Baryon Mass Fractions in Clusters
The joint 68% and 95% contours on Ωm and ΩΛ from the current Chandra fgas(z) data (red/pink). Also shown are the constraints from current SNIa data (green; "gold" sample of Riess et al. 2004 combined with 1-year Supernova Legacy Survey data of Astier et al. 2006) and current CMB studies (light blue; WMAP 3-year; Spergel et al. 2007). The inner contours show the predicted constraints from the Constellation-X fgas experiment (orange) and fgas+Planck data (dark blue).
Current measurements of the evolving cluster mass function based on the Chandra observations of high- and low-z clusters discovered in ROSAT surveys (Vikhlinin et al. 2007). The models are for the "concordance" ΛCDM cosmological model. These data (48 low-z and 40 high-z clusters) provide constraints on the dark energy equation of state parameter, Δω ~ ±0.12, when combined with WMAP.
Constellation-X will directly measure the expansion history of the Universe using absolute distance measurements to galaxy clusters, determined both from measurements of the X-ray gas mass fraction (fgas) in the largest relaxed clusters and using the combination of those measurements with follow-up observations of the SZ effect.
The matter content of the largest clusters of galaxies is expected to provide a fair sample of the matter content of the Universe. The ratio of baryonic-to-total mass in clusters should therefore closely match the ratio of the cosmological parameters Ωb/Ωm (e.g. White et al. 1993). The baryonic mass in clusters is dominated by X-ray emitting gas, the mass of which exceeds the mass in stars by a factor 6, with other sources of baryonic matter being negligible (Fukugita, Hogan & Peebles 1998; Lin & Mohr 2004). The combination of robust measurements of fgas (the ratio of X-ray gas mass to total mass) with determinations of ½b and the Hubble constant from cosmic microwave background (CMB) data (or e.g. the abundances of light elements at high redshifts and the local distance ladder) can therefore be used to measure Ωm. This method provided the first compelling evidence that we live in a low matter density Universe (White et al. 1993) and currently gives one of our tightest and most robust constraints on Ωm (e.g. Allen et al. 2004, 2007; LaRoque et al. 2006).
Measurements of the X-ray gas mass fraction, fgas in clusters as a function of redshift can also be used to probe the acceleration of the Universe. This constraint originates from the dependence of fgas measurements (derived from the observed X-ray gas temperature and density profiles, assuming hydrostatic equilibrium) on the assumed distance to the clusters: fgas proportional to d1.5 (e.g. Sasaki 1996; Pen 1997; Allen et al. 2004). The latest results from this experiment (Allen et al. 2007; see also Ettori et al. 2003, Allen et al. 2004, LaRoque et al. 2006) are based on Chandra data for 42 hot (kT > 5 keV), X-ray luminous (LX > 1045 erg s-1), dynamically relaxed systems spanning the redshift range 0 < z < 1. The restriction to relaxed clusters leads to minimal systematic scatter in the results. In order to determine cosmological constraints, the fgas measurements are fitted with a model that accounts for the expected apparent variation of the observed fgas(z) values as the true, underlying cosmology is varied. The resulting constraints on DE parameters are given in the Figure; the current Chandra data give marginalized constraints of Ωm = 0.28±0.05 and &OmegaΛ = 0.86±0.22 (68% confidence limits). Note that the intrinsic scatter is undetected in current Chandra data for 42 clusters, for which the weighted-mean statistical fgas error is only 5% (Allen et al 2007).
