. 1983) and R = F (Lugger 1989).

Fig. 1. Surface brightness profile of the intracluster gas in A665, in the ROSAT bands R4 to R7 (0.44 to ). Points represented by an empty circle have been excluded from the fit because at these radii some background or foreground X-ray sources appear in the map. The dashed line is the fitted background level.

2.1. The case of Abell 665

This cluster is one for which large baryon fraction estimates have been published in the literature. As these are surprisingly high, we have found interesting to re-analyse this cluster using a ROSAT archival image and the calibration routines of Snowden et al. (1994). We found that the gas surface brightness profile is well fitted by a Hubble-King law, and the X-ray emission can be traced out to a very large radius. The background level, which has been fitted together with the other parameters, is estimated with comfortable confidence. Spherical symmetry was assumed to derive the surface brightness profile in wide annuli, although the X-ray map shows significant departure from sphericity; however, the effect of ellipticity on derived masses is known to be negligible (Buote & Canizares 1996). The central electron volume density was computed by matching the theoretical count rate with the collected within a radius (after subtraction of the background), which amounts to solving:

with SI and the angular distance , and where stands for the energy dependence of the transmission efficiency.

The results of this analysis are the following (for the bands R4 to R7 of ROSAT): , (which corresponds to at the distance of A665), and ) with a central surface brightness and a background surface brightness . We used the gas temperature and foreground absorbing hydrogen column density given by Hughes & Tanaka (1992) from their Ginga analysis, together with the formula of Mewe et al. (1986) for the Gaunt factor and that of Morrison & McCammon (1983) for the interstellar absorption cross section. At , the inferred gas mass is , which is similar to the values found by Durret et al. (1994) and Hughes & Tanaka (1992). The hydrostatic mass is . Our mass estimate from NFW's dark matter profile, computed with the EMN normalization (see section below) is , and the resulting total mass is . The baryon fraction amounts to respectively ()% and ()%. Hence A665 is a quite ordinary rich cluster whose baryon fraction seems reasonable if compared to previous values.

We have also compared our gas mass estimates for the whole sample with other published analyses and found good agreement while the main differences are on , coming from the estimation of total masses as will be discussed in Sect. 5.

© European Southern Observatory (ESO) 2000

Online publication: October 2, 2000
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