The Cross-Correlation of High-Redshift 21 cm and Galaxy Surveys

We study the detectability of the cross-correlation between 21 cm emission from the intergalactic medium and the galaxy distribution during (and before) reionization. We show that first-generation 21 cm experiments, such as the Mileura Widefield Array (MWA), can measure the cross-correlation to a precision of several percent on scales k~0.1/Mpc if combined with a deep galaxy survey detecting all galaxies with m>10^10 Msol over the entire ~800 square degree field of view of the MWA. LOFAR can attain even better limits with galaxy surveys covering its ~50 square degree field of view. The errors on the cross-power spectrum scale with the square root of the overlap volume, so even reasonably modest surveys of several square degrees should yield a positive detection with either instrument. In addition to the obvious scientific value, the cross-correlation has four key advantages over the 21 cm signal alone: (1) its signal-to-noise exceeds that of the 21 cm power spectrum by a factor of several, allowing it to probe smaller spatial scales and perhaps to detect inhomogeneous reionization more efficiently; (2) it allows a cleaner division of the redshift-space distortions (although only if the galaxy redshifts are known precisely); (3) by correlating with the high-redshift galaxy population, the cosmological nature of the 21 cm fluctuations can be determined unambiguously; and (4) the required level of foreground cleaning for the 21 cm signal is vastly reduced.