The Lyman-alpha Forest Power Spectrum from the Sloan Digital Sky Survey

TL;DR

This work delivers a high-precision measurement of the Lyα forest flux power spectrum $P_F(k,z)$ from about 3000 SDSS quasars, exploiting an extensive data set to achieve percent-level statistical errors. The authors develop a meticulous analysis pipeline, including reprocessing of spectra, per-spectrum noise calibration, and robust background subtraction to remove metal contamination, notably incorporating SiIII–Lyα cross-correlation into the modeling. They validate their approach with realistic mock spectra and bootstrap error estimates, quantify and correct a small bias due to mean normalization, and perform extensive consistency checks across subsamples and alternative procedures. The resulting $P_F(k,z)$, with a full error and covariance structure, provides a stringent observational input for modeling of the intergalactic medium and for constraining cosmological parameters, with a plan to present the cosmological interpretation in a companion paper. The analysis highlights the importance of controlling systematics—especially metal Background, noise calibration, and spectral resolution—for high-precision Lyα forest studies.

Abstract

We measure the power spectrum, P_F(k,z), of the transmitted flux in the Ly-alpha forest using 3035 high redshift quasar spectra from the Sloan Digital Sky Survey. This sample is almost two orders of magnitude larger than any previously available data set, yielding statistical errors of ~0.6% and ~0.005 on, respectively, the overall amplitude and logarithmic slope of P_F(k,z). This unprecedented statistical power requires a correspondingly careful analysis of the data and of possible systematic contaminations in it. For this purpose we reanalyze the raw spectra to make use of information not preserved by the standard pipeline. We investigate the details of the noise in the data, resolution of the spectrograph, sky subtraction, quasar continuum, and metal absorption. We find that background sources such as metals contribute significantly to the total power and have to be subtracted properly. We also find clear evidence for SiIII correlations with the Ly-alpha forest and suggest a simple model to account for this contribution to the power. While it is likely that our newly developed analysis technique does not eliminate all systematic errors in the P_F(k,z) measurement below the level of the statistical errors, our tests indicate that any residual systematics in the analysis are unlikely to affect the inference of cosmological parameters from P_F(k,z). These results should provide an essential ingredient for all future attempts to constrain modeling of structure formation, cosmological parameters, and theories for the origin of primordial fluctuations.

Figures (39)

• Figure 1: The distribution of the spectral pixels used to probe the Ly$\alpha$ forest (black, solid histogram; scale on left axis), and the redshift distribution of our primary sample of 3035 quasars (red, dotted histogram; right axis). Note the gap at $z\sim 2.7$ in the quasar redshift distribution, caused by a class of stars being indistinguishable from quasars in the SDSS photometry 2002AJ....123.2945R.
• Figure 2: Example spectrum of a $z=3.7$ quasar with unusually high S/N. The regions we use to measure the Ly$\alpha$ forest power and background power are indicated by vertical dotted lines, along with a couple of alternate regions that we will discuss (note that the background and Ly$\alpha$ forest observed in the same quasar spectrum correspond to different redshifts).
• Figure 3: Examples of the chunks of spectra used to measure power, with (a,b) showing quasars at $z_q=$(3.24,2.45) over the rest wavelength range $1113~{\rm \AA}<\lambda_{{\rm rest}}<1185$ Å, and (c) showing a quasar at $z_q=3.30$ over the rest wavelength range $1041~{\rm \AA}<\lambda_{{\rm rest}}< 1113$ Å. Top panel: quasar flux (solid black line), sky flux (dotted blue line), our continuum estimate (red short-dashed line), and the read-noise as an equivalent photon flux (green long-dashed line). Middle panel: S/N level shown as a ratio of our continuum to the different rms noise levels (see text), $\sigma_w$ (black solid line), $\sigma_p$, (blue dotted line), and $\sigma_c$ (red dashed line). Bottom panel: Calibration correction vector, $\bar{S}$ (blue dotted line), rms resolution in units of 100 km/s (red dashed line), and evolution of the mean transmission fraction, $\bar{F}(z)$ (black solid line). The perfect degeneracy in our analysis between the overall normalization of the continuum and $\bar{F}(z)$ has been broken arbitrarily, so only the evolution of $\bar{F}(z)$ is meaningful (see text).
• Figure 4: The points show the measured power in difference spectra, created by subtracting separate exposures for the same quasar. Noise power has been subtracted based on the standard pipeline noise estimates for each exposure. The lines show 16% of the subtracted noise term. The different colors, lines, and symbols identify redshift bins, in a pattern that we will use repeatedly throughout the paper. From bottom to top --- z=2.2: black, solid line, open square; z=2.4: blue, dotted line, 4-point star (cross); z=2.6: cyan, dashed line, filled square; z=2.8: green, long-dashed line, open triangle; z=3.0: magenta, dot-dashed line, 3-point star; z=3.2: red, dot-long-dashed line, filled triangle; z=3.4: black, thin solid line, open pentagon; z=3.6: blue, thin dotted line, 5-point star; z=3.8: cyan, thin dashed line, filled pentagon. The different redshifts have been shifted vertically by arbitrary amounts on this logarithmic plot.
• Figure 5: Resolution test. The solid, black line with error bars shows the power measured in $\sim 3000$ sky spectra in the range $5560{\rm \AA}< \lambda<5598$Å (dominated by the strong sky line at 5577Å) divided by the asymptotic small $k$ power and by the estimated resolution/pixelization kernel $W^2(k)$ for each spectrum. If the resolution estimate was perfect, and the sky line was narrow and the only flux present, this division would give exactly 1. The large error bars are the spectrum-to-spectrum variation, the small ones are the error on the mean. The blue, long-dashed line shows the power not divided by $W^2(k)$, i.e., basically an averaged version of $W^2(k)$, which drops to $\sim 0.25$ by $k=0.02(\, {\rm km\, s}^{-1})^{-1}$. The red, dotted line shows the result of our test for mock spectra constructed with a Gaussian at 5579Å and two more at 5566 and 5591 Å with 0.003 times its amplitude, representing OH lines. The green, short-dashed line shows $\exp[(k~7\, {\rm km\, s}^{-1})^2]$. The vertical, cyan, dotted lines bound the $k$ region in which we will present Ly$\alpha$ forest results, while the horizontal, cyan, dotted line just guides the eye to 1.