4.6. The baryon fraction in high redshift clusters
A reasonable assumption is that the baryon fraction in clusters should remain more or less constant with redshift, as there is no motivation for introducing a variation with time of this quantity. When one infers the baryon fraction from X-ray observations of clusters at cosmological distances, the background cosmology is coming in the inferred value, through angular and luminosity distances. Therefore for a given observed cluster, the inferred gas fraction would vary accordingly to the cosmology. This opens a way to constraint the cosmology, if one assumes that the apparent baryon fraction has to be constant (Sasaki, 1996; Pen, 1997), or equivalently that the emissivity profiles of clusters has to be identical when scaling laws are taken into account (Neumann and Arnaud, 2001). Application of this test probably needs a large statistical sample, but a preliminary application can be done on a distant cluster observed by XMM: RXJ1120.
Figure 6. From the observed X-ray surface brightness of the distant cluster RXJ1120 (Arnaud et al., 2002) the gas fraction density profile (red filled circles) is compared to the results from the local clusters derived by Roussel et al. (2000) (blue open triangles) and those found in the outer regions by Sadat and Blanchard (2001) (red rhombuses). The profile shape is very close to those of local clusters. The amplitude is right for an m = 1. model, while a lambda model (open red triangles) is in strong disagreement with the data.
This distant cluster is a perfect candidate for the application of this test: the X-ray emission has been detected up to a distance close to the virial radius (Arnaud et al., 2001), the cluster is a ~ 6 keV cluster, with a relaxed configuration. The gas profile can be derived up to a radius of the order of the virial radius without extrapolation. The inferred radial gas profile possesses two remarkable properties: i) the shape of the gas profile in this distant cluster is in very good agreement with the shape of the profile inferred from local clusters by Sadat and Blanchard (2001), giving an interesting further piece of evidence in favor of this shape ii) the amplitude matches the amplitude of the local sample only for a high matter density universe, while an universe dominated by a cosmological constant is strongly disfavored.