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

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6. Discussion and conclusions

We have analysed a sample of 33 galaxy clusters and groups covering a wide range of temperatures. For all clusters, X-ray and optical data were gathered from the literature (except for Abell 665 whose ROSAT PSPC data have been reanalysed by us). This has allowed us to investigate the structure of the various baryonic components of X-ray clusters. Mass estimates were derived from two different methods: first we have followed the standard hydrostatic isothermal equation (IHE method), secondly we have estimated the virial mass and mass profile by using the universal dark matter profile of NFW in which the virial radius is deduced from the scaling relation argument (SLM method), the normalization constant being taken from EMN and from BN.

We find that virial masses (i.e. masses enclosed inside a fixed contrast density radius) are systematically and significantly lower when one is using the hydrostatic isothermal equation. After this paper was submitted, we have been aware of a recent similar study by Nevalainen et al. (2000) who found that taking into account temperature profiles exacerbates this difference, as inferred masses are then smaller. Examination of the baryon fraction versus contrast density has shown that the baryon fraction is more dispersed using the IHE. We have shown that this is not due to uncertainties on the [FORMULA] measurement but rather reflects the fact that the IHE method does not provide as reliable a mass estimate as the SLM, neither in the inner parts nor in the outer regions. Moreover the tightening of [FORMULA] profiles supports the idea that baryon profiles in clusters do have a rather regular structure, i.e. that gas distribution is nearly self-similar, which is consistent with the recent studies by Vikhlinin et al. (1999) and by Neumann & Arnaud (1999) who found evidence of regularity in gas density profiles. However, when plugging their mean standard density profile into the hydrostatic equation, these last authors found a mean total mass profile which is different from the NFW profile (their mass profile is lower than the one derived from numerical simulations). They have used the hydrostatic isothermal equation to estimate their total mass which probably explains this discrepancy.

Our mean gas fraction at the virial radius [FORMULA], using the SLM, is found to be in the range 12.6-14.6% (for [FORMULA]), in rough agreement with Arnaud and Evrard (1999), when the BN or EMN normalization is used. The mean baryonic fraction is [FORMULA]-16.0%. It is important to emphasize that our analysis shows that a larger baryon fraction could be obtained when the sole hydrostatic equation is used, but it is reasonable to think that this is an overestimation due to the mass estimator itself. Our analysis is consistent with an intrinsic dispersion of 20% in baryon fractions (but this could be due to some systematics), which means that our mean baryon fraction is uncertain by less than 0.01.

As the observed luminosity-temperature does not follow the simple scaling expected from self-similarity, it is likely that non-gravitational heating such as galactic winds and additional energy input by Type II supernovae play an important rôle in the physics of the X-ray gas and may result in inflating the gas distribution. Metzler & Evrard (1997) have studied this possibility and found that this is achieved more easily in low temperature clusters (shallow potential wells). The consequence of such an effect is an increasing gas fraction outwards within a cluster and a decreasing gas fraction with decreasing temperature. This effect is expected to be more pronounced in groups and cold clusters. From our sample, we do not observe such a trend of the baryon (gas) fraction with [FORMULA] whatever the method we use, suggesting that non-gravitational heating does not have a dominant influence at the scale of the virial radius. In turn, we confirm that the baryon fraction apparently increases significantly from the center to outer parts of clusters.

Several previous studies have shown a clear trend of increasing [FORMULA] with [FORMULA], while we do not find such a clear trend. Neither do we find a trend of [FORMULA] with [FORMULA], which is consistent with the absence of an [FORMULA]-[FORMULA] correlation, although we find a slightly decreasing [FORMULA] (derived from the IHE method) with increasing [FORMULA], but with a large dispersion. This result is important as it shows that the scatter in the baryon fractions derived from the IHE method is probably not due to the sole errors in the [FORMULA] measurement, but is rather due to the IHE mass estimator itself.

Our sample does not show any evidence of the strong indication highlighted by D90 that in low temperature systems, a larger fraction of baryons is present in the stellar component. Although a trend could be present in our sample, the data are certainly consistent with a stellar to gas mass ratio being constant with temperature (or mass), a further argument that non-gravitational processes are playing a minor rôle in the overall distribution of gas in clusters.

