Matter Composition

Above, the cluster's X-ray surface brightness profile was used to determine the gas density profile. Its integration yields the integral gas mass profile of the cluster. It turns out that in rich clusters the gas mass at large radii, which makes up for about 12% of the clusters gravitational mass, is about 5-6 times larger than the mass residing in the optical galaxies as inferred from their light and the known mass-to-light ratio for different galaxy types. Thus the X-ray emitting ICM is the largest visible

Fig. 23.5 Left: ICM gas mass fraction in the galaxy cluster Abell 1413 from an XMM-Newton observation as a function of the cluster mean matter density inside a given radius in units of the mean density of the Universe, 5, by Pratt and Arnaud [119]. Right: Gas mass fractions for the galaxy clusters in the HIFLUGCS sample of the X-ray brightest galaxy clusters in the sky studied by Reiprich [122] as a function of ther mean ICM temperature. The gas mass fraction for the massive clusters is fairly constant while a deficiency is observed for the galaxy groups with ICM temperatures below 2-3 keV. (Note that the results in the figure are given for a Hubble constant of h50 = 1)

matter component. The major part of the clusters binding mass is ascribed to an unknown form of matter usually termed "dark matter." This "missing mass" problem has been recognized as early as the thirties of the last century by Zwicky [164] from first estimates of the dynamical mass of the Coma cluster, but even though the additional matter component of the hot ICM has been subsequently discovered, the gap between inferred total mass and observed matter could not be closed. The result for the gas mass fraction profile for the example of A1413 is shown in the left panel of Fig. 23.5. In the outer region the gas mass fraction is asymptotically approaching a value of about 11-12% h3Q (note that the results in the figure are given for a Hubble constant of h50 = H0/(50 km s-1 Mpc-1) = 1). The right panel of the figure shows the results on the gas mass fraction for a whole sample of the X-ray brightest clusters in the sky [122], displaying a fairly constant gas mass fraction for massive cluster systems and smaller fractions for the groups with ICM temperatures below 2-3 keV ICM temperature. Other studies of the cluster baryon fraction based on Chandra observations, e.g., by Allen et al. [2] and Ettori et al. [49] and many other determinations yield very similar results.

Since galaxy clusters are formed essentially by gravitational collapse, which samples all forms of matter almost indiscriminently into the cluster potential, this ratio should give a rough measure of the ratio of baryons to all forms of matter including in the Universe including the dark matter.2 This cosmic ratio has also been measured by other means, like the fluctuation spectrum of the cosmic microwave background (e.g., Spergel et al. [139]) or the primordial deuterium abundance in connection with nucleosynthesis calculations [29] with results summarized in

2 N-body/hydrodynamical simulations suggest that the ICM has a slightly wider distribution in the final cluster, resulting in a correction of the universal versus cluster baryon fraction of the order of 10%, e.g. [48,157].

Fig. 23.5 Left: ICM gas mass fraction in the galaxy cluster Abell 1413 from an XMM-Newton observation as a function of the cluster mean matter density inside a given radius in units of the mean density of the Universe, 5, by Pratt and Arnaud [119]. Right: Gas mass fractions for the galaxy clusters in the HIFLUGCS sample of the X-ray brightest galaxy clusters in the sky studied by Reiprich [122] as a function of ther mean ICM temperature. The gas mass fraction for the massive clusters is fairly constant while a deficiency is observed for the galaxy groups with ICM temperatures below 2-3 keV. (Note that the results in the figure are given for a Hubble constant of h50 = 1)

Table 23.1 Baryon mass density fraction in the Universe determined by different methods

Method ab h2 Qb for h = 0.7 Cluster baryon fraction

(assuming that Qm = 0.3) (0.3) 0.0390 (±0.004) Nucleosynthesis and primordial deuterium 0.0205 (±0.0019) 0.0407 (±0.0038) WMAP CMB

fluct. spectrum 0.0224 (±0.0009) 0.0444 (± 0.0018)

Galaxy cluster composition, nucleosynthesis combined with the observed primordial deuterium abundance, and the relative heights of the peaks in the cosmic microwave background fluctuation power spectrum (from WAMP).

Table 23.1. There is good agreement within the quoted error limits of about 10% among all three methods. This provides good support for the reliability of the mass and gas mass determination in galaxy clusters. The baryon fraction in clusters is also used for cosmological tests (Sect. 23.10).

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