Broadband distortion modeling in Lyman-$\alpha$ forest BAO fitting

In recent years, the Lyman-$\alpha$ 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-$\alpha$ 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-$\alpha$ forest spectrum. Implementing the distortion model in fits for the baryon acoustic oscillation (BAO) peak position in the Lyman-$\alpha$ 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 $\beta_{F}$ 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 $\beta_{F}$ and the combination $b_{F}(1+\beta_{F})$ by more than a factor of seven. The measured values at redshift $z=2.3$ are $\beta_{F}=1.39^{+0.11\ +0.24\ +0.38}_{-0.10\ -0.19\ -0.28}$ and $b_{F}(1+\beta_{F})=-0.374^{+0.007\ +0.013\ +0.020}_{-0.007\ -0.014\ -0.022}$ (1$\sigma$, 2$\sigma$ and 3$\sigma$ statistical errors). Our fitting software and the input files needed to reproduce our main results are publicly available.