Abstract
Abstract We present a novel, fast method to recover the density field through the statistics of the transmitted flux in high-redshift quasar absorption spectra. The proposed technique requires the computation of the probability distribution function of the transmitted flux (PF) in the Lyαforest region and, as a sole assumption, the knowledge of the probability distribution function of the matter density field (PΔ). We show that the probability density conservation of the flux and matter density unveils a flux–density (F–Δ) relation which can be used to invert the Lyαforest without any assumption on the physical properties of the intergalactic medium. We test our inversion method atz= 3through the following steps: (i) simulation of a sample of synthetic spectra for whichPΔis known; (ii) computation ofPF; and (iii) inversion of the Lyαforest through theF–Δrelation. Our technique, when applied to only 10 observed spectra characterized by a signal-to-noise ratio≥100, provides an exquisite (relative errorεΔ≲ 12per cent in≳50 per cent of the pixels) reconstruction of the density field in≳90 per cent of the line of sight. We finally discuss strengths and limitations of the method.
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