Extensive analysis of reconstruction algorithms for DESI 2024 baryon acoustic oscillations

Abstract

Reconstruction of the baryon acoustic oscillation (BAO) signal has been a standard procedure in BAO analyses over the past decade and has helped to improve the BAO parameter precision by a factor of ~2 on average. The Dark Energy Spectroscopic Instrument (DESI) BAO analysis for the first year (DR1) data uses the ``standard'' reconstruction framework, in which the displacement field is estimated from the observed density field by solving the linearized continuity equation in redshift space, and galaxy and random positions are shifted in order to partially remove nonlinearities. There are several approaches to solving for the displacement field in real survey data, including the multigrid (MG), iterative Fast Fourier Transform (iFFT), and iterative Fast Fourier Transform particle (iFFTP) algorithms. In this work, we analyze these algorithms and compare them with various metrics including two-point statistics and the displacement itself using realistic DESI mocks. We focus on three representative DESI samples, the emission line galaxies (ELG), quasars (QSO), and the bright galaxy sample (BGS), which cover the extreme redshifts and number densities, and potential wide-angle effects. We conclude that the MG and iFFT algorithms agree within 0.4% in post-reconstruction power spectrum on BAO scales with the RecSym convention, which does not remove large-scale redshift space distortions (RSDs), in all three tracers. The RecSym convention appears to be less sensitive to displacement errors than the RecIso convention, which attempts to remove large-scale RSDs. However, iFFTP deviates from the first two; thus, we recommend against using iFFTP without further development. In addition, we provide the optimal settings for reconstruction for five years of DESI observation. The analyses presented in this work pave the way for DESI DR1 analysis as well as future BAO analyses.

Figures (35)

• Figure 1: Galaxy number density in the DESI AbacusSummit mocks with Y5 footprint as well as in the DESI DR1 data as a function of redshift for the selected DESI samples analyzed in this study. We use the entire BGS sample in $0.1<z<0.4$, ELG over $0.8<z<1.1$, and QSO over $1.6<z<2.1$. The BGS number density is lower than the actual DESI DR1 sample (not the DR1 sample used for BAO analysis plotted in this figure) because of the magnitude cut. The ELG distribution presented here overestimates the real DESI Y5 number densities.
• Figure 2: Convergence test for our choice of cell size with monopole (left) and quadrupole (right) power spectrum of the ELG sample for a grid resolution of 4 Mpc/$h$ (blue solid) and 6 Mpc/$h$ (cyan dashed), compared to a reference resolution at 2 Mpc/$h$ (red dash dotted). In the $y$-axis label, $P_{0,2{\rm Mpc}/h}$ and $P_{2,2{\rm Mpc}/h}$ are the monopole and quadrupole power spectra of the reference resolution, 2 Mpc/$h$. Each line here is one simulation. The deviation in the 4 Mpc/$h$ cell size is less than 0.2% for monopole and less than 1% for quadrupole, which are within our error budget.
• Figure 3: Reconstructed power spectrum monopole (left) and quadrupole (right) using the MG algorithm with number of randoms used being 10$\times$ (blue solid) and 5$\times$ (purple dashed) the number of galaxies in the field, compared to the 20$\times$ randoms baseline (red dash dotted). Each line here is an average of 25 simulations. The power spectra for the number of randoms at 10$\times$ and 20$\times$ are in agreement to better than 0.01% in monopole and 0.1% in quadrupole. Although the difference between 5$\times$ and 20$\times$ appears to be larger compared to the difference between 10$\times$ and 20$\times$, the magnitude of the difference is less than 0.13% in monopole and less than 0.6% in quadrupole.
• Figure 4: The distribution of displacement vector differences between MG and iFFT (3 iterations) displacements of the ELG sample using one mock. The displacement vectors are decomposed into along the line-of-sight $\boldsymbol{\hat{r}}$ and perpendicular to the line-of-sight directions (left), and the perpendicular to the line-of-sight direction is further decomposed into $\boldsymbol{\hat{\theta}}$ (middle) and $\boldsymbol{\hat{\phi}}$ (right) directions in spherical coordinates. Along the line of sight, the spread of the distribution is larger compared to perpendicular to the line of sight, indicating that the different ways of treating the redshift direction by the two algorithms result in more differences in the displacement in the redshift direction, but the magnitude of the differences is small even in the parallel direction compared to the average line-of-sight displacement of ELG ($\sim$1.9 Mpc/$h$). The two algorithms have less differences perpendicular to the line-of-sight, as shown in the middle and right panels with the component perpendicular to the line of sight further decomposed.
• Figure 5: Line-of-sight component of the displacement magnitude difference between MG and iFFT (3 iterations) (both applied with a 15 Mpc/$h$ smoothing) projected to DESI Y5 NGC footprint, shown for ELG$0.8<z<0.85$ (left), $0.9<z<0.95$ (middle) and $1.05<z<1.1$ (right) redshift slices. We show the sine of the declination such that the bins are uniform. The high redshift end shows slightly larger differences. Overall, the magnitude of differences whether on the redshift boundary or not is small compared to the average line-of-sight displacement magnitude of ELG ($\sim$ 1.9 Mpc/$h$). There also does not appear to be larger differences clustered along survey boundaries.