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The impact of the IGM thermal state on the Ly$\alpha$ flux 3D power spectrum from linear to highly non-linear scales
Cosmology and Nongalactic Astrophysics · Submitted 25 Aug 2026
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our results demonstrate that numerical effects can be comparable to, or exceed, the relic astrophysical signatures encoded in $P_{\rm 3D,\alpha}$, making numerical convergence essential for interpreting precise Ly$\alpha$ forest measurements.
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Recently initiated and upcoming spectroscopic surveys, such as DESI and WST, will provide more than $10^6$ high-$z$ quasar spectra, enabling dense sky coverage by the Ly$\alpha$ forest. This is expected to establish the three-dimensional (3D) Ly$\alpha$ forest power spectrum, $P_{\rm 3D,\alpha}$, as a probe of the thermal and ionization history of the intergalactic medium (IGM). To exploit this opportunity, we quantify the imprints of reionization on the post-reionization IGM using high-fidelity numerical models. We use the Sherwood and Sherwood-Relics cosmological hydrodynamical simulations with box sizes up to $160\,h^{-1}\,\rm cMpc$ to investigate the impact of box size, mass resolution, and extracted grid resolution on $P_{\rm 3D,\alpha}$ over $2.4\leq z\leq4.8$. After applying a Zel'dovich control variate correction, simulation volume has a modest impact over most scales and orientations, whereas degrading the mass resolution produces differences of up to $\sim13\%$. Insufficient resolution of the grid used for the optical-depth calculation can artificially enhance small-scale power by up to $\sim35\%$. The timing of $\mathrm{H\,I}$ reionization leaves only a percent-level imprint on $P_{\rm 3D,\alpha}$ at $z=2.4$, whereas varying the photoheating rate by a factor of two changes the large-scale power by $\sim4-8\%$. Our results demonstrate that numerical effects can be comparable to, or exceed, the relic astrophysical signatures encoded in $P_{\rm 3D,\alpha}$, making numerical convergence essential for interpreting precise Ly$\alpha$ forest measurements. The strongest astrophysical imprint arises from spatially inhomogeneous $\mathrm{H\,I}$ reionization, which enhances the large-scale power by up to $\sim70\%$ at $z=4.2$. This highlights the potential of post-reionization Ly$\alpha$ forest measurements as a probe of the thermal history and spatial morphology of cosmic reionization.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Recently initiated and upcoming spectroscopic surveys, such as DESI and WST, will provide more than $10^6$ high-$z$ quasar spectra, enabling dense sky coverage by the Ly$\alpha$ forest. | background 1.00 | 0.04 | 0.02 | asserted 0.89 |
| s1 | This is expected to establish the three-dimensional (3D) Ly$\alpha$ forest power spectrum, $P_{\rm 3D,\alpha}$, as a probe of the thermal and ionization history of the intergalactic medium (IGM). | background 0.98 | 0.06 | 0.04 | hedged possibility 0.92 |
| s2 | To exploit this opportunity, we quantify the imprints of reionization on the post-reionization IGM using high-fidelity numerical models. | contribution 0.90 | 0.82 | 0.03 | asserted 0.95 |
| s3 | We use the Sherwood and Sherwood-Relics cosmological hydrodynamical simulations with box sizes up to $160\,h^{-1}\,\rm cMpc$ to investigate the impact of box size, mass resolution, and extracted grid resolution on $P_{\rm 3D,\alpha}$ over $2.4\leq z\leq4.8$. | method 0.98 | 0.90 | 0.03 | asserted 0.97 |
| s4 | After applying a Zel'dovich control variate correction, simulation volume has a modest impact over most scales and orientations, whereas degrading the mass resolution produces differences of up to $\sim13\%$. | result 1.00 | 0.95 | 0.07 | asserted 1.00 |
| s5 | Insufficient resolution of the grid used for the optical-depth calculation can artificially enhance small-scale power by up to $\sim35\%$. | result 1.00 | 0.89 | 0.06 | asserted 0.84 |
| s6 | The timing of $\mathrm{H\,I}$ reionization leaves only a percent-level imprint on $P_{\rm 3D,\alpha}$ at $z=2.4$, whereas varying the photoheating rate by a factor of two changes the large-scale power by $\sim4-8\%$. | result 1.00 | 0.91 | 0.06 | asserted 1.00 |
| s7 | Our results demonstrate that numerical effects can be comparable to, or exceed, the relic astrophysical signatures encoded in $P_{\rm 3D,\alpha}$, making numerical convergence essential for interpreting precise Ly$\alpha$ forest measurements. | interpretation 0.92 | 0.91 | 0.74 | asserted 1.00 |
