LOFAR insights into the epoch of reionization from the cross-power spectrum of 21 cm emission and galaxies

Using a combination of N-body simulations, semi-analytic models and radiative transfer calculations, we have estimated the theoretical cross-power spectrum between galaxies and the 21 cm emission from neutral hydrogen during the epoch of reionization. In accordance with previous studies, we find that the 21 cm emission is initially correlated with haloes on large scales (greater than or similar to 30 Mpc), anticorrelated on intermediate (similar to 5 Mpc) and uncorrelated on small (less than or similar to 3 Mpc) scales. This picture quickly changes as reionization proceeds and the two fields become anticorrelated on large scales. The normalization of the cross-power spectrum can be used to set constraints on the average neutral fraction in the intergalactic medium and its shape can be a powerful tool to study the topology of reionization. When we apply a drop-out technique to select galaxies and add to the 21 cm signal the noise expected from the LOw Frequency ARray (LOFAR) telescope, we find that while the normalization of the cross-power spectrum remains a useful tool for probing reionization, its shape becomes too noisy to be informative. On the other hand, for an Ly alpha Emitter (LAE) survey both the normalization and the shape of the cross-power spectrum are suitable probes of reionization. A closer look at a specific planned LAE observing program using Subaru Hyper-Suprime Cam reveals concerns about the strength of the 21 cm signal at the planned redshifts. If the ionized fraction at z similar to 7 is lower than the one estimated here, then using the cross-power spectrum may be a useful exercise given that at higher redshifts and neutral fractions it is able to distinguish between two toy models with different topologies.