Recovering Redshift Distributions with Cross-Correlations: Pushing The Boundaries

TL;DR

This work extends cross-correlation methods for recovering redshift distributions by incorporating small-scale, non-linear clustering information while addressing galaxy-bias evolution. It demonstrates that, with appropriate scale choices and an iterative bias-correction framework, φ(z) can be recovered reliably for narrow distributions, and shows how tomographic binning and spectroscopic-only bias corrections can enhance accuracy. The study uses LasDamas and Millennium mock catalogs to explore a range of bias scenarios, revealing that non-linear scales increase sensitivity to bias but also boost information content, and that outlier detection and contamination assessment are feasible with small-scale measurements. The results offer practical guidance for applying cross-correlation redshift recovery to upcoming large photometric surveys, including strategies for scale selection, tomography, and bias mitigation.

Abstract

Determining accurate redshift distributions for very large samples of objects has become increasingly important in cosmology. We investigate the impact of extending cross-correlation based redshift distribution recovery methods to include small scale clustering information. The major concern in such work is the ability to disentangle the amplitude of the underlying redshift distribution from the influence of evolving galaxy bias. Using multiple simulations covering a variety of galaxy bias evolution scenarios, we demonstrate reliable redshift recoveries using linear clustering assumptions well into the non-linear regime for redshift distributions of narrow redshift width. Including information from intermediate physical scales balances the increased information available from clustering and the residual bias incurred from relaxing of linear constraints. We discuss how breaking a broad sample into tomographic bins can improve estimates of the redshift distribution, and present a simple bias removal technique using clustering information from the spectroscopic sample alone.

Figures (9)

• Figure 1: Recovered Gaussian redshift distributions for the LasDamas constant bias (left) and Millennium evolving bias (right) spectroscopic samples for three decade width sets of $r_{min}$ and $r_{max}$. Red points are the results before the iterative bias correction is applied, while black points with gray errors are after the iteration. The blue histogram shows the actual redshift distribution of the photometric sample. The more centrally peaked distribution is less sensitive to bias evolution than the broader bimodal distribution.
• Figure 2: Recovered bimodal redshift distributions for the LasDamas constant bias (left) and Millennium evolving bias (right) spectroscopic samples for three decade width sets of $r_{min}$ and $r_{max}$. Red points are the results before the iterative bias correction is applied, while black points with gray errors are after the iteration. The blue histogram shows the actual redshift distribution of the photometric sample. In the case of no bias evolution the recovery works well on all scales, while evolving bias induces a skew in the recovered distribution.
• Figure 3: Measured deviation from the true redshift mean and width of the bimodal (left) and Gaussian (right) distributions for all four spectroscopic data sets. The truth is shown as the black dot, $3-30$ kpc (red), $30-300$ kpc (green), $300-3000$ kpc (blue), and $3-3000$ kpc (gray shaded) are shown for comparison.
• Figure 4: Linear galaxy bias as a function of redshift for the three LasDamas samples described in Section \ref{['damas']}. Red indicates the constant bias sample, green the sample with linear density evolution, and blue the sample with "mixed" bias evolution. .
• Figure 5: Top: Recovered redshift distribution for the bimodal Millennium light cone sample for an annulus of $3-30kpc$. Bottom: the same sample split into two redshift bins (overlapping points omitted for clarity). The bottom panel shows that the amplitudes of the bimodal recovered low redshift (red) and high redshift (blue) samples are significantly less biased than the union of the two samples recovered at once.