| s8 | The strongest astrophysical imprint arises from spatially inhomogeneous $\mathrm{H\,I}$ reionization, which enhances the large-scale power by up to $\sim70\%$ at $z=4.2$. | result 1.00 | 0.89 | 0.18 | asserted 1.00 |
| s9 | This highlights the potential of post-reionization Ly$\alpha$ forest measurements as a probe of the thermal history and spatial morphology of cosmic reionization. | interpretation 1.00 | 0.53 | 0.17 | hedged possibility 0.79 |
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The paper
Original abstract
Recently initiated and upcoming spectroscopic surveys, such as DESI and WST, will provide more than $10^6$ high-$z$ quasar spectra, enabling dense sky coverage by the Ly$\alpha$ forest. This is expected to establish the three-dimensional (3D) Ly$\alpha$ forest power spectrum, $P_{\rm 3D,\alpha}$, as a probe of the thermal and ionization history of the intergalactic medium (IGM). To exploit this opportunity, we quantify the imprints of reionization on the post-reionization IGM using high-fidelity numerical models. We use the Sherwood and Sherwood-Relics cosmological hydrodynamical simulations with box sizes up to $160\,h^{-1}\,\rm cMpc$ to investigate the impact of box size, mass resolution, and extracted grid resolution on $P_{\rm 3D,\alpha}$ over $2.4\leq z\leq4.8$. After applying a Zel'dovich control variate correction, simulation volume has a modest impact over most scales and orientations, whereas degrading the mass resolution produces differences of up to $\sim13\%$. Insufficient resolution of the grid used for the optical-depth calculation can artificially enhance small-scale power by up to $\sim35\%$. The timing of $\mathrm{H\,I}$ reionization leaves only a percent-level imprint on $P_{\rm 3D,\alpha}$ at $z=2.4$, whereas varying the photoheating rate by a factor of two changes the large-scale power by $\sim4-8\%$. Our results demonstrate that numerical effects can be comparable to, or exceed, the relic astrophysical signatures encoded in $P_{\rm 3D,\alpha}$, making numerical convergence essential for interpreting precise Ly$\alpha$ forest measurements. The strongest astrophysical imprint arises from spatially inhomogeneous $\mathrm{H\,I}$ reionization, which enhances the large-scale power by up to $\sim70\%$ at $z=4.2$. This highlights the potential of post-reionization Ly$\alpha$ forest measurements as a probe of the thermal history and spatial morphology of cosmic reionization.
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What it cites · 108 sentences without a confident label
Uses the method or tool of 21 papers
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Following [ref] , the non-linear term is parameterized as [equation] where [equation] This parametrization captures three key physical effects.
The Non-Linear Power Spectrum of the Lyman Alpha Forest · Analytical form fitting · 1.00
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To interpret the measured three-dimensional flux power spectrum, we adopt a parametric model that separates linear-theory contributions from non-linear corrections, following the formalism introduced by [ref] and subsequently adopted in a range of simulation-based and observational analyses of the Ly$α$ forest power spectrum (e.g. [ref] ).
The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Baryon acoustic oscillations with Lyman-$\alpha$ forests · Analytical form fitting · 0.96
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To interpret the measured three-dimensional flux power spectrum, we adopt a parametric model that separates linear-theory contributions from non-linear corrections, following the formalism introduced by [ref] and subsequently adopted in a range of simulation-based and observational analyses of the Ly$α$ forest power spectrum (e.g. [ref] ).
The ACCEL$^2$ project: simulating Lyman-$\alpha$ forest in large-volume hydrodynamical simulations · Analytical form fitting · 0.96
Uses data or values from 3 papers
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These IGM models were produced within the Sherwood–Relics simulation suite [ref] .
The Sherwood-Relics simulations: overview and impact of patchy reionization and pressure smoothing on the intergalactic medium · The effect of reionization on post-reionization $P_3D,α$ · 0.87
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The simulations adopt a $Λ$CDM cosmology consistent with Planck constraints, with parameters $Ω_m=0.308$, $Ω_Λ=0.692$, $Ω_b=0.0482$, $h=0.678$, $σ_8=0.829$, and $n_s=0.961$ [ref] , and primordial helium fraction by mass $Y=0.24$ [ref] .
