Prospects for detecting clusters of galaxies through X-ray absorption

We investigate the feasibility of detecting high-redshift clusters in absor ption against background active galactic nuclei (AGNs) with the next genera tion of X-ray telescopes. The four limiting factors for detecting clusters in absorption are the sensitivity of the X-ray spectrometers, the abundance of X-ray-bright AGNs, the absorption equivalent width, and the sky coverin g factor of the hot gas in clusters. Based on isothermal and polytropic tem perature profiles for the gas in clusters, we compute the absorption equiva lent widths of the most abundant heavy elements in clusters with emission-w eighted temperatures between 1 keV (typical of groups) and 12 keV (typical of the hottest known clusters). For typical AGN X-ray spectra, we find that the easiest lines to detect in absorption arise from He-like Si and S and Fe xx in groups, He-like Fe in 2-10 keV clusters, and H-like Fe in the hott est clusters. The sky covering factor of the hot gas is then determined as a function of absorption equivalent width for a nonevolving cluster populat ion and for evolving cluster populations in an open (Omega = 0.3) and flat (Omega = 1.0) universe. In an open universe, approximately 5% of the sky is covered by hot gas with an equivalent width greater than 1 eV for He-like Fe absorption. In a high-density universe, the corresponding sky covering f actor is only 1%. Based on the X-ray luminosity function of AGNs, we find t hat there are several thousand AGNs beyond z = 1 and several hundred AGNs b eyond z = 2 that are bright enough to produce detectable absorption feature s in clusters with future X-ray calorimeters. These results show that an ob serving program of high-redshift, X-ray-bright AGNs will have the added ben efit of detecting a significant sample of high-redshift clusters. High-reds hift clusters can easily be missed in X-ray imaging surveys, since their X- ray surface brightness can be below the X-ray background.