Pith. