Constraints on the Thompson optical depth to the CMB from the Lyman-$α$ forest

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Main Authors: Garcia-Gallego, Olga, Iršič, Vid, Haehnelt, Martin G., Bolton, James S.
Format: Preprint
Published: 2025
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author Garcia-Gallego, Olga
Iršič, Vid
Haehnelt, Martin G.
Bolton, James S.
author_facet Garcia-Gallego, Olga
Iršič, Vid
Haehnelt, Martin G.
Bolton, James S.
contents We present the first constraints on the electron optical depth to reionization, $τ_{\mathrm{e}}$, from the Lyman-$α$ forest alone for physically motivated reionization models that match the reionization's end-point, $z_{\rm{end}}$, required by the same astrophysical probe, and for symmetric reionization models with fixed duration, $Δz$, commonly adopted in CMB reionization analyses. Compared to traditional estimates from the latter, the Lyman-$α$ forest traces the ionization state of the IGM through its coupling with the thermal state. We find an explicit mapping between the two solving the chemistry and temperature evolution equations for hydrogen and helium. Our results yield $τ_{\mathrm{e}}$=$0.042^{+0.047}_{-0.02}$ (95% C.L) and $τ_{\mathrm{e}}$=$0.042^{+0.024}_{-0.015}$ for reionization models with $z_{\rm{end}}$ and $Δz$-fixed, respectively, disfavoring a high $τ_{\mathrm{e}}$=0.09 by 2.57$σ$ and 4.31$σ$. With mock Lyman-$α$ forest data that mimics the precision of future larger quasar sample datasets, we would potentially obtain tighter $τ_{\mathrm{e}}$ constraints and exclude such a high $τ_{\mathrm{e}}$ with a higher significance, paving the way for novel constraints on the epoch of reionization from a large-scale structure probe independent of the CMB.
format Preprint
id arxiv_https___arxiv_org_abs_2510_00107
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Constraints on the Thompson optical depth to the CMB from the Lyman-$α$ forest
Garcia-Gallego, Olga
Iršič, Vid
Haehnelt, Martin G.
Bolton, James S.
Cosmology and Nongalactic Astrophysics
High Energy Physics - Phenomenology
High Energy Physics - Theory
We present the first constraints on the electron optical depth to reionization, $τ_{\mathrm{e}}$, from the Lyman-$α$ forest alone for physically motivated reionization models that match the reionization's end-point, $z_{\rm{end}}$, required by the same astrophysical probe, and for symmetric reionization models with fixed duration, $Δz$, commonly adopted in CMB reionization analyses. Compared to traditional estimates from the latter, the Lyman-$α$ forest traces the ionization state of the IGM through its coupling with the thermal state. We find an explicit mapping between the two solving the chemistry and temperature evolution equations for hydrogen and helium. Our results yield $τ_{\mathrm{e}}$=$0.042^{+0.047}_{-0.02}$ (95% C.L) and $τ_{\mathrm{e}}$=$0.042^{+0.024}_{-0.015}$ for reionization models with $z_{\rm{end}}$ and $Δz$-fixed, respectively, disfavoring a high $τ_{\mathrm{e}}$=0.09 by 2.57$σ$ and 4.31$σ$. With mock Lyman-$α$ forest data that mimics the precision of future larger quasar sample datasets, we would potentially obtain tighter $τ_{\mathrm{e}}$ constraints and exclude such a high $τ_{\mathrm{e}}$ with a higher significance, paving the way for novel constraints on the epoch of reionization from a large-scale structure probe independent of the CMB.
title Constraints on the Thompson optical depth to the CMB from the Lyman-$α$ forest
topic Cosmology and Nongalactic Astrophysics
High Energy Physics - Phenomenology
High Energy Physics - Theory
url https://arxiv.org/abs/2510.00107