Modelling the impact of quasar redshift errors on the full-shape analysis of correlations in the Lyman-$α$ forest

TL;DR

This paper develops a physically motivated model for the contamination of Lyα forest full-shape analyses by continuum redshift errors in quasar redshifts. It extends prior cross-correlation modeling to the Lyα auto-correlation, introducing three parameters that describe the redshift-error dispersion and the amplitudes of contamination in auto- and cross-correlations. Through DESI DR1-like mocks, the authors demonstrate that jointly fitting auto- and cross-correlations with this contamination model removes most of the induced biases on BAO and AP parameters, while leaving the growth-rate proxy $f\sigma_8$ largely intact. They also propose practical mitigation by removing a tiny fraction of correlating pairs, suitable for real data to reduce residual contamination, with caveats for full-shape analyses. Overall, the work provides a robust framework to account for continuum redshift-error contamination in Lyα full-shape cosmology and informs data-quality cuts for DESI using DR1 and future datasets.

Abstract

In preparation for the first cosmological measurements from the full-shape of the Lyman-$α$ (Ly$α$) forest from DESI, we must carefully model all relevant systematics that might bias our analysis. It was shown in Youles et al. (2022) that random quasar redshift errors produce a smoothing effect on the mean quasar continuum in the Ly$α$ forest region. This in turn gives rise to spurious features in the Ly$α$ auto-correlation, and its cross-correlation with quasars. Using synthetic data sets based on the DESI survey, we confirm that the impact on BAO measurements is small, but that a bias is introduced to parameters which depend on the full-shape of our correlations. We combine a model of this contamination in the cross-correlation (Youles et al. 2022) with a new model we introduce here for the auto-correlation. These are parametrised by 3 parameters, which when included in a joint fit to both correlation functions, successfully eliminate any impact of redshift errors on our full-shape constraints. We also present a strategy for removing this contamination from real data, by removing $\sim$0.3% of correlating pairs.

Figures (12)

• Figure 1: The effect of continuum redshift errors on the Ly$\alpha$-quasar cross-correlation (left) and the Ly$\alpha$-Ly$\alpha$ auto-correlation (right) computed from our mock datasets. Each dataset is the stack of 100 DESI DR1 mocks. We take the weighted average over the first 4 bins in transverse separation $r_\perp$ ([0,16] $h^{-1}$Mpc) where the effect of redshift errors is strongest, and plot as function of line-of-sight separation $r_\parallel$. We only include negative $r_\parallel$ for the cross-correlation, since as shown in figure \ref{['fig:2dzerr_auto']} there is no impact at $r_\parallel>0$$h^{-1}$Mpc. Note that at $\sim\pm60$$h^{-1}$Mpc we see bumps in the correlations due to SiII(1190/1193) lines.
• Figure 2: (Top) difference in the Ly$\alpha$ auto-correlation measured from contaminated (with continuum redshift errors) and uncontaminated datasets, as a function of ($r_\perp,r_\parallel$). (Bottom) difference in the Ly$\alpha$-quasar cross-correlation from contaminated and uncontaminated datasets.
• Figure 3: (Top) the mean continuum distortion function $\gamma=\hat{\overline{C}}/\overline{C} - 1$ as a function of rest-frame wavelength. $\hat{\overline{C}}(\lambda_{\rm rf}, \sigma_{\rm v})$ is the mean continuum with redshift errors $\sigma_{\rm v}$, as shown in the plot above. Roman numerals mark the location of prevalent features in $\gamma$, which contaminate our correlation functions. We include the approximate comoving distance between a quasar at $z = 2.3$ and pixels in its forest, along the top axis. (Bottom) the Ly$\alpha$ forest mean continuum (equation \ref{['eq:meancontdelta']}) of our mock datasets with 0 $\rm kms^{-1}$, 400 $\rm kms^{-1}$ and 1000 $\rm kms^{-1}$ of redshift errors added. The later is for visualisation while 400 $\rm kms^{-1}$ is used in the actual analysis.
• Figure 4: The difference in the Ly$\alpha$ autocorrelation function between contaminated (with continuum redshift errors) and uncontaminated datasets (grey), overlaid with direct measurements of $\langle \delta \gamma \rangle$ (red dashed) and $\langle \gamma \gamma \rangle$ (blue dotted). We plot only the first $r_\perp$ bin where the contamination is strongest.
• Figure 5: The evolution of continuum redshift error contamination with the maximum rest-frame wavelength of the Ly$\alpha$ forest. The 1205Å limit (red) is the limit used in the analysis of this paper. We include Roman numerals to indicate the features in $\gamma$ (figure \ref{['fig:comb_cont_gamma']}) which correspond to spurious correlations in this figure.