Broadband distortion modeling in Lyman-$α$ forest BAO fitting

In recent years, the Lyman-$α$ absorption observed in the spectra of high-redshift quasars has been used as a tracer of large-scale structure by means of the three-dimensional Lyman-$α$ forest auto-correlation function at redshift $z\simeq 2.3$, but the need to fit the quasar continuum in every absorption spectrum introduces a broadband distortion that is difficult to correct and causes a systematic error for measuring any broadband properties. We describe a $k$-space model for this broadband distortion based on a multiplicative correction to the power spectrum of the transmitted flux fraction that suppresses power on scales corresponding to the typical length of a Lyman-$α$ forest spectrum. Implementing the distortion model in fits for the baryon acoustic oscillation (BAO) peak position in the Lyman-$α$ forest auto-correlation, we find that the fitting method recovers the input values of the linear bias parameter $b_{F}$ and the redshift-space distortion parameter $β_{F}$ for mock data sets with a systematic error of less than 0.5\%. Applied to the auto-correlation measured for BOSS Data Release 11, our method improves on the previous treatment of broadband distortions in BAO fitting by providing a better fit to the data using fewer parameters and reducing the statistical errors on $β_{F}$ and the combination $b_{F}(1+β_{F})$ by more than a factor of seven. The measured values at redshift $z=2.3$ are $β_{F}=1.39^{+0.11\ +0.24\ +0.38}_{-0.10\ -0.19\ -0.28}$ and $b_{F}(1+β_{F})=-0.374^{+0.007\ +0.013\ +0.020}_{-0.007\ -0.014\ -0.022}$ (1$σ$, 2$σ$ and 3$σ$ statistical errors). Our fitting software and the input files needed to reproduce our main results are publicly available.

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