Determining distances to clusters of galaxies using resonant X-ray emission lines

Bright clusters of galaxies can be seen out to cosmological distances, and thus they can be used to derive cosmological parameters. Although the continuum X-ray emission from the intracluster gas is optically thin, the optical depth of resonant lines of ions of heavy elements can be larger than unity. In this Letter, we study the feasibility of deriving distances to clusters of galaxies by determining the spatial distribution of the intracluster gas from X-ray imaging and the optical depth from resonant emission lines (the XREL method). We solve the radiative transfer problem for line scattering in the hot intracluster gas using Monte Carlo simulations. We discuss the spatial and spectral resolutions needed to use the XREL method for accurate determination of distances, and hence cosmological parameters, and show that accurate distances will be obtained by applying this technique with the next generation of high-resolution X-ray spectrometers.