The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Baryon acoustic oscillations with Lyman-$α$ forests

TL;DR

The paper delivers a high-precision BAO measurement from Lyα forest data using the full SDSS DR16 eBOSS release, obtained from both Lyα auto-correlation and Lyα–quasar cross-correlation. It introduces enhanced modeling of physical and instrumental systematics, along with two realistic mock suites, enabling robust BAO recovery and covariance estimation. The joint analysis yields DH(z)/rd = 8.99 ± 0.19 and DM(z)/rd = 37.5 ± 1.1 at z = 2.33, consistent with Planck flat-ΛCDM at about the 1.5σ level, and demonstrates the value of Lyα BAO as a low-redshift cosmological probe. The work provides the picca toolkit and the Lyα transmitted flux catalogs publicly, facilitating future Lyα-based cosmological studies and cross-survey comparisons.

Abstract

We present a measurement of baryonic acoustic oscillations (BAO) from Lyman-$α$ (Ly$α$) absorption and quasars at an effective redshift $z=2.33$ using the complete extended Baryonic Oscillation Spectroscopic Survey (eBOSS). The sixteenth and final eBOSS data release (SDSS DR16) contains all data from eBOSS and its predecessor, the Baryonic Oscillation Spectroscopic Survey (BOSS), providing $210,005$ quasars with $z_{q}>2.10$ that are used to measure Ly$α$ absorption. We measure the BAO scale both in the auto-correlation of Ly$α$ absorption and in its cross correlation with $341,468$ quasars with redshift $z_{q}>1.77$. Apart from the statistical gain from new quasars and deeper observations, the main improvements over previous work come from more accurate modeling of physical and instrumental correlations and the use of new sets of mock data. Combining the BAO measurement from the auto- and cross-correlation yields the constraints of the two ratios $D_{H}(z=2.33)/r_{d} = 8.99 \pm 0.19$ and $D_{M}(z=2.33)/r_{d} = 37.5 \pm 1.1$, where the error bars are statistical. These results are within $1.5σ$ of the prediction of the flat-$Λ$CDM cosmology of Planck~(2016). The analysis code, \texttt{picca}, the catalog of the flux-transmission field measurements, and the $Δχ^{2}$ surfaces are publicly available.

Figures (23)

• Figure 1: A high signal-to-noise eBOSS quasar spectrum as a function of observed wavelength. The two spectral regions are Ly$\alpha$ (blue), $104<\lambda_{\rm RF}<120 \, \mathrm{nm}$, and Ly$\beta$ (orange), $92<\lambda_{\rm RF}<102 \, \mathrm{nm}$. The two solid curves give the two independent best fit models for $\overline{F}(z)C_{q}(\lambda_{\rm RF})$, and the dashed curves the unabsorbed continuum $C_{q}(\lambda_{\rm RF})$ assuming the $\overline{F}(z)$ of 2012MNRAS.422.3019C. The quasar has a redshift $z_{q} = 3.058$ and is defined in the catalog DR16Q by $\mathrm{Thing\_id} = 498518806$. The Ly$\alpha$ ($\approx493~{\rm nm}$) and the overlapping Ly$\beta$+OVI emission lines ($\approx420~{\rm nm}$) are marked with vertical gray dashed lines.
• Figure 2: Footprint of the eBOSS DR16 survey in a Mollweide projection. The South Galactic Cap (SGC) is on the left and the North Galactic Cap (NGC) is on the right. The gray curve shows the position of the Galactic plane. The color scale gives the ratio of the weighted number of pairs for the auto-correlation between eBOSS DR16 and BOSS DR12.
• Figure 3: Left: Redshift distribution of Ly$\alpha$(Ly$\alpha$) and Ly$\alpha$(Ly$\beta$) pixels (numbers divided by 50) and of quasars. Right: Normalized weighted redshift distribution of pixel-pixel pairs in the auto-correlation. The pairs are in the BAO region of the correlation functions: $r \in [80,120] \, h^{-1}\mathrm{Mpc}$. The orange histogram gives the contribution of correlations involving pixels in the Ly$\alpha$ region, i.e. the Ly$\alpha$(Ly$\alpha$)$\,\times\,$Ly$\alpha$(Ly$\alpha$) correlation function. The green histogram for one pixel in the Ly$\beta$ region, the other in the Ly$\alpha$ region, i.e. the Ly$\alpha$(Ly$\alpha$)$\,\times\,$Ly$\alpha$(Ly$\beta$) correlation function. The blue histogram is the combination of the two. The black dotted line shows the effective redshift of the measurements, i.e. the pivot redshift for the BAO measurement (Section \ref{['section::Fit_to_the_data']}).
• Figure 4: The distribution of weights (equation \ref{['equation::definition_of_weight_auto']}) in four wavelength bands. The left and right panels are for the Ly$\alpha$ and Ly$\beta$ regions, respectively. For $\lambda<400$ nm (blue), the distribution has a peak at zero weight (corresponding to noisy spectra) and a second peak at the maximum weight allowed by LSS. With increasing wavelength and the accompanying decreasing noise, the weight distribution becomes more and more concentrated near the maximum weight. Compared to the Ly$\alpha$ forest, the maximum weight of the Ly$\beta$ forest is reduced by a factor $\approx2$ because of the increased absorption fluctuations and the wavelength distribution is shifted to lower wavelengths.
• Figure 5: Measured (left) and best fit model (right) Ly$\alpha$ auto-correlation function for two pixels in the Ly$\alpha$ region: Ly$\alpha$(Ly$\alpha$) $\times$ Ly$\alpha$(Ly$\alpha$). The correlation is multiplied by the separation $|r|$ and the color bar is saturated and symmetric around zero for visualization purpose. The BAO can be observed as a quarter of a ring at $r \sim 100 \, h^{-1}\mathrm{Mpc}$.