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 similar to 0.1 Mpc(-1) if combined with a deep galaxy survey detecting all galaxies with m > 1010 M-circle dot over the entire similar to 800 deg(2) field of view of the MWA. LOFAR can attain even better limits with galaxy surveys covering its similar to 50 deg(2) 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 ratio 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.