Reconstructing the gravitational lensing potential from the Lyman-α forest

¹ Dipartimento di Fisica & Astronomia, Università di Bologna, via Gobetti 93/2, 40129 Bologna, Italy
e-mail: robertbenton.metcalf@unibo.it
² INAF-Osservatorio Astronomico di Bologna, via Ranzani 1, 40127 Bologna, Italy
³ Jodrell Bank Centre for Astrophysics, University of Manchester, Alan Turing Building, Oxford Road, Manchester M13 9PL, UK
⁴ McWilliams Center for Cosmology, Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA

Received: 30 March 2020
Accepted: 17 May 2020

Abstract

We demonstrate a method for reconstructing the weak lensing potential from the Lyman-α forest data. We derive an optimal estimator for the lensing potential on the sky based on the correlation between pixels in real space. This method effectively deals with irregularly spaced data, holes in the survey, missing data, and inhomogeneous noise. We demonstrate an implementation of the method with simulated spectra and weak lensing. It is shown that with a source density of ≳0.5 per square arcmin and ∼200 pixels in each spectrum (λ/Δλ = 1300) the lensing potential can be reconstructed with high fidelity if the relative absorption in the spectral pixels is signal dominated. When noise dominates the measurement of the absorption in each pixel the noise in the lensing potential is higher, but for reasonable numbers of sources and noise levels and a high fidelity map the lensing potential is obtainable. The lensing estimator could also be applied to lensing of the cosmic microwave background, 21 cm intensity mapping, or any case in which the correlation function of the source can be accurately estimated.