Cosmology with Clusters
Dark Energy Constraints from Absolute Cluster Distances
It is now clear that relaxed, simple clusters of galaxies can be used as "standard candles" (Allen et al. 2004) for relative distances using the observationally-verified prediction that the baryonic fraction of the cluster mass in rich clusters is independent of redshift. X-ray observations are crucial since ~90% of all the baryons are in the hot X-ray-emitting gas. The transformation from the observed X-ray temperature and surface brightness to gas mass depends on the absolute distance of the cluster, so its measure as a function of the constant baryonic mass fraction over redshift gives strong constraints on the amount and evolution of dark energy.
Anticipated Constellation-X constraints from cluster baryonic fraction measurements. The purple contours represent the 68 and 90% confidence errors on the cosmological parameters w and ΩM if Constellation-X obtains 5% errors on f(gas) and assuming present uncertaintites in the Hubble constant and baryonic fraction of the Universe. The green and blue represent the 68 and 90% uncertainties if the errors on fgas can be reduced further by extending baryonic fraction measurements to a virial radius (R500) and assuming some modest improvement in the errors on the priors for the universal baryonic fraction and the Hubble constant (anticipated by the time of the Constellation-X launch).
With its large collecting area, Constellation-X will be able to observe the large samples (> 500 objects) over a wide redshift range (to z ~ 1) with the high precision required to use this distance determination method. Simulations show that Constellation-X data alone can obtain uncertainties on w to ±0.05 and, in combination with the CMB data, constraints on w and its evolution that are substantially smaller.
For Constellation-X to use this technique, it must reach scales in the cluster where gravity is dominant and have sufficient angular resolution to recognize merging clusters and separate out the complex physics in the centers of clusters. The Constellation-X collecting area will allow measurements of accurate temperature profiles for massive clusters out to z~1 in a reasonable exposure (~25 ks).
The Sunyaev-Zeldovich (S-Z) effect provides another, independent, method of obtaining absolute cluster distances. While this method has a long history, it is only with the advent of new microwave background detectors and the XMM-Newton and Chandra observatories that the first accurate results have been possible. Currently, the method is limited by systematic errors to 15% uncertainty in distance. Constellation-X spectroscopic data and new S-Z measurements are expected to reduce this error significantly and produce precise distances. Distances with a precision of ~5% from joint X-ray and S-Z analysis would lead to measurements of cosmological parameters (Molnar et al 2004; Fox & Pen 2002) at a level of accuracy competitive with other techniques.
Another, very different technique for measuring cluster distances relies on X-ray resonance absorption against either background sources or the cluster itself compared to the cluster emission (Krolik & Raymond 1988; Sarazin 1989; David 2000). This method requires high-resolution spectroscopy at moderate spatial resolution, which is only possible with Constellation-X. Sarazin (1989) showed that there are over 1000 clusters whose distance can be determined by Constellation-X using this technique, allowing a large number of further, totally independent distances to be determined.
Reference
Allen, S. W., Schmidt, R. W., Ebeling, H., Fabian, A. C., and van Speybroeck, L., 2004, MNRAS, 353, 457David, L. P., 2000, ApJ, 529, 682
Fox, D. C., and Pen, U.-L., 2002, ApJ, 574, 38
Krolik, J. H., and Raymond, J. C., 1988, ApJ, 335, 39
Monar, S. M., Haiman, Z., Birkinshaw, M., and Mushotzky, R. F., 2004, ApJ, 601, 22
Sarazin, C. L., 1989, ApJ, 345, 12
