Measuring redshifts using X-ray spectroscopy of galaxy clusters: results from Chandra data and future prospects

Context. 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 practice, the blind search of the Fe line in X-ray spectra is a difficult task and is affected not only by limited S/N (particularly at high redshift), but also by several systematic errors, associated with varying Fe abundance values, ICM temperature gradients, and instrumental characteristics. Aims. We assess the accuracy with which the redshift of galaxy clusters can be recovered from an X-ray spectral analysis of Chandra archival data. We present a strategy to compile large surveys of clusters whose identification and redshift measurement are both based on X-ray data alone. Methods. We apply a blind search for K-shell and L-shell Fe line complexes in X-ray cluster spectra using Chandra archival observations of galaxy clusters. The Fe line can be detected in the ICM spectra by simply analyzing the C-statistics variation Delta C-stat as a function of the redshift parameter, when all the other model parameters are frozen to the best-fit values. 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 effective means of discarding wrong redshift measurements and estimating the actual error in z(X). Results. 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 complete samples of X-ray clusters with reliable redshift measurements, thus avoiding time-consuming optical spectroscopic observations. Our analysis shows that, in the case of WFXT, a blind Fe line search is 95% successful for spectra with more than 1000 net counts, whenever Delta C-stat > 9, corresponding formally to a 3 sigma confidence level. The average error in the redshift z(X) decreases rapidly for higher values of Delta C-stat. Finally, we discuss how to estimate the completeness of a large cluster samples with measured z(X). This methodology will make it possible to trace cosmic growth by studying the evolution of the cluster mass function directly using X-ray data.