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

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5. Correlations of the baryon population properties with temperature

In order to properly understand the baryon fraction in clusters it is necessary to understand what the relative contributions of the gas and stellar components are. Several previous studies found that the stellar component is more dominant in low temperature systems, the lower gas content of small clusters being possibly due to feedback processes. Our sample, large and spanning a wide range in temperature, allows us to study these questions in detail.

5.1. The [FORMULA]-[FORMULA] correlation

In this section, we examine a possible correlation between the X-ray gas temperature and the ratio of gas mass to stellar mass, [FORMULA], at various radii. A strong correlation has been previously found by D90: from the analysis of twelve groups and clusters with temperatures ranging from 1 to [FORMULA], D90 found that this ratio varies by more than a factor of five from groups to rich clusters. An increase of [FORMULA] with cluster richness has also been reported by Arnaud et al. (1992).

This trend has been interpreted as due to the galaxy formation being less efficient in hot clusters than in colder systems. D90 suggest that the scenario for structure formation of hierarchical clustering, in which large structures form after little ones by successive mergers, is adequate to explain their result: in fact, as mergers go on, the intra-cluster gas is progressively heated by shocks to higher and higher temperatures, as the size of the structures involved increases; the higher [FORMULA], the more difficult it becomes for the gas to collapse and to form new galaxies. Hence, after some time, further galaxy formation would be prevented in hot clusters, producing an anti-bias.

In Fig. 6 we have plotted [FORMULA] against temperature at the radii [FORMULA] and [FORMULA]. As can been seen, mean figures for groups, cool clusters and hot clusters seem to show the sequence observed by D90, but in a less pronounced way: we find that cool clusters have [FORMULA] which is [FORMULA] times smaller than for hotter ones instead of a factor of [FORMULA] in D90. Moreover, this apparent sequence weakens when plotted at [FORMULA]: [FORMULA] is only twice smaller for groups than for hot clusters.

[FIGURE] Fig. 6. Gas to galaxy mass ratio versus X-ray temperature. Open circles are for groups, filled circles are for clusters, and crosses refer to poor quality optical or gas masses.

It should be kept in mind that in Fig. 6, we adopted a constant galactic mass to luminosity ratio for clusters and groups, whereas it is expected to be lower for late type galaxies than for E-S0. As morphological segregation tends to raise the fraction of early type galaxies in rich clusters, taking into account this variation of [FORMULA] with morphological type would in fact further flatten the observed correlation between [FORMULA] and [FORMULA], as would do taking into account the difference in galactic output from groups to clusters. We conclude that our sample does not show a strong evidence, if any, of increasing [FORMULA] with [FORMULA] as previously found by D90.

5.2. The [FORMULA]-[FORMULA] correlation

Our sample allows to test the somewhat puzzling evidence that cool clusters have a lower mean gas fraction than hot clusters. This trend has been first reported by D95 and seems to be confirmed (Arnaud & Evrard 1999). A modest increase of the gas fraction with [FORMULA] has also been reported by Mohr et al. (1999). Such a trend is unexpected in a self-similar cluster evolution, [FORMULA] and [FORMULA] at a given overdensity being expected to be constant, but would be naturally explained by non-gravitational processes such as galaxy feedback (for instance, early supernovae-driven galactic outflows), able to heat the intergalactic gas enough to make it expand out (Metzler & Evrard 1994, 1997; Ponman et al. 1999). This is achieved more easily in shallower potential wells like those of groups, which could even experience substantial gas expulsion, thus reducing their gas fractions. Such scenarii are necessary to explain the [FORMULA] relationship (Cavaliere et al. 1997).

