Statistical Detection of IGM Structures during Cosmic Reionization using Absorption of the Redshifted 21 cm line by HI against Compact Background Radio Sources

Detecting neutral hydrogen structures in the intergalactic medium (IGM) during cosmic reionization via absorption (21 cm forest) against a background radiation is considered independent and complementary to the three-dimensional tomography and power spectrum techniques. The direct detection of this absorption requires very bright ($\gtrsim 10$-100 mJy) background sources at high redshifts ($z\gtrsim 8$), which are evidently rare; very long times of integration; or instruments of very high sensitivity. This motivates a statistical one-dimensional (1D) power spectrum approach along narrow sightlines but with fainter background objects ($\sim 1$-10 mJy), which are likely to be more abundant and significant contributors at high redshifts. The 1D power spectrum reduces cosmic variance and improves sensitivity especially on small spatial scales. Using standard radiative transfer and fiducial models for the instrument, the background sources, and the evolution of IGM structures during cosmic reionization, the potential of the 1D power spectrum along selected narrow directions is investigated against uncertainties from thermal noise and the chromatic synthesized point spread function (PSF) response. Minimum requirements on the number of high-redshift background sources, the telescope sensitivity, and the PSF quality are estimated for a range of instrumental, background source, and reionization model parameters. The 1D power spectrum is intrinsically stronger at higher redshifts. A $\sim 1000$ hr observing campaign targeting $\sim 100$ narrow sightlines to radio-faint, high-redshift background objects with modern radio telescopes, especially the Square Kilometre Array, can detect the 1D power spectrum on a range of spatial scales and redshifts, and potentially discriminate between models of cosmic reionization.