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Astron. Astrophys. 360, L43-L46 (2000)

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3. Application to X-ray clusters

Since the reconstruction of gas temperature profile is sensitive to the initial input of [FORMULA] especially the [FORMULA] parameter, whether or not we can reliably derive the temperature profile depends critically on the goodness of the single [FORMULA] model fit to the X-ray surface brightness profile. We thus restrict ourselves to the X-ray flux-limited sample of 45 clusters published recently by Mohr, Mathiesen & Evrard (1999), in which there are sufficiently large data points to set robust constraints on the [FORMULA] model fit. The inclusion of a cluster is based on the following two criteria: (1)The X-ray surface brightness profile can be well fitted by a single [FORMULA] model with [FORMULA]; (2)The maximum extension ([FORMULA]) of the X-ray observed surface brightness profile should be large enough to guarantee the validity of the [FORMULA] model at the outermost regions of clusters. Here we set [FORMULA] Mpc. Unfortunately, it turns out that there are only three clusters which meet our criteria (Table 1): A119, A2255 and A2256. In fact, our first criterion implies that the effect of cooling flows in the central regions of clusters should be negligibly small. This explains the fact that the three selected clusters all have large core radii. Note that the presence of cooling flows may lead to the failure of a single [FORMULA] model fit to the X-ray surface brightness profiles. In other words, our method cannot be applied to the clusters with strong cooling flows. While the X-ray imaging data of the clusters can be somewhat accurately acquired, the present X-ray spectral measurements have yielded the emission-weighted temperatures rather than the central values [FORMULA] appearing in the [FORMULA] parameter. Therefore, we have to use the emission-weighted temperature as a first approximation of [FORMULA]. Alternatively, we adopt the universal baryon fraction [FORMULA] to reconcile our cosmological model of [FORMULA] (for [FORMULA]).


Table 1. Cluster sample

Using the available X-ray data of the three clusters from Mohr et al. (1999), we have performed numerical searches for the solutions of Eqs. (8) and (9) by iterations until the boundary conditions Eqs. (10) and (11) are satisfied. The resulting parameters [FORMULA], [FORMULA] and [FORMULA] are summarized in Table 1, together with a comparison with the corresponding values for an isothermal gas distribution estimated in previous work (Wu & Xue 2000). Most importantly, such a procedure enables us to completely fix the radial profiles of gas density, temperature and baryon fraction for the three clusters. Here we have no intention to illustrate the radial variations of [FORMULA] and [FORMULA], which essentially follow the theoretical expectations (Wu & Chiueh 2000). Rather, we display in Fig. 1 the radial profiles of the emission-weighted temperatures for the three clusters constructed from our algorithm. Surprisingly, none of the temperature profiles of these three clusters are consistent with the conventional speculations, and a visual examination of Fig. 1 reveals that they are neither characterized by isothermality nor represented simply by the polytropic equation of state. Nevertheless, these temperature profiles indeed demonstrate a similar radial variation, reflecting probably the underlying structural regularity. Basically, the radial variation of the gas temperature resembles a distorted `S' in shape: There exist two turnover points roughly at [FORMULA] and [FORMULA], respectively, where [FORMULA], which separate the temperature curve [FORMULA] into three parts - a decreasing [FORMULA] with radius inside the cluster core of [FORMULA], following a slightly increasing [FORMULA] until [FORMULA], and finally a moderately decreasing [FORMULA] out to the virial radius. Overall, the absolute values of the gas temperature do not demonstrate a dramatic change within clusters.

[FIGURE] Fig. 1. A comparison of the derived radial temperature profiles of three clusters (A119, A2255 and A2256) with the results of 11 clusters observed with BeppoSAX (Irwin & Bregman 2000). The observed data are normalized by the mean temperature for each cluster, while the derived temperature curves are scaled by [FORMULA] for comparison. The horizontal axis is in units of the virial radius.

The azimuthally-averaged radial temperature profiles of 11 clusters derived by Irwin & Bregman (2000) from an analysis of the BeppoSAX data are superimposed on Fig. 1. It appears that our derived temperature profiles are in good agreement with their observed ones over entire radius range. In fact, the significant temperature discrepancy raised in different X-ray spectral measurements occurs in the inner parts of clusters. In the outer regions, it seems that many observations have provided a moderately decreasing temperature profile, which is essentially consistent with our theoretical predictions. Alternatively, our result is also compatible with the gas temperature distribution at large radii revealed by numerical simulations that demonstrate a temperature decline of [FORMULA] of the central value at the virial radius (Frenk et al. 1999).

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© European Southern Observatory (ESO) 2000

Online publication: August 23, 2000