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

Understand

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.