The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: BAO and RSD measurements from anisotropic clustering analysis of the Quasar Sample in configuration space between redshift 0.8 and 2.2

TL;DR

The paper delivers a comprehensive anisotropic clustering analysis of the SDSS-IV eBOSS DR16 quasar sample to measure BAO and redshift-space distortion signals in configuration space. By combining full-shape multipole modelling with BAO-only fits and integrating Fourier-space results, the study yields precise constraints on D_M/r_drag, D_H/r_drag, and fσ8 at z_eff ≈ 1.48, while rigorously validating systematics with extensive mock challenges and EZmocks. The results are largely consistent with Planck ΛCDM, with the joint configuration- and Fourier-space analysis providing tight, robust measurements that enhance our understanding of cosmic expansion and structure growth at z ~ 1.5. The work also demonstrates the robustness of quasars as tracers of the underlying matter field and establishes a framework for rigorous systematic error budgeting in large-scale structure analyses.

Abstract

We measure the anisotropic clustering of the quasar sample from Data Release 16 (DR16) of the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey (eBOSS). A sample of $343,708$ spectroscopically confirmed quasars between redshift $0.8<z<2.2$ are used as tracers of the underlying dark matter field. In comparison with DR14 sample, the final sample doubles the number of objects as well as the survey area. In this paper, we present the analysis in configuration space by measuring the two-point correlation function and decompose using the Legendre polynomials. For the full-shape analysis of the Legendre multipole moments, we measure the BAO distance and the growth rate of the cosmic structure. At an effective redshift of $z_{\rm eff}=1.48$, we measure the comoving angular diameter distance $D_{\rm M}(z_{\rm eff})/r_{\rm drag} = 30.66\pm0.88$, the Hubble distance $D_{\rm H}(z_{\rm eff})/r_{\rm drag} = 13.11\pm0.52$, and the growth rate $fσ_8(z_{\rm eff}) = 0.439\pm0.048$. The accuracy of these measurements is confirmed using an extensive set of mock simulations developed for the quasar sample. The uncertainties on the distance and growth rate measurements have been reduced substantially ($\sim 45\%$ and $\sim30\%$) with respect to the DR14 results. We also perform a BAO-only analysis to cross check the robustness of the methodology of the full-shape analysis. Combining our analysis with the Fourier space analysis, we arrive at $D^{\bf{c}}_{\rm M}(z_{\rm eff})/r_{\rm drag} = 30.22 \pm 0.79$, $D^{\bf{c}}_{\rm H}(z_{\rm eff})/r_{\rm drag} = 13.26 \pm 0.47$, and $fσ_8^{\bf{c}}(z_{\rm eff}) = 0.464 \pm 0.045$.

Figures (16)

• Figure 1: Footprint of the eBOSS QSOs, split into the NGC (left) and SGC (right). The DR14 sample is shown in orange, while the DR16 sample is shown in blue (and also includes the entire orange region).
• Figure 2: Left: The 2D correlation function $\xi\left(s_{\perp}, s_{ \|}\right)$ measured from the DR16 quasar sample. The solid contour is from the theory prediction. Right: The measured correlation function for monopole ($\ell=0$, blue), quadrupole ($\ell=2$, red) and hexadecapole ($\ell=4$, gray), with the best fitting full-shape model shown by the solid lines.
• Figure 3: Comparison between our measured correlation function and the best-fit BAO model. In the top panel, we show the monopole, where we have subtracted the smooth component of the model from both the model and the data. In the bottom panel, we display the quadrupole and subtract the quadrupole of a model that has the same parameters as the best-fit, but with $\epsilon = 0$.
• Figure 4: Comparison of matter power spectrum between RESPRESSO (dotted-orange), gRPT (dotted-green) and Minerva N-body simulation (blue, with $2\%$ error indicated by the grey band) at $z=1.0$.
• Figure 5: Comparison of the cross matter-velocity divergence power spectrum, $P_{\delta \theta}$, and the auto velocity divergence power spectrum, $P_{\theta \theta}$, at $z=1.0$. Power spectra calculated using the fitting formulae are shown by the solid red and brown curves for $P_{\delta \theta}$ (with input from RESPRESSO for the auto matter power spectrum) and $P_{\theta \theta}$, respectively. Power spectra calculated using gRPT are indicated by the dotted blue curves.