DESI DR1 Ly$α$ 1D power spectrum: Validation of estimators

TL;DR

This work validates the DESI DR1 Lyalpha forest $P_{1D}$ measurement by employing two estimators—the optimal quadratic maximum likelihood estimator and the FFT estimator—across comprehensive synthetic data and 675,000 CCD simulations. It develops and tests bias corrections for continuum fitting and masking, and introduces a robust, hybrid covariance approach that combines Gaussian and bootstrap estimates. The study demonstrates percent-level accuracy for the $P_{1D}$ measurements, quantifies spectrograph-resolution systematics, and provides detailed prescriptions for masking corrections and their multiplicativity. The findings establish a reliable end-to-end framework for small-scale Lyalpha cosmology with DESI, while highlighting future pathways to refine mocks, model HCDs/BALs, and achieve even tighter cosmological inferences.

Abstract

The Data Release 1 (DR1) of the Dark Energy Spectroscopic Instrument (DESI) is the largest sample to date for small-scale Ly$α$ forest cosmology, accessed through its one-dimensional power spectrum ($P_{\mathrm{1D}}$). The Ly$α$ forest $P_{\mathrm{1D}}$ is extracted from quasar spectra that are highly inhomogeneous (both in wavelength and between quasars) in noise properties due to intrinsic properties of the quasar, atmospheric and astrophysical contamination, and also sensitive to low-level details of the spectral extraction pipeline. We employ two estimators in DR1 analysis to measure $P_{\mathrm{1D}}$: the optimal estimator and the fast Fourier transform (FFT) estimator. To ensure robustness of our DR1 measurements, we validate these two power spectrum and covariance matrix estimation methodologies against the challenging aspects of the data. First, using a set of 20 synthetic 1D realizations of DR1, we derive the masking bias corrections needed for the FFT estimator and the continuum fitting bias needed for both estimators. We demonstrate that both estimators, including their covariances, are unbiased with these corrections using the Kolmogorov-Smirnov test. Second, we substantially extend our previous suite of CCD image simulations to include 675,000 quasars, allowing us to accurately quantify the pipeline's performance. This set of simulations reveals biases at the highest $k$ values, corresponding to a resolution error of a few percent. We base the resolution systematics error budget of DR1 $P_{\mathrm{1D}}$ on these values, but do not derive corrections from them since the simulation fidelity is insufficient for precise corrections.

Figures (12)

• Figure 1: ( Left) The average percent error and scatter in the generated mock $r$-band flux values binned in redshift. We achieve a good match at $z_\mathrm{qso} < 4$, which constitutes the majority of the DR1 quasar sample. ( Right) SNR with respect to observed wavelength. We achieve a good agreement between the data ( blue) and the mocks ( orange). Solid lines represent the median, and the area between the 32nd and 68th percentiles is shaded.
• Figure 2: The difference matrices $\Delta \mathbf{R}$ at three stages of the optimal estimator's regularization scheme. The redshift increases from left (top) to right (bottom) in each panel. The initial estimate shown in the left panel has strong off-diagonal terms in the first few redshift bins and has significant noise at higher redshifts. The middle panel shows the 2D smoothed difference matrix $\widetilde{\Delta \mathbf{R}}$ in which the noise is largely suppressed. The right panel shows the difference for the final bootstrap estimate after it is forced to be larger than the Gaussian covariance matrix.
• Figure 3: ( Left) PDF of $\chi^2-$squared values for the no-systematics case from the optimal estimator. The Gaussian covariance matrix fails the KS test by yielding a p-value of 0.03, while the bootstrap covariance matrix passes it by yielding a p-value of 0.64. ( Right) The ratio between the estimated $P_{\mathrm{1D}}$ from the stack of 20 mock realizations and the true power minus one. The ratios are shifted vertically for clarity. Dashed lines indicate the expected value of zero for each redshift bin. The area within 1% of the expected value is shaded. The fluctuations are between $0.5\%$ and $1\%$ for $z\leq 3.6$. Higher redshifts fluctuate more, so they are not shown for clarity.
• Figure 4: Fitted linear relation for $b(k)$ for redshifts bins with over 3$\sigma$ detection significance for the optimal estimator. The solid lines are derived from fully contaminated mocks, and the dashed lines are derived from uncontaminated mocks. The $b(k)$ values for the contaminated mocks are larger than those for the uncontaminated case for all redshifts except $z=3.8$. The difference arises from the continuum-fitting response to the underlying large-scale density field and the survey window function.
• Figure 5: The relative difference between the power spectrum from mock transmissions ($P_\mathrm{trans}$) and the input power spectrum ($P_\mathrm{input}$) for the FFT estimator. The highest three redshift bins yield large error bars and are omitted for clarity. We find that the conversion between wavelength and velocity units introduces small biases at $k \leq 1~$Å$^{-1}$ across all redshift bins as the small separations assumption gradually breaks down.