Calibrating redshift distributions at z > 2 with Lyman-α forest cross-correlations

We explore the feasibility of using Lyman-α (Lyα) forests to calibrate the ensemble redshift distribution of the high-redshift tail (2 < z < 3) of photometric galaxies. We use CoLoRe simulations to create mock DESI 5-year Lyα forests and Rubin Observatory LSST 10-year photometric galaxies up to z = 3, and measure the galaxy redshift distribution via their angular cross-correlations. Due to large redshift-space distortions in the Lyα forest, the conventional n(z) estimator for clustering redshifts does not apply, and we develope a theoretical framework to model the angular cross-correlation directly. Using the simulations, we explore effects of instrumental noise, continuum fitting, contamination in the Lyα forest, cross-correlation angular scales (θ), and redshift bin size (Δz) on the signal-to-noise (SNR) of the measurements. We find that continuum fitting methods strongly impact the SNR of the measurements. With our baseline continuum fitting method, LyCAN, at angular scales θ ~ 10 arcmin and Δz = 0.1, we measure the cross-correlation signal at 24σ. If the shape of the redshift distribution and galaxy bias evolution are known well for z < 2, the cross-correlation can constrain the mean redshift of the galaxy sample to σ z/(1+z̄) = 0.006 at a mean redshift of z̄=2. This demonstrates that Lyα cross-correlation is a reliable and promising method to calibrate the high-redshift tails of photometric Stage IV galaxy surveys.