Title: Insights into the 21 cm field from the vanishing cross-power spectrum at the epoch of reionization

Abstract: The early stages of the Epoch of Reionization, probed by the 21 cm line, are sensitive to the detailed properties and formation histories of the first galaxies. We use 21cmFAST and a simple, self-consistent galaxy model to examine the redshift evolution of the large-scale cross-power spectrum between the 21 cm field and line-emitting galaxies. A key transition in redshift occurs when the 21 cm field shifts from being positively correlated with the galaxy distribution to being negatively correlated. Importantly, this transition redshift is insensitive to the properties of the galaxy tracers but depends sensitively on the thermal and ionization histories traced through the 21 cm field. Specifically, we show that the transition occurs when both ionization fluctuations dominate over 21 cm spin temperature fluctuations and when the average spin temperature exceeds the temperature of the cosmic microwave background. We illustrate this with three different 21 cm models which have largely the same neutral fraction evolution but different heating histories. We find that the transition redshift has a scale dependence, and that this can help disentangle the relative importance of heating and ionization fluctuations. The best prospects for constraining the transition redshift occur in scenarios with late X-ray heating, where the transition occurs at redshifts as low as $z \sim 6-8$. In our models, this requires high-redshift galaxy surveys with sensitivities of $\sim 10^{-18}~\rm erg/s/cm^2$ for optical lines and $\sim 10^{-19}~\rm erg/s/cm^2$ for FIR lines. Future measurements of the transition redshift can help discriminate between 21 cm models and will benefit from reduced systematics.