Baryon acoustic oscillations from the complete SDSS-III Ly$α$-quasar cross-correlation function at $z=2.4$

TL;DR

This paper delivers a high-precision BAO measurement from the Lyα forest–quasar cross-correlation at z ≈ 2.4 using the full SDSS-III DR12 dataset, aided by a new data-reduction pipeline and mock-based validation. The authors model the cross-correlation with a physically-motivated framework that separates BAO peak and smooth components, accounts for metals, UV fluctuations, HCDs, and continuum-fitting distortions, and uses a distortion matrix to capture continuum biases. They report D_H(z)/r_d = 9.01 ± 0.36 and D_M(z)/r_d = 35.7 ± 1.7 from cross-correlation alone, which aligns with flat-ΛCDM at the ~1.8σ level, and when combined with Lyα auto-correlation, yield D_H(z)/r_d ≈ 8.94–9.01 and D_M(z)/r_d ≈ 36.6, reducing degeneracies and achieving a ~2.3σ tension with Planck results. The analysis is validated with extensive mocks demonstrating unbiased BAO peak recovery and robust covariance treatment, and the results are placed in the broader context of BAO measurements across redshifts. These findings reinforce the concordance framework while highlighting mild tension that motivates continued high-redshift BAO studies with upcoming surveys.

Abstract

We present a measurement of baryon acoustic oscillations (BAO) in the cross-correlation of quasars with the Ly$α$-forest flux-transmission at a mean redshift $z=2.40$. The measurement uses the complete SDSS-III data sample: 168,889 forests and 234,367 quasars from the SDSS Data Release DR12. In addition to the statistical improvement on our previous study using DR11, we have implemented numerous improvements at the analysis level allowing a more accurate measurement of this cross-correlation. We also developed the first simulations of the cross-correlation allowing us to test different aspects of our data analysis and to search for potential systematic errors in the determination of the BAO peak position. We measure the two ratios $D_{H}(z=2.40)/r_{d} = 9.01 \pm 0.36$ and $D_{M}(z=2.40)/r_{d} = 35.7 \pm 1.7$, where the errors include marginalization over the non-linear velocity of quasars and the metal - quasar cross-correlation contribution, among other effects. These results are within $1.8σ$ of the prediction of the flat-$Λ$CDM model describing the observed CMB anisotropies. We combine this study with the Ly$α$-forest auto-correlation function [2017A&A...603A..12B], yielding $D_{H}(z=2.40)/r_{d} = 8.94 \pm 0.22$ and $D_{M}(z=2.40)/r_{d} = 36.6 \pm 1.2$, within $2.3σ$ of the same flat-$Λ$CDM model.

Figures (20)

• Figure 1: Mollweide projection of the BOSS DR12 footprint in equatorial coordinates used in this study. The light gray points represent the position of the Galactic plane. The blue points are the positions of the forests from DR12 used here $z_{\mathrm{forest}} \in [2,6]$. The light blue points are the positions of the new forests not included in the DR11 study of 2014JCAP...05..027F.
• Figure 2: Example of a BOSS quasar spectrum of at $z=2.91$. The spectrograph resolution at $\lambda\sim400~{\rm nm}$ is $\sim0.2~{\rm nm}$. The red and blue lines cover the forest region used here, $\lambda_{\rm RF} \in [104,120]~\mathrm{nm}$. This region is sandwiched between the quasar's $\mathrm{Ly}\beta$ and $\mathrm{Ly}\alpha$ emission lines at 102.572 nm and 121.567 nm respectively. The blue line is the model of the continuum for this particular quasar, $C_q(\lambda_{\rm RF})$, and the red line is the product of the continuum and the mean absorption, $\overline{F}(z) C_q(\lambda_{\rm RF})$, as calculated by the method described in Sect. \ref{['section::Measurement_of_the_transmission_field']}.
• Figure 3: Left panel presents the distribution of the redshift of quasars (blue) and forest pixels (green) with the redshift for the latter calculated assuming $\mathrm{Ly}\alpha$ absorption. The pixels are weighted as described in Sect. \ref{['subsection::The_Lya_forest_quasar_cross_correlation::The_correlation_function']}. The right panel displays the weighted distribution of the redshift of the $1.8\times10^9$ pixel-quasar pairs in the BAO region: $r_{pair} \in [80,120]~h^{-1}~\mathrm{Mpc}$. The redshift of a pair is defined by: $z_{pair} = (z_{pixel}+z_{\rm QSO})/2$. The weighted mean redshift of the pairs (dashed black line) defines the mean redshift, $z_{\rm eff}=2.40$, of the measurement of the BAO peak position.
• Figure 4: Mean normalized covariance matrix, $Corr_{AB}\equiv C_{AB}/\sqrt{C_{AA}C_{BB}}$, as a function of $\Delta r_{\parallel} = |r_{\parallel}^{A}-r_{\parallel}^{B}|$ for the three lowest values of $\Delta r_{\perp} = |r_{\perp}^{A}-r_{\perp}^{B}|$. The top figures are for $\Delta r_{\perp}=0$, with the righthand panel showing only points with $Corr_{AB}<0.1$. The bottom two figures are for $\Delta r_{\perp}=4~h^{-1}~\mathrm{Mpc}$ (left) and $\Delta r_{\perp}=8~h^{-1}~\mathrm{Mpc}$ (right). Shown are the correlations given by the sub-sampling, by the sum of all the diagram expansion, and by the shuffle of forests. The shuffle technique fails for $(\Delta r_{\perp}>0, \Delta r_{\parallel}<30~h^{-1}~\mathrm{Mpc})$ where inter-forest correlations dominate.
• Figure 5: Measured (left) and the best fit model (right) of the $\mathrm{Ly}\alpha$-forest-quasar cross-correlation. The distortion matrix (\ref{['equation::distortion_matrix_measure']}) has been applied to the model. The correlation is multiplied by a factor $r$. The BAO scale appears here as a half ring of radius $r \approx 100~h^{-1}~\mathrm{Mpc}$. The color code is saturated for clarity.