Finally, it appears that the properties of X-ray clusters are still difficult to quantify because of the lack of large homogeneous samples of clusters for which both optical and X-ray data are available. Such a situation is likely to improve with Chandra and XMM. Nevertheless, the sample we have studied reveals that clusters show important differences in the detail of the structure of their baryonic content, but that their global properties, baryon fraction and stellar content do not show strong systematic differences with temperature.

Notes on individual clusters

  • A85: Optical data for this cluster are unsafe and extend only out to 900 kpc. We used the observations of Murphy (1984) but, as the fit with an unusual galaxy density profile he performs is rather poor (and suffers from an inconsistency between [FORMULA] and [FORMULA]), we chose to replace it with a standard King profile.

  • A401: As Buote & Canizares (1996) do not give the central electron density, we computed it with our program in the same way as for Abell 665, since both objects were observed with ROSAT PSPC, using the galactic hydrogen column density of David et al. (1993) and the count rate inside a given radius provided by Ebeling et al. (1996).

  • A2029: The same as for A401 applies.

  • A2163: Optical data for this cluster are unsafe. No galaxy distribution was available. We therefore fitted the integrated luminosity profile given in Squires et al. (1997), but it was not corrected for background galaxies and it extends only to [FORMULA] whereas [FORMULA].

  • AWM7: We used the list of galactic positions and magnitudes within [FORMULA] of the central cD of Beers et al. (1984) to build an integrated luminosity profile, corrected for incompleteness using their limiting magnitude and the standard Schechter luminosity function. The optical core radius was imposed to be the same as the X-ray core radius, which gives very similar results as excluding the three innermost galaxies (otherwise, the fitted core radius is too small and in fact, the King form is not a good representation of the central parts of clusters).

  • Hydra A: The same procedure as for A2163 was applied, with the three points given by D90: [FORMULA] at [FORMULA], [FORMULA] at [FORMULA] and [FORMULA] at [FORMULA].

  • HCG 62: We derived an integrated number count profile from the list of galactic positions of Zabludoff & Mulchaey (1998) (using their velocity criteria to select true members) and fitted it with the function in Eq. 7, assigning to each galaxy the mean luminosity derived from the limiting magnitude of the observations and the standard Schechter luminosity function. The number of galaxies contained in this "compact group" is much larger than usually assumed (45 members with [FORMULA] instead of 4 in Hickson 1982).

  • HCG 94: Ebeling et al. (1995) claim this object has been misclassified and, from its X-ray emission, looks more like a poor cluster rather than a compact group. Only 7 galaxies are generally attributed to HCG 94 but we made use of the indication of Ebeling et al. that 12 more galaxies are observed within a [FORMULA] radius and at [FORMULA], to which we attribute a mean luminosity as for HCG 62. The fit by Eq. 7 we perform relies entirely on this point (fixing the core radius at the X-ray value) since inclusion of the central galaxies would lead to a physically unacceptable core radius). Therefore, optical data for this object are unsafe.

  • NGC 533: As no central electron density is given by Mulchaey et al. (1996), we computed it from the gas mass that they obtain at a given radius. For the optical part, this is the same case as HCG 62. This group contains 36 members with [FORMULA] instead of 4 in Geller & Huchra (1983).

  • NGC 2300: The same as for AWM7 applies, using magnitudes from the RC3 and excluding the two central galaxies from the fit instead of fixing the core radius.

  • NGC 4261: Since the central electron density Davis et al. (1995) give is inconsistent with their total gas mass, we computed it (this is again the same case as for A401 and A2029). We also used optical data directly from Nolthenius (1993) and applied the same method as for AWM7 with magnitudes taken from the RC3 (except we did not have to impose the core radius).

  • RXJ 1340.6 has not been included in figures showing mass ratios as a function of overdensity, because it is a very peculiar case: the interior of the central giant elliptical galaxy is seen through a very large range of overdensities (at least out to [FORMULA]).

  • Several clusters have unreliable X-ray temperatures: A76, A426 (very strong cooling flow), A1377, A1775 (likely very strong cooling flow) and A2218 (steeply outwards-decreasing temperature profile).

  • Error bars on gas mass for groups include an estimate of the metallicity uncertainty, which results in an uncertainty on the electron density. This effect was taken into account only for groups, because it is significant mostly in the case of low temperatures.

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© European Southern Observatory (ESO) 2000

Online publication: October 2, 2000