The effects of continuum fitting on Lyman-$α$ forest correlations

TL;DR

This work analyzes how continuum-fitting distortions impact Lyman-α forest correlations used to probe large-scale structure and BAO. It formalizes a distortion-matrix approach that projects physical, undistorted model correlations into the same distortions observed in data, enabling accurate parameter fits. Through extensive mock tests, the study demonstrates that the distortion matrix captures most of the continuum-fitting effects, preserving the BAO peak position to within percent-level accuracy, while identifying small residual biases in forest bias parameters. The results support current DESI analyses and outline concrete avenues for further refinement, such as extending the matrix and incorporating additional systematic effects, to further tighten cosmological constraints from Lyα data.

Abstract

Correlations of fluctuations of the flux in Lyman-$α$ forests of high-redshift quasars have been observed by the Baryonic Acoustic Oscillation Spectroscopy Survey (BOSS) and the Dark Energy Spectroscopy Instrument (DESI) survey where they have revealed the effects of baryon acoustic oscillations (BAO). In order to fit the correlation functions to a physical model and thereby constrain cosmological parameters, it is necessary to take into account the effects of fitting the observed spectra to a template about which the fluctuations are measured. In this paper we use mock spectra to test the distortion matrix technique that has been used since the final BOSS data release to appropriately distort the models. We show that while percent-level effects on the derived forest bias parameters may be present, the technique works sufficiently well that the determination of the BAO peak position is not affected at the percent level. We introduce modifications in the technique used by DESI that were not in the original applications and suggest further possibilities for improvements.

Figures (15)

• Figure 1: A high signal-to-noise DESI quasar spectrum as a function of observed wavelength. The black curve is the estimated continuum, $\overline{F}(z_\lambda) C_{q}(\lambda_{{\rm rest}})$, over the restframe wavelength range $1040<\lambda_{{\rm rest}}<1200\text{\normalfont\AA}$ used in this study.
• Figure 2: Two quasars and their forests. The measured correlation $\langle\delta^m_{q\lambda}\delta^{m}_{q^\prime\lambda^\prime}\rangle$ will have admixtures of all $\langle\delta^t_{q\lambda^{\prime\prime}}\delta^t_{q^\prime \lambda^{\prime\prime\prime}}\rangle$. If the intrinsic correlation $\langle\delta^t_{q\lambda}\delta^t_{q^\prime\lambda^\prime}\rangle$ is small, the measured correlations can be dominated by nearby pixels $(\lambda^{\prime\prime},\lambda^{\prime\prime\prime})$ as illustrated here.
• Figure 3: Comparison of true and measured auto-correlation functions for the stack of 10 completed-survey DESI mock data sets Herrera_2024. The left panel shows the true auto-correlation function, $\xi^t(r_\perp,r_\parallel)$ (multiplied by $r^2$ for better visualization), and the right panel shows the difference between the true auto-correlation and the measured auto-correlation, $\xi^m(r_\perp,r_\parallel)$. For small $r_\perp$ and large $r_\parallel$, the large positive values of the difference come about because the continuum fitting effectively subtracts a portion of the large positive values of $\xi^t$ at small $r$. For large $r_\perp$, the positive (negative) differences at small (large) $r_\parallel$ result from subtracting a portion of the neighboring positive (negative) correlations. The green lines show the lines $\mu=r_\parallel/r=0.95$, 0.8 and 0.5.
• Figure 4: The auto-correlation (top four panels) and the cross-correlation (bottom four panels) for the stack of 10 completed-survey DESI mock data sets Herrera_2024. The solid lines show the correlations of the projected measured field, $\delta^{mp}_{q\lambda}$, averaged over the $\mu$ range as labeled. The black dotted lines show the measured correlation of the projected true field, $\delta^{tp}_{q\lambda}$. The dashed lines show the correlations of the true field, $\delta^t_{q\lambda}$. The error bars are representative of the expected DESI results. For the cross-correlation, points with $\mu<0$ are plotted at $r<0$.
• Figure 5: The auto-correlation function for the stack of 10 completed-survey DESI mock data sets. The solid red lines show the correlations of the projected measured field, $\delta^{mp}_{q\lambda}$, averaged over the $\mu$ range as labeled. The dashed red lines show the measured correlation of the true field, $\delta^t_{q\lambda}$. The dotted black lines show the correlations of the true field corrected by the distortion matrix, $DM*\xi^{t}(z_0)$. The error bars are representative of the expected completed-survey DESI results.