Galaxy-cluster masses via 21st-century measurements of lensing of 21-cm fluctuations

We discuss the prospects to measure galaxy-cluster properties via weak lensing of 21-cm fluctuations from the dark ages and the epoch of reionization (EOR). We choose as a figure of merit the smallest cluster mass detectable through such measurements. We construct the minimum-variance quadratic estimator for the cluster mass based on lensing of 21-cm fluctuations at multiple redshifts. We discuss the tradeoff between frequency bandwidth, angular resolution, and number of redshift shells available for a fixed noise level for the radio detectors. Observations of lensing of the 21-cm background from the dark ages will be capable of detecting M>~10^12 Msun/h mass halos, but will require futuristic experiments to overcome the contaminating sources. Next-generation radio measurements of 21-cm fluctuations from the EOR will, however, have the sensitivity to detect galaxy clusters with halo masses M>~10^13 Msun/h, given enough observation time (for the relevant sky patch) and collecting area to maximize their resolution capabilities.