  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 21cm emission from neutral hydrogen during the epoch
of reionization. In accordance with previous studies, we find that the 21cm
emission is initially correlated with halos on large scales (> 30 Mpc),
anti-correlated on intermediate (~ 5 Mpc), and uncorrelated on small (< 3 Mpc)
scales. This picture quickly changes as reionization proceeds and the two
fields become anti-correlated 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 tool to study the topology
of reionization. When we apply a drop-out technique to select galaxies and add
to the 21cm signal the noise expected from the 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 a Lyalpha 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 21cm signal at the planned
redshifts. If the ionized fraction at z ~ 7 is lower that 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.