The PHLEK Survey: A New Determination of the Primordial Helium Abundance · Modelling the post-reionization intergalactic medium · 0.98
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For each simulation model and redshift separately, we rescale the computed optical depths by a spatially uniform multiplicative factor, $A_eff$, such that the resulting mean transmitted flux matches the observed redshift evolution from [ref] .
Warm Dark Matter as a solution to the small scale crisis: new constraints from high redshift Lyman-alpha forest data · Numerical simulation-based computation · 0.96
Compares with 6 papers
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Restricting the analysis to $k_max=3 h cMpc^-1$ removes the high-redshift upturn found in our fiducial $k_max=10 h cMpc^-1$ fits and brings the inferred evolution into better agreement with [ref] and [ref] .
The ACCEL$^2$ project: simulating Lyman-$\alpha$ forest in large-volume hydrodynamical simulations · Analytical form fitting · 0.99
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Restricting the analysis to $k_max=3 h cMpc^-1$ removes the high-redshift upturn found in our fiducial $k_max=10 h cMpc^-1$ fits and brings the inferred evolution into better agreement with [ref] and [ref] .
The Non-Linear Power Spectrum of the Lyman Alpha Forest · Analytical form fitting · 0.99
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As discussed in Section [ref], this choice has a substantially stronger impact on the inferred bias parameters, particularly $b_η$: restricting the fitting range removes the high-redshift upturn obtained in the fiducial fits and brings its evolution into better agreement with [ref] , [ref] , and the mEFT analysis of the same simulations in the accompanying work [ref] .
Physical Calibration of a Minimal Effective Field Theory of the Three-Dimensional Lyman-$\alpha$ Forest · Impact of $q_2$ and the range of scales on the fitting procedure · 0.98
Cites as support 20 papers
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This resolution–volume combination has been shown to be sufficient for converged Ly$α$ forest statistics [ref] .
The Lyman-$\alpha$ forest in optically-thin hydrodynamical simulations · Comparison to other simulations used for Ly$α$ forest studies · 0.99
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This resolution–volume combination has been shown to be sufficient for converged Ly$α$ forest statistics [ref] .
Resolving the high redshift Lyman-alpha forest in smoothed particle hydrodynamics simulations · Comparison to other simulations used for Ly$α$ forest studies · 0.99
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The weak sensitivity to $z_r$ found here is particularly relevant given the growing observational evidence for reionization ending at $z_r<5.6$, including observed large scatter in Ly$α$ forest transmission between sightlines [ref] , Ly$α$ forest transmission spikes at $z>5$ [ref] , low abundance of Ly$α$ emitting galaxies around long Ly$α$ absorption troughs [ref] , clustering of Ly$α$ emitters [ref] , Ly$α$ and Ly$β$ forest spectra containing long dark gaps [ref] , presence of damping-wing absorption at $z<5.6$ [ref] , mean free path of ionizing photons at $z=6$ [ref] , as well as various metal absorption and emission lines [ref] .
Probing Ultra-late Reionization: Direct Measurements of the Mean Free Path over $5<z<6$ · The effect of reionization on post-reionization $P_3D,α$ · 0.96
Cites as background 24 papers
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On large scales, the forest can be described as a biased tracer of the underlying matter distribution with redshift-space distortions, leading to the well-known Kaiser-like form [ref] .
The large-scale Quasar-Lyman \alpha\ Forest Cross-Correlation from BOSS · Introduction · 0.93
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On large scales, the forest can be described as a biased tracer of the underlying matter distribution with redshift-space distortions, leading to the well-known Kaiser-like form [ref] .
Toward a Measurement of the Cosmological Geometry at z~2: Predicting Lyman-alpha Forest Correlation in Three Dimensions, and the Potential of Future Data Sets · Introduction · 0.93
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Traditionally, Ly$α$ forest analyses have focused on two primary statistical observables: the one-dimensional (1D) flux power spectrum along individual sightlines, and the three-dimensional (3D) correlation function reconstructed from multiple sightlines [ref] .
The impact of relativistic effects on the 3D Quasar-Lyman-$\alpha$ cross-correlation · Introduction · 0.91
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