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Quasar-Lyman $α$ Forest Cross-Correlation from BOSS DR11 : Baryon Acoustic Oscillations

Andreu Font-Ribera, David Kirkby, Nicolas Busca, Jordi Miralda-Escudé, Nicholas P. Ross, Anže Slosar, Jim Rich, Éric Aubourg, Stephen Bailey, Vaishali Bhardwaj, Julian Bautista, Florian Beutler, Dmitry Bizyaev, Michael Blomqvist, Howard Brewington, Jon Brinkmann, Joel R. Brownstein, Bill Carithers, Kyle S. Dawson, Timothée Delubac, Garrett Ebelke, Daniel J. Eisenstein, Jian Ge, Karen Kinemuchi, Khee-Gan Lee, Viktor Malanushenko, Elena Malanushenko, Moses Marchante, Daniel Margala, Demitri Muna, Adam D. Myers, Pasquier Noterdaeme, Daniel Oravetz, Nathalie Palanque-Delabrouille, Isabelle Pâris, Patrick Petitjean, Matthew M. Pieri, Graziano Rossi, Donald P. Schneider, Audrey Simmons, Matteo Viel, Christophe Yeche, Donald G. York

TL;DR

This study uses over 164,000 quasars from SDSS-III BOSS DR11 to measure the quasar-Ly$\alpha$ cross-correlation at $z\sim2.36$ and extract BAO scales along and across the line of sight. The analysis models the cross-spectrum with biases and redshift-space distortions, incorporating a broadband distortion term to account for continuum-fitting systematics, and fits for the dilation parameters $\alpha_{\parallel}$ and $\alpha_{\perp}$. From these, the authors translate BAO measurements into $H(z)$ and $D_A(z)$ using a Planck-derived sound horizon $r_s$, finding $c/(H(z=2.36)\, r_s)=9.0\pm0.3$ and $D_A(z=2.36)/r_s=10.8\pm0.4$, corresponding to $H(z=2.36)=226\pm8\ \mathrm{km\ s^{-1}\ Mpc^{-1}}$ and $D_A(z=2.36)=1590\pm60\ \mathrm{Mpc}$. The work includes extensive systematic tests, covariance validation, and public release of the cross-correlation measurements and the baofit code, culminating in a robust high-$z$ BAO constraint that complements Ly$\alpha$ auto-correlation results and enables joint cosmological analyses.

Abstract

We measure the large-scale cross-correlation of quasars with the Lyman alpha forest absorption, using over 164,000 quasars from Data Release 11 of the SDSS-III Baryon Oscillation Spectroscopic Survey. We extend the previous study of roughly 60,000 quasars from Data Release 9 to larger separations, allowing a measurement of the Baryonic Acoustic Oscillation (BAO) scale along the line of sight $c/(H(z=2.36) ~ r_s) = 9.0 \pm 0.3$ and across the line of sight $D_A(z=2.36) / ~ r_s = 10.8 \pm 0.4$, consistent with CMB and other BAO data. Using the best fit value of the sound horizon from Planck data ($r_s=147.49 Mpc$), we can translate these results to a measurement of the Hubble parameter of $H(z=2.36) = 226 \pm 8 km/s / Mpc$ and of the angular diameter distance of $D_A(z=2.36) = 1590 \pm 60 Mpc$. The measured cross-correlation function and an update of the code to fit the BAO scale (baofit) are made publicly available.

Quasar-Lyman $α$ Forest Cross-Correlation from BOSS DR11 : Baryon Acoustic Oscillations

TL;DR

This study uses over 164,000 quasars from SDSS-III BOSS DR11 to measure the quasar-Ly cross-correlation at and extract BAO scales along and across the line of sight. The analysis models the cross-spectrum with biases and redshift-space distortions, incorporating a broadband distortion term to account for continuum-fitting systematics, and fits for the dilation parameters and . From these, the authors translate BAO measurements into and using a Planck-derived sound horizon , finding and , corresponding to and . The work includes extensive systematic tests, covariance validation, and public release of the cross-correlation measurements and the baofit code, culminating in a robust high- BAO constraint that complements Ly auto-correlation results and enables joint cosmological analyses.

Abstract

We measure the large-scale cross-correlation of quasars with the Lyman alpha forest absorption, using over 164,000 quasars from Data Release 11 of the SDSS-III Baryon Oscillation Spectroscopic Survey. We extend the previous study of roughly 60,000 quasars from Data Release 9 to larger separations, allowing a measurement of the Baryonic Acoustic Oscillation (BAO) scale along the line of sight and across the line of sight , consistent with CMB and other BAO data. Using the best fit value of the sound horizon from Planck data (), we can translate these results to a measurement of the Hubble parameter of and of the angular diameter distance of . The measured cross-correlation function and an update of the code to fit the BAO scale (baofit) are made publicly available.

Paper Structure

This paper contains 27 sections, 24 equations, 7 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Data Sample
  3. Quasar sample
  4. Ly$\alpha$ sample
  5. Independent sub-samples
  6. Cross-correlation
  7. Continuum fitting
  8. From flux to $\delta_F$
  9. Estimator and covariance matrix
  10. Measured cross-correlation
  11. Fitting the BAO Scale
  12. BAO model
  13. Theoretical model for the cross-correlation
  14. Quasar redshift errors
  15. Broadband distortion
  16. ...and 12 more sections

Figures (7)

  • Figure 1: Left panel: Redshift distribution of the 164,017 quasars used as density tracers (red in NGC, blue in SGC), and of the 130,825 quasars with Ly$\alpha$ spectra (green in NGC, purple in SGC). Right panel: DR11 footprint in J2000 equatorial coordinates with the 66 sub-samples indicated in different colors.
  • Figure 2: Left panel: Observed quasar-Ly$\alpha$ cross-correlation, $r^2 \xi(r_\parallel,r_\perp)$, as a function of line of sight ($r_\parallel$) and transverse ($r_\perp$) separations. Mid panel: Cosmological contribution to the best fit model (see next section). Right panel: contribution of the broadband distortion to the best fit model. The fit to the observed cross-correlation is the sum of the middle and right panels. As discussed in the text, the asymetric nature of the broadband distortion can be explained by the continuum fitting method.
  • Figure 3: $\Delta \chi^2$ as a function of $\alpha_\parallel$,$\alpha_\perp$ (defined in equation \ref{['eq:alpha']}) in our fiducial analysis, after marginalizing over the remaining 18 parameters. The solid contours correspond to $\Delta \chi^2=2.27$, $5.99$ and $11.62$, equivalent to Gaussian probabilities of $68\%$, $95\%$ and $99.7\%$. The fiducial model is consistent at the $\sim 1.5\sigma$ level.
  • Figure 4: Histogram of $\chi^2$ values for the different eigenmodes of the covariance matrix, compared to a zero-mean Gaussian with variance $(440-20)/440$, where 440 is the number of bins in the fit, and 20 is the number of free parameters. The agreement between the distributions supports the validity of our covariance matrix.
  • Figure 5: Transverse (left) and parallel (right) correlations, defined as $\xi(r,\mu=0)=\xi_0(r)-\xi_2(r)/2$ and $\xi(r,\mu=1)=\xi_0(r)+\xi_2(r)$, after projecting out the mode responsible for most of the correlation between separations. The best fit theory is shown in a solid black curve, its BAO-only part in a red dashed curve and the distortion in a dotted green curve. The orange dot-dashed curve shows the cosmological signal for our fiducial cosmology ($\alpha=1$), using a quasar bias of $b_q=3.64$ and a Ly$\alpha$ redshift-space distortion parameter $\beta_F=1.1$, as measured in 2013JCAP...05..018F. All datapoints and lines are weighted by $r^2$ and are plotted after the projection (see text for details).
  • ...and 2 more figures