Probing Reionization With the 21 Cm Galaxy Cross-Power Spectrum

The cross-correlation between high-redshift galaxies and 21 cm emission from the high-redshift intergalactic medium promises to be an excellent probe of the Epoch of Reionization. On large scales, the 21 cm and galaxy fields are anticorrelated during most of the reionization epoch. However, on scales smaller than the size of the H II regions around detectable galaxies, the two fields become roughly uncorrelated. Consequently, the 21 cm galaxy cross-power spectrum provides a tracer of bubble growth during reionization, with the signal turning over on progressively larger scales as reionization proceeds. The precise turnover scale depends on the minimum host mass of the detectable galaxies, and the galaxy selection technique. Measuring the turnover scale as a function of galaxy luminosity constrains the characteristic bubble size around galaxies of different luminosities. The cross-spectrum becomes positive on small scales if ionizing photons fail to escape from low-mass galaxies, and these galaxies are detectable longward of the hydrogen ionization edge, because in this case some identifiable galaxies lie outside the ionized regions. The Murchison Widefield Array (MWA) and Low Frequency Array can potentially measure the 21 cm galaxy cross-spectrum in conjunction with mild extensions to the existing Subaru survey for z = 6.6 Ly alpha emitters. A futuristic galaxy survey covering a sizable fraction of the MWA field of view (similar to 800 deg(2)) can probe the scale dependence of the cross-spectrum, constraining the filling factor of H II regions at different redshifts during reionization, and providing other valuable constraints on reionization models.