How to estimate the 3D power spectrum of the Lyman-$\alpha$ forest

Abstract

We derive and numerically implement an algorithm for estimating the 3D power spectrum of the Lyman-$\alpha$ (Ly-$\alpha$) forest flux fluctuations. The algorithm exploits the unique geometry of Ly-$\alpha$ forest data to efficiently measure the cross-spectrum between lines of sight as a function of parallel wavenumber, transverse separation and redshift. The key to fast evaluation is to approximate the global covariance matrix as block-diagonal, where only pixels from the same spectrum are correlated. We then compute the eigenvectors of the derivative of the signal covariance with respect to cross-spectrum parameters, and project the inverse-covariance-weighted spectra onto them. This acts much like a radial Fourier transform over redshift windows. The resulting cross-spectrum inference is then converted into our final product, an approximation of the likelihood for the 3D power spectrum expressed as second order Taylor expansion around a fiducial model. We demonstrate the accuracy and scalability of the algorithm and comment on possible extensions. Our algorithm will allow efficient analysis of the upcoming Dark Energy Spectroscopic Instrument dataset.

29 pages, many figures. Minor changes in v2, accepted in JCAP

References in corpus (3)

• Cosmological Constraints from the SDSS Luminous Red Galaxies
• Baryon Acoustic Oscillations in the Lyα forest of BOSS DR11 quasars
• Baryon Acoustic Oscillations in the Ly-α forest of BOSS quasars

Cited by in corpus (20)

• DESI 2024 IV: Baryon Acoustic Oscillations from the Lyman Alpha Forest
• Optimal 1D Ly$\alpha$ Forest Power Spectrum Estimation -- II. KODIAQ, SQUAD & XQ-100
• Second Data Release of the COSMOS Lyman-alpha Mapping and Tomographic Observation: The First 3D Maps of the Detailed Cosmic Web at 2.05<z<2.55
• Simulating intergalactic gas for DESI-like small scale Lymanα forest observations
• Optimal 1D Ly-$\alpha$ Forest Power Spectrum Estimation I: DESI-Lite Spectra
• Impact of inhomogeneous reionization on the Lyman-α forest
• The 3D Lyman-$\alpha$ Forest Power Spectrum from eBOSS DR16
• The Ly$\alpha$ forest flux correlation function: a perturbation theory perspective
• Non-linearities in the Lyman-$\alpha$ forest and in its cross-correlation with dark matter halos
• Modeling the Lyman-$\alpha$ forest with Eulerian and SPH hydrodynamical methods
• A neural network emulator for the Lyman-$\alpha$ 1D flux power spectrum
• The ACCEL2 Project: Precision Measurements of EFT Parameters and BAO Peak Shifts for the Lyman-$\alpha$ Forest
• Measurement of the small-scale 3D Lyman-$\alpha$ forest power spectrum
• Planting a Lyman alpha forest on AbacusSummit
• The Compressed 3D Lyman-Alpha Forest Bispectrum
• ForestFlow: predicting the Lyman-$\alpha$ forest clustering from linear to nonlinear scales
• Modeling the Cosmological Lyman-$\alpha$ Forest at the Field Level
• Unified reconstruction of the Lyman-alpha power spectrum with Hamiltonian Monte Carlo
• Probing dark energy using anisotropies in the clustering of post-EoR HI distribution
• Bridging Simulations and EFT: A Hybrid Model of the Lyman-Alpha Forest Field