Maximum A Posteriori Ly-alpha Estimator (MAPLE): Band-power and covariance estimation of the 3D Ly-alpha forest power spectrum

TL;DR

This paper introduces MAPLE, a new maximum a posteriori estimator that accurately reconstructs the 3D Ly-alpha forest power spectrum and its covariance, accounting for survey geometry and sampling density.

Contribution

The paper presents a novel Wiener-filter based algorithm, MAPLE, for joint estimation of band-powers and covariance of the 3D Ly-alpha forest power spectrum, adaptable to complex survey geometries.

Findings

Effective reconstruction of P3D in idealized tests

Handles complex survey geometries and sampling densities

Code is publicly available for community use

Abstract

We present a novel maximum a posteriori estimator to jointly estimate band-powers and the covariance of the three-dimensional power spectrum (P3D) of Lyman-alpha forest flux fluctuations, called MAPLE. Our Wiener-filter based algorithm reconstructs a window-deconvolved P3D in the presence of complex survey geometries typical for Lyman-alpha surveys that are sparsely sampled transverse to and densely sampled along the line-of-sight. We demonstrate our method on idealized Gaussian random fields with two selection functions: (i) a sparse sampling of 30 background sources per square degree designed to emulate the currently observing the Dark Energy Spectroscopic Instrument (DESI); (ii) a dense sampling of 900 background sources per square degree emulating the upcoming Prime Focus Spectrograph Galaxy Evolution Survey. Our proof-of-principle shows promise, especially since the algorithm can be extended to marginalize jointly over nuisance parameters and contaminants, i.e.offsets introduced by continuum fitting. Our code is implemented in JAX and is publicly available on GitHub.