The ubiquitous presence of the Fe line complex in the X-ray spectra of galaxy clusters offers the possibility of measuring their redshift without resorting to spectroscopic follow-up observations. In this paper we assess the accuracy with which the r
edshift of galaxy clusters can be recovered from an X-ray spectral analysis of Chandra archival data. This study indicates a strategy to build large surveys of clusters whose identification and redshift measurement are both based on X-ray data alone. We apply a blind search for K--shell and L--shell Fe line complex in X-ray cluster spectra using Chandra archival observations of galaxy clusters. The Fe line in the ICM spectra can be detected by simply analyzing the C-statistics variation $Delta C_{stat}$ as a function of the redshift parameter. We repeat the measurement under different conditions, and compare the X-ray derived redshift $z_X$ with the one obtained by means of optical spectroscopy $z_o$. We explore how a number of priors on metallicity and luminosity can be effectively used to reduce catastrophic errors. The $Delta C_{stat}$ provides the most efficient means for discarding wrong redshift measures and to estimate the actual error on $z_X$. We identify a simple and efficient procedure for optimally measuring the redshifts from the X-ray spectral analysis of clusters of galaxies. When this procedure is applied to mock catalogs extracted from high sensitivity, wide-area cluster surveys, such as those proposed with Wide Field X-ray Telescope (WFXT) mission, it is possible to obtain a complete samples of X-ray clusters with reliable redshift measurements, thus avoiding time-consuming optical spectroscopic observations. This methodology will make it possible to trace cosmic growth by studying the evolution of the cluster mass function directly using X-ray data.
Galaxy clusters have their unique advantages for cosmology. Here we collect a new sample of 10 lensing galaxy clusters with X-ray observations to constrain cosmological parameters.The redshifts of lensing clusters lie between 0.1 and 0.6, and the red
shift range of their arcs is from 0.4 to 4.9. These clusters are selected carefully from strong gravitational lensing systems which have both X-ray satellite observations and optical giant luminous arcs with known redshift. Giant arcs usually appear in the central region of clusters, where mass can be traced with luminosity quite well. Based on gravitational lensing theory and cluster mass distribution model we can derive an Hubble constant independent ratio between two angular diameter distances. One is the distance of lensing source and the other is that between the deflector and the source. Since angular diameter distance relies heavily on cosmological geometry, we can use these ratios to constrain cosmological models. Meanwhile X-ray gas fractions of galaxy clusters can also be a cosmological probe. Because there are a dozen parameters to be fitted, we introduce a new analytic algorithm, Powells UOBYQA (Unconstrained Optimization By Quadratic Approximation), to accelerate our calculation. Our result proves that this algorithm is an effective fitting method for such continuous multi-parameter constraint. We find an interesting fact that these two approaches are sensitive to $Omega_{Lambda}$ and $Omega_{M}$ separately. Combining them we can get quite good fitting values of basic cosmological parameters: $Omega_{M}=0.26_{-0.04}^{+0.04}$, and $Omega_{Lambda}=0.82_{-0.16}^{+0.14}$ .
The cosmic coincidence problem is a serious challenge to dark energy model. We suggest a quantitative criteria for judging the severity of the coincidence problem. Applying this criteria to three different interacting models, including the interactin
g quintessence, interacting phantom, and interacting Chaplygin gas models, we find that the interacting Chaplygin gas model has a better chance to solve the coincidence problem. Quantitatively, we find that the coincidence index C for the interacting Chaplygin gas model is smaller than that for the interacting quintessence and phantom models by six orders of magnitude.
