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

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4. Discussion and conclusions

In the absence of the detailed information on the radial temperature profiles of clusters from X-ray spectroscopic measurements, we have made an attempt to derive the gas temperature profiles by combining the X-ray surface brightness measurements and the NFW profile as the underlying dark matter distribution of clusters. This has become possible when the intracluster gas is required to satisfy the hydrostatic equilibrium and the volume-averaged baryon fraction within the viral radius is required to asymptotically match the universal value. Consequently, we have obtained semi-analytically the temperature profiles of three clusters selected carefully from the ROSAT observed cluster sample. These derived temperature profiles are consistent with the new observations of 11 BeppoSAX clusters (Irwin & Bregman 2000) and other measurements made at large cluster radii (e.g. Markevitch et al. 1998) as well as the result given by numerical simulations (e.g. Frenk et al. 1999).

Regardless of the small sample, the three clusters exhibit a temperature profile similar in shape when the length scales are normalized to their virial radii, perhaps indicative of the underlying structural regularity. The present study provides a helpful clue to resolving the temperature profile discrepancy: It is very likely that the lack of the high-quality data of the spatially resolved spectral observations would yield an emission-weighted temperature roughly close to isothermality within [FORMULA] of the virial radius, which does not exclude the possibility that a slightly increasing temperature profile may be marginally detectable in the range of [FORMULA]. This explains the recent observations of Irwin & Bregman (2000) and other studies (e.g. Kikuchi et al. 1999; White 2000; etc.). However, our model does not predict the flat temperature profile toward the inner regions of clusters as reported particularly by Markevitch et al. (1998), although a moderately decreasing temperature profile will ultimately take place in the outer clusters ([FORMULA]).

A conclusive test for the universality of our derived temperature profiles can be provided by future X-ray spectroscopic measurements. Indeed, it will be useful to apply the present method to other X-ray clusters with good X-ray surface brightness profiles measured to large radii and high-quality data of the spatially-resolved spectral observations at least within the central regions. This may allow us to further justify our model and include the measurement uncertainties which have been neglected in the present study. The inconsistency of the predicted temperature profiles with the X-ray spectroscopic results will challenge the prevailing models of structure formations as well as the conventional scenario of cluster dynamics such as the hydrostatic equilibrium. Finally, we should point out that our proposed method to obtain the temperature profiles of clusters can be significantly contaminated by nongravitational heating processes especially from the supernova-driven protogalactic winds. Recall that the asymptotic tendency of the derived temperature profiles at large radii depends sensitively on the [FORMULA] parameter, while the energy injection of supernovae and active galaxies into the intracluster gas will result in a shallower X-ray surface brightness distribution (David et al. 1990; Ponman, Cannon & Navarro 1999; Llyod-Davies, Ponman & Cannon 2000). Without correction to this effect the theoretically predicted temperature profiles may rise too rapidly at large radii. Note that at large radii the NFW mass profile diverges logarithmically with r, which differs significantly from the variation of the gas mass profile (roughly [FORMULA]) expected from the assumption of isothermality. For a cluster with smaller [FORMULA], [FORMULA] and [FORMULA], an increasing temperature profile near virial radius is thus required to maintain the universality of the cluster baryon fraction. Therefore, a robust, theoretical determination of the temperature profiles of clusters should also allow nongravitational heating processes to be included.

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© European Southern Observatory (ESO) 2000

Online publication: August 23, 2000