DESI DR1 Lyα 1D power spectrum: The Fast Fourier Transform estimator measurement

TL;DR

We report a high-precision measurement of the one-dimensional Lyα forest power spectrum from DESI-DR1 using a Fast Fourier Transform estimator, with a data-driven cross-exposure noise approach and an explicit covariance framework. The analysis includes extensive instrumental characterization, robust data-splits tests, and a comprehensive systematic uncertainty budget, enabling a robust comparison with eBOSS and high-resolution results and providing a solid baseline for cosmological interpretation. A companion QMLE study is consistent with these FFT results, and together they constitute the most precise DR1 Lyα 1D power spectrum to date, informing constraints on small-scale matter fluctuations, neutrino masses, and dark matter models. Looking ahead, larger DESI data releases and cross-survey efforts with improved noise and masking techniques will further tighten cosmological inferences from $P_{1\mathrm{D},\alpha}$ on small scales.

Abstract

We present the one-dimensional Lyman-$α$ forest power spectrum measurement derived from the data release 1 (DR1) of the Dark Energy Spectroscopic Instrument (DESI). The measurement of the Lyman-$α$ forest power spectrum along the line of sight from high-redshift quasar spectra provides information on the shape of the linear matter power spectrum, neutrino masses, and the properties of dark matter. In this work, we use a Fast Fourier Transform (FFT)-based estimator, which is validated on synthetic data in a companion paper. Compared to the FFT measurement performed on the DESI early data release, we improve the noise characterization with a cross-exposure estimator and test the robustness of our measurement using various data splits. We also refine the estimation of the uncertainties and now present an estimator for the covariance matrix of the measurement. Furthermore, we compare our results to previous high-resolution and eBOSS measurements. In another companion paper, we present the same DR1 measurement using the Quadratic Maximum Likelihood Estimator (QMLE). These two measurements are consistent with each other and constitute the most precise one-dimensional power spectrum measurement to date, while being in good agreement with results from the DESI early data release.

Figures (16)

• Figure 1: Histogram of the quasar redshifts in the DR1 data release. All quasars with redshift $2.0 < z < 5.0$ are represented in blue. The distribution of Broad Absorption Line (BAL) quasars defined by the Absorption Index criterion ($AI >0$) appears in yellow, and the distribution of quasars with Balnicity Index criterion ($BI>0$) is in green. The distribution of quasars containing at least one detected Damped Ly$\alpha$ (DLA) object in their spectra is shown in red.
• Figure 2: (left) Average raw ($\left\langle P_{\mathrm{raw},s}(k) \right\rangle_{s \in z, k\in A}$) and noise ($\left\langle P_{\mathrm{noise},s}(k) \right\rangle_{s \in z, k\in A}$) power spectra for the DR1 dataset as a function of the wavenumber expressed in Å$^{-1}$. (right) Difference between raw and noise power spectra on the same dataset and resulting asymptotic difference $\alpha$.
• Figure 3: Comparison between the power spectrum without noise correction (UNCORR), the noise-corrected power spectrum corrected by subtracting the $\alpha$ term (CORR), and the power spectrum obtained with the cross-exposure estimator defined by equation \ref{['eq:crossexp']} (XEXP). The normalized one-dimensional power spectrum ($\Delta_{1\mathrm{D},\alpha}(k) = k P_{1\mathrm{D},\alpha}/\pi$) is shown on the top panel, and the ratio between them is shown on the two others. For this comparison, all $P_{1\mathrm{D},\alpha}$ have no corrections or metal power spectrum subtraction, and only DLA and atmospheric emission lines are masked. Only the first six redshift bins are shown for clarity. For the same reason, the error bar associated with only one redshift bin ($z=2.4$) is shown in the ratios comparing the three measurements.
• Figure 4: Ratios of the baseline power spectrum (BASE) to the power spectrum obtained from analysis variations. The baseline $P_{1\mathrm{D},\alpha}$ is the uncorrected power spectrum without metal subtraction. (left) Variation of the DLA treatment: without DLA masked in calculating $P_{1\mathrm{D},\alpha}$ (NOMASK) and with a high-purity catalog (PURITY). The level of failure in the PURITY test is well below the DLA completeness systematics associated with the final measurement in section \ref{['subsec:syst']} (right) Variation of BAL treatment. The baseline removes the BAL quasar spectra detected with the $BI > 0$ criterion. The variations considered are removing the BAL quasar spectra with the $AI > 0$ criterion (AICUT), not removing any quasars from the data set, and masking all BAL absorption with the $AI > 0$ criterion (AIMASK), and removing $BI$ BAL quasar and masking $AI$ BAL absorptions (BIC_AIM). The failure of the AICUT test shows that AI BAL significantly affect the baseline, motivating us to change the baseline.
• Figure 5: Ratios of the new baseline power spectrum (NEWBASE) with the AICUT BAL variation of figure \ref{['fig:dla_bal_splits']} for which all BAL quasars passing the $AI > 0$ criterion are removed. The new baseline removes $BI$ BAL quasars, masks $AI$ BAL absorption, and is corrected from the effect of masking with correction derived in KR25.