The 21cm–galaxy cross-correlation: Realistic forecast for 21cm signal detection and reionisation constraints

Context. The 21cm–galaxy cross-correlations are expected to play a key role in the confirmation of the cosmological 21cm signal. Aims. We investigate which survey configurations detect the 21cm–Lyman-α emitter (LAE) cross-correlation signal and assess its ability to distinguish reionisation scenarios. Methods. Our pipeline computes observational uncertainties for the 21cm–galaxy cross-power spectrum, accounting for key survey parameters. These include field of view (FoV); limiting luminosity of galaxy surveys, Lα; redshift uncertainty, σz; and 21cm foreground wedge assumptions. Using this pipeline, we calculated the signal-to-noise ratio (S/N) of the 21cm–LAE cross-power spectrum for two scenarios: one where faint galaxies dominate the ionising photon budget and one where reionisation is driven by bright galaxies. Results. We find that: (i) S/N increases with a larger FoV, fainter Lα, and smaller σz, with the FoV having the strongest impact when σz is small. (ii) Under a moderate foreground wedge, photometric-like surveys yield an insufficient S/N, and medium-deep (Lα ≳ 1042.5 erg s−1), wide-area (FoV > 20 deg2) slitless spectroscopic or spectroscopic surveys are required. (iii) Under an optimistic foreground wedge, detection is possible with deep (Lα ≳ 1042.3 erg s−1), wide-area (FoV ≳ 80 deg2) photometric-like surveys, or with shallower, small-area (FoV ≃ 2 − 3 deg2) slitless spectroscopic surveys. (iv) To distinguish the two reionisation scenarios at z = 7, moderate foreground wedge scenarios require deep-wide spectroscopic surveys; under optimistic foreground wedge, assumptions shallower (Lα ≃ 1042.8 erg s−1), medium-area (FoV ≃ 10 deg2) slitless spectroscopic surveys suffice. (v) Maximising the S/N for both detection and model discrimination requires sampling the large-scale peak of the cross-power spectrum, which shifts to larger physical scales as reionisation proceeds, and the less ionisation fronts follow the gas density, thus making surveys at z > 7, or when the Universe was more neutral (⟨χHII⟩> 0.5), more promising despite lower galaxy number densities. Conclusions. Our results show that large-area spectroscopic surveys and 21cm foreground cleaning are key for using 21cm–LAE cross-correlations to constrain reionisation beyond the global ionisation state of the intergalactic medium.