A Robust Estimator for the Lyman-α Forest 1D Power Spectrum at High Redshift
Abstract
The Lyman-α (Lyα) forest flux power spectrum P(k) is sensitive to a range of astrophysical and cosmological effects, including the thermal state of and large-scale fluctuations in the intergalactic medium and the nature of dark matter. Measuring P(k) becomes increasingly challenging at high redshift, where fewer quasar spectra are available and higher Lyα optical depths result in lower transmitted flux. In addition, observational effects and missing data complicate standard Fourier-transform estimators. Here, we validate a likelihood-based estimator for P(k). The method constructs the pixel-level covariance matrix of the transmitted flux field using precomputed k-space integrals that account for instrumental resolution and pixelization, enabling direct maximum-likelihood inference of P(k). We test the estimator using mock Lyα forest spectra at z ≥ 5, including analytic Gaussian realizations generated from known power spectra and forward-modeled simulation spectra incorporating observational effects relevant to high-redshift quasar surveys, such as finite spectral resolution, pixel sampling, noise, and missing data. We compare the recovered power spectra with both the input spectra and standard Fourier-transform estimates. We find that the likelihood-based estimator recovers the input power spectrum across the tested scales well within expected error and remains robust to the observational effects considered. This work establishes a framework for measuring Lyα forest clustering with a robust, nearly optimal power spectrum estimator, with particular focus on quantifying large-scale fluctuations that may arise from ultraviolet background fluctuations or the late stages of reionization.
Related
- Forecast for the detectability of patchy hydrogen reionization in WEAVE-QSO measurements of the Lyman-α forest power spectrum at redshift z ≥ 4
- Forecast for the detectability of patchy hydrogen reionization in WEAVE-QSO measurements of the Lyman-α forest power spectrum at redshift z ≥ 4
- Improving cosmological distance measurements at high redshift using Lyman-Alpha forest BAO reconstruction
- Lyman-α forest 1D flux power spectrum constraints on QSO-assisted reionization models
- Gravitational-wave constraints on H0 are robust to putative redshift evolution in the binary black hole mass spectrum at current sensitivity
BibTeX
@misc{wolfson2026robust,
title = {{A Robust Estimator for the Lyman-$α$ Forest 1D Power Spectrum at High Redshift}},
author = {Molly Wolfson and Joseph F. Hennawi and Frederick B. Davies and Zarija Lukić},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31626},
eprint = {2610.31626},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31626},
}
RIS
TY - UNPB
TI - A Robust Estimator for the Lyman-α Forest 1D Power Spectrum at High Redshift
AU - Molly Wolfson
AU - Joseph F. Hennawi
AU - Frederick B. Davies
AU - Zarija Lukić
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31626
UR - https://arxiv.org/abs/2610.31626
AB - The Lyman-α (Lyα) forest flux power spectrum P(k) is sensitive to a range of astrophysical and cosmological effects, including the thermal state of and large-scale fluctuations in the intergalactic medium and the nature of dark matter. Measuring P(k) becomes increasingly challenging at high redshift, where fewer quasar spectra are available and higher Lyα optical depths result in lower transmitted flux. In addition, observational effects and missing data complicate standard Fourier-transform estimators. Here, we validate a likelihood-based estimator for P(k). The method constructs the pixel-level covariance matrix of the transmitted flux field using precomputed k-space integrals that account for instrumental resolution and pixelization, enabling direct maximum-likelihood inference of P(k). We test the estimator using mock Lyα forest spectra at z ≥ 5, including analytic Gaussian realizations generated from known power spectra and forward-modeled simulation spectra incorporating observational effects relevant to high-redshift quasar surveys, such as finite spectral resolution, pixel sampling, noise, and missing data. We compare the recovered power spectra with both the input spectra and standard Fourier-transform estimates. We find that the likelihood-based estimator recovers the input power spectrum across the tested scales well within expected error and remains robust to the observational effects considered. This work establishes a framework for measuring Lyα forest clustering with a robust, nearly optimal power spectrum estimator, with particular focus on quantifying large-scale fluctuations that may arise from ultraviolet background fluctuations or the late stages of reionization.
ER -