In order to examine this issue, we plot in Fig. 7 the baryon fraction versus the temperature at different radii: [FORMULA], [FORMULA] and [FORMULA]. Error bars were estimated by considering uncertainties on the temperature, and also on metallicity for groups. Uncertainties on X-ray emission are small and lead to tiny errors on the gas mass in the observed range ([FORMULA]), while in the outer part, where observations are lacking, robust estimates of the uncertainties cannot be obtained, given that these uncertainties are systematic in nature. In the case of groups, the metallicity uncertainty can lead to significant errors on the gas mass, and was therefore taken into account. As it can be seen, we do observe no obvious trend with [FORMULA]. The data are more consistent with [FORMULA] being constant and this whatever the mass estimator used. Although a weak tendency could be seen (in the frame of SLM masses), it appears swamped in the high dispersion affecting objects of a same temperature. Therefore we do not confirm the trend of increasing [FORMULA] with [FORMULA] (or size) as previously found by D95. This is a rather robust conclusion as our sample covers a wide range of temperature, from 1 to [FORMULA]. This result is consistent with the similarity of baryon fraction profiles we found (Fig. 3) and the absence of trend of [FORMULA] with [FORMULA] indicating that non-gravitational processes such as galactic feedback are not dominant in determining the large scale structure of the intracluster medium.

[FIGURE] Fig. 7. Baryon fractions in the sample as a function of X-ray temperature. Top: at [FORMULA]. Middle: at [FORMULA]. Bottom: at [FORMULA]. Left: hydrostatic masses. Right: SLM masses. Groups are shown as open circles and objects with poor quality temperature measurements (and therefore masses) as crosses.

5.3. The [FORMULA]-[FORMULA] correlation

Analysing the baryon fraction versus temperature may hide or reflect some correlations which are present among other parameters. Of special interest is to check whether a correlation with [FORMULA] exists.

We first searched for a trend between [FORMULA] and the temperature. Previous studies have shown that low temperature systems exhibit a more extended ICM distribution (low [FORMULA] values) than hotter ones (Arnaud & Evrard 1999). From Fig. 8 we can see that no clear trend of increasing [FORMULA] with [FORMULA] is found. Although smaller [FORMULA] are found at the cool side, this might be due to a larger dispersion in [FORMULA] for the smallest potentials. We note that our result is consistent with the recent analysis of Mohr et al. (1999).

[FIGURE] Fig. 8. The slope [FORMULA] derived from the best-fit of a [FORMULA]-model to X-ray images plotted versus the temperature. On the right panel is plotted the baryon fraction (at [FORMULA]) in the IHE [FORMULA]-model (filled symbols) compared to the SLM (open symbols) as a function of [FORMULA].

We have also examined the way the baryon fraction varies with [FORMULA] (Fig. 8). The baryon fraction derived from the hydrostatic [FORMULA] model, [FORMULA], does not vary with [FORMULA] in an obvious way: if anything it decreases with increasing [FORMULA] (while no obvious correlation is found with [FORMULA], see Fig. 7). Such a trend, if real, would be unexpected. Using the SLM mass estimates, the baryon fraction is much more constant and less dispersed, even at a fixed [FORMULA] (for [FORMULA] the dispersion on [FORMULA] is 0.23 with SLM estimates while it is 0.31 with the IHE). The fact that [FORMULA] is constant with [FORMULA] again differs from what one would expect if reheating would have a dominant rôle in redistributing the gas inside clusters.

5.4. Implications on mass estimates

As we have seen (Sect. 4.2) the baryon fraction estimated with the SLM method is less dispersed than with the IHE method. This effect has been noted previously (Evrard 1997) and has been interpreted as due to the observational uncertainties in the estimation of [FORMULA]. The mass estimates (at some radius R) can be written as:




The fact that baryon fractions estimated with [FORMULA] are more dispersed can be understood just because of the extra dispersion introduced by [FORMULA] (EMN; Arnaud & Evrard 1999). For this to be due to the sole errors in the measurement of [FORMULA], it would imply that the dispersion in the measurements dominates the intrinsic dispersion, resulting in a tight correlation between [FORMULA] and [FORMULA], which is not obvious from Fig. 8: most clusters have a [FORMULA] in the narrow range [FORMULA], and the sample restricted to this range shows a larger dispersion for the baryon fraction computed with the IHE. Therefore, we conclude that the large dispersion observed in the baryon fractions estimated from the hydrostatic [FORMULA] model is intrinsic to the method itself leading to less reliable mass estimates, rather than to the uncertainty on [FORMULA] measurements.

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Online publication: October 2, 2000