Fitting Methods for Baryon Acoustic Oscillations in the Lyman-α Forest Fluctuations in BOSS Data Release 9

TL;DR

This paper develops and tests near-optimal, three-dimensional fitting methods to extract BAO information from the Lyman-$\alpha$ forest in SDSS-III BOSS DR9. It builds a comprehensive model that combines linear theory with redshift-space distortions, anisotropic non-linear broadening, and broadband distortions, and introduces independent line-of-sight and transverse BAO scale factors to measure $\alpha_{\parallel}$ and $\alpha_{\perp}$. A localized, CAMB-based peak model plus a robust broadband distortion framework enable BAO extraction while controlling systematics, with internal covariance validation and data-reduction techniques to distill cosmological information. The work provides publicly available fitting software and inputs, confirming BAO measurements at $z\sim2.4$ and setting the stage for future, larger DR samples to tighten cosmological constraints.

Abstract

We describe fitting methods developed to analyze fluctuations in the Lyman-α forest and measure the parameters of baryon acoustic oscillations (BAO). We apply our methods to BOSS Data Release 9. Our method is based on models of the three-dimensional correlation function in physical coordinate space, and includes the effects of redshift-space distortions, anisotropic non-linear broadening, and broadband distortions. We allow for independent scale factors along and perpendicular to the line of sight to minimize the dependence on our assumed fiducial cosmology and to obtain separate measurements of the BAO angular and relative velocity scales. Our fitting software and the input files needed to reproduce our main BOSS Data Release 9 results are publicly available.

Figures (26)

• Figure 1: Physical coordinates for pixel pairs with observed Lyman-$\alpha$ absorption wavelengths $\lambda_i \le \lambda_j$. Grid lines of $z_{ij}$ (vertical blue, values left to right are 2.25, 2.75, 3.25), $\Delta v_{ij}/c$ (horizontal red, values bottom to top cover 0.001--0.049 with 0.002 spacing, with additional contours at 0, 0.059, and 0.083) represent the nominal sampling grid used in a fit. The shaded gray region shows the pixel pairs contributing to a typical BAO fit, bounded by $\lambda_1 > 3600$ Å , $r_{\parallel} < 170$ Mpc/h, and $z_{ij} < 3.25$. Contours of $\Delta\theta$ (thick black curves) at which the 3D separation is 110 Mpc/h (values from bottom left corner out are 100, 80, 60, 40, 20, 0 arcmins) identify pixel pairs contributing to the BAO peak region at different angular separations.
• Figure 2: Cosmological linear models calculated for $z_0 = 2.25$ and assuming a flat universe with $\Omega_\Lambda = 0.73$, $h = 0.7$, $\Omega_{\text{b}} h^2 = 0.0227$, and $n_s = 0.97$. Panels show the ($k$-weighted) power spectrum (top-left) and the ($r^2$-weighted) correlation function monopole (top-right), quadrupole (bottom-left), and hexadecapole (bottom-right). Curves are calculated with CAMB 2000ApJ...538..473L (thick,red) and using ref. 1998ApJ...496..605E (light,blue) with solid curves showing the full cosmological model and dotted (dashed) curves showing the corresponding CAMB "sideband" ("no-wiggles" of ref. 1998ApJ...496..605E) smooth model.
• Figure 3: Cosmological peak models calculated using the CAMB "sideband" method described in the text (left, red) and the "no-wiggles" method of ref. 1998ApJ...496..605E (right, blue) described in the text. Curves show $\mu =$ 0.4 (solid), 0.7 (dashed), and 1.0 (dotted). There is no $r^2$ weighting applied here.
• Figure 4: Evolution of the peak position with $\mu$ for the cosmological peak models shown in Figure \ref{['fig:mu-slices']}. Curves show $\beta =$ 1.0 (solid), 1.4 (dashed), and 1.8 (dotted). Fractional shifts are measured relative to the position of the monopole peak for each model.
• Figure 5: Effects of anisotropic non-linear broadening implemented with eqn. (\ref{['eqn:nl-broadening-defn']}) and applied to $z_0 = 2.25$ linear CAMB predictions 2000ApJ...538..473L using $\Sigma_{\parallel} = 6.41$ Mpc/h and $\Sigma_{\perp} = 3.26$ Mpc/h. Curves show no broadening (thick red, same as curves in Figure \ref{['fig:cosmo-models']}), isotropic broadening (dotted red) by $(\Sigma_{\parallel}^2+\Sigma_{\perp}^2)^{1/2}/2 = 5.09$ Mpc/h, the approximate anisotropic model described in the text (dashed blue) with $\beta_0 = 1.4$, and the envelope of full anisotropic calculations (light blue shaded) for $\beta =$ 0.5--2.5. Left-hand panels show the $k$-weighted multipoles $P_{\ell,NL}(k,z_0)$ with $b^2 C_{\ell}(\beta)$ divided out, for $\ell = 0$ (top), $\ell = 2$ (middle), and $\ell = 4$ (bottom). Right-hand panels show the corresponding $r^2$-weighted correlation function multipoles $\xi_{\ell}(r,z_0)$.