3D Correlations in the Lyman-$α$ Forest from Early DESI Data

TL;DR

This work presents the first three-dimensional Lyα forest correlations from DESI early data, measuring auto- and Lyα–quasar cross-correlations and detecting the BAO peak at 3.8σ. It develops a 13-parameter linear-perturbation model that incorporates non-linear corrections, quasar radiation effects, metal contamination, high-column-density systems, and instrumental systematics, and fits it to DESI EDR+M2 data alongside eBOSS DR16 for validation. The analysis demonstrates strong methodological consistency with eBOSS, yields constraints on Lyα and quasar biases, and confirms DESI’s capability to probe BAO at z>2 with upcoming year-1 data. Although the current statistical power is limited, the results validate the end-to-end approach and highlight areas for refinement, preparing for robust cosmological measurements in DESI year 1. The work also provides a framework for handling complex systematics, including metal lines and DLAs, in future Lyα forest analyses.

Abstract

We present the first measurements of Lyman-$α$ (Ly$α$) forest correlations using early data from the Dark Energy Spectroscopic Instrument (DESI). We measure the auto-correlation of Ly$α$ absorption using 88,509 quasars at $z>2$, and its cross-correlation with quasars using a further 147,899 tracer quasars at $z\gtrsim1.77$. Then, we fit these correlations using a 13-parameter model based on linear perturbation theory and find that it provides a good description of the data across a broad range of scales. We detect the BAO peak with a signal-to-noise ratio of $3.8σ$, and show that our measurements of the auto- and cross-correlations are fully-consistent with previous measurements by the Extended Baryon Oscillation Spectroscopic Survey (eBOSS). Even though we only use here a small fraction of the final DESI dataset, our uncertainties are only a factor of 1.7 larger than those from the final eBOSS measurement. We validate the existing analysis methods of Ly$α$ correlations in preparation for making a robust measurement of the BAO scale with the first year of DESI data.

Figures (10)

• Figure 1: Footprint of quasar targets in DESI Early Data Release (purple), the first two months of main survey (red), and eBOSS DR16 (blue) dmdb2020. The EDR and M2 surveys cover an area of 250.1 deg$^2$ and 1290.9 deg$^2$.
• Figure 2: Redshift distribution of high-redshift quasars in DESI EDR+M2 and eBOSS DR16 dmdb2020, with 147 899 and 341 468 in each sample respectively. Only quasars between $z=1.77$ and $z=3.75$ feature in our analysis.
• Figure 3: An example of a DESI EDR spectra at $z=2.44$. Black dashed lines indicate the central wavelength of the strongest quasar emission lines, including the Ly$\alpha$ used in our analysis. The shaded blue region shows the Ly$\alpha$ forest between the Ly$\alpha$ and Ly$\beta$ lines, the latter only partially observed in this specific example. Also of note is the MgII line, used in the pipeline to re-classify galaxies as quasars and the region between the CIV and CIII] lines, used for the re-calibration step described in section \ref{['sec:lyacat']}.
• Figure 4: The DESI EDR+M2 (blue points) and eBOSS DR16 dmdb2020 (shaded green) Ly$\alpha$ auto-correlation compressed into weighted averages of $\mu$=$r_\parallel/r$, where $r=\sqrt{r^2_\parallel+r^2_\perp}$. We also include the best-fitting model to EDR+M2 described in section \ref{['sec:modelling']} (blue dashed). We have multiplied the correlation by $r^2$ to visualise the BAO peak, which is visible in both data sets. From these plots, we can see the consistency between our measurements and those in eBOSS DR16 - a validation of the quality of DESI data at an early survey stage. Note that the presence of three other bumps in the line of sight plot (bottom right) at 20, 60 and 111$h^{-1}$Mpc is due to correlations between the Ly$\alpha$ and SiIII(1207), SiII(1190)/SiII(1193) and SiII(1260) lines respectively. We model these contributions to the correlation in section \ref{['sec:metals']}.
• Figure 5: The 3D EDR+M2 (blue points) and eBOSS DR16 dmdb2020 (green shaded regions) Ly$\alpha$-quasar cross-correlation, and the baseline fit (blue dashed) to EDR+M2 described in section \ref{['sec:modelling']}. Because we have negative values of $r_\parallel$ (when $z_{\rm q}>z_{Ly\alpha}$), we have negative values of $\mu=r_\parallel/r$ and therefore average over $\mu\in[-1,1]$. The cross-correlation is expectedly noisier than the auto-correlation, but still we see a good level of consistency between eBOSS and DESI at this early stage.