Semi-analytical covariance matrices for two-point correlation function for DESI 2024 data

Supplementary material to DESI's publication "Semi-analytical covariance matrices for two-point correlation function for DESI 2024 data" to comply with the data management plan.

In the paper, we present an optimized way of producing the fast semi-analytical covariance matrices for the Legendre moments of the two-point correlation function, taking into account survey geometry and mimicking the non-Gaussian effects. We validate the approach on simulated (mock) catalogs for different galaxy types, representative of the Dark Energy Spectroscopic Instrument (DESI) Data Release 1, used in 2024 analyses. We find only a few percent differences between the mock sample covariance matrix and our results, which can be expected given the approximate nature of the mocks, although we do identify discrepancies between the shot-noise properties of the DESI fiber assignment algorithm and the faster approximation (emulator) used in the mocks. Importantly, we find a close agreement (≤ 8% relative differences) in the projected errorbars for distance scale parameters for the baryon acoustic oscillation measurements. This confirms our method as an attractive alternative to simulation-based covariance matrices, especially for non-standard models or galaxy sample selections, making it particularly relevant to the broad current and future analyses of DESI data.

Important note: this version (2.0) of the supplementary material corresponds to the JCAP version of the article, or v3 and above on arXiv. Version 1.0 corresponds to arXiv v1 and v2.

Contents: ASDF files (reading instructions for Python). This format was chosen because it supports both nested dictionary-like structures and numpy arrays.

List and short descriptions:

• normalized_errorbars.asdf: data from Figures 3 and 4, projected errorbars for the BAO scales from each RascalC single-mock run, divided by those from the EZmock sample covariance. BAO model has been updated to use spline-based broadband terms, instead of polynomial in 1.0. This only resulted in minor differences.
• shot_noise_rescaling.asdf: source data for Tables 2 and 4, the shot-noise rescaling values for all the data and single-mock runs for different tracers, pre- and post-recon, SGC and NGC.
• shot_noise_rescaling_extra.asdf: source data for Table 3, the shot-noise rescaling values for all the data and a single realization of different mocks for LRG and ELG, pre-recon only, SGC and NGC. New in version 2.0.
• comparison_measures_RascalC_sample_cov.asdf: source data for Tables 5-10, the covariance matrix comparison measures computed between the (inverted) RascalC covariance from each single-mock run and the EZmock sample covariance, and perfect reference values for them. Includes different ranges for correlation function multipoles and projections to different cosmological parameters using an inverse Fisher matrix. BAO model has been updated to use spline-based broadband terms, instead of polynomial in 1.0. This only resulted in minor differences.
• measures_perfect_ref_samples.asdf: 10000 realizations of the covariance matrix comparison measures from multivariate normal samples with a known (unity) covariance matrix and different numbers of bins, to study the distribution of these quantities in the perfect case.
• measures_perfect_ref_stats.asdf: means and standard deviations of the covariance matrix comparison measures in the perfect case for 1000 samples and different numbers of bins. Each has three variants: empirical, theoretical and fiducial. Empirical are estimated using the samples saved in the previous file. Theoretical are calculated with formulas from https://arxiv.org/abs/2306.06320. Fiducial value is chosen between the previous two for each quantity's mean and std independently: the theoretical is preferred, unless the empirical estimate is at least 3 sigma different. The fiducial statistical properties have been used in the "Perfect" rows of Tables 5-10.