Lensing of 21-cm absorption haloes of z ∼ 2-30 first galaxies

Extended 21-cm absorption regions ( dubbed '21-cm absorption haloes') around first galaxies at z similar to 30 are likely the first distinctive structures accessible to radio observations. Though the radio array capable of detecting and resolving them must have similar to 200 km(2) total collecting area, given the great impact of such detections to the understanding of the reionization process and cosmology, such radio survey would be extremely profitable. As an example, we point out a potentially useful byproduct of such survey. The resolved 21-cm absorption 'haloes', likely close to spherical, can serve as ( almost) ideal sources for measuring the cosmic shear and mapping the matter distribution to z similar to 30. We investigate the expected lensing signal and consider a variety of noise contributions on the shear measurement. We find that signal-to-noise ratio (S/N) similar to 1 can be achieved for individual 'haloes'. Given millions of 21-cm absorption 'haloes' across the sky, the total S/N will be comparable to traditional shear measurement of similar to 109 galaxies at z similar to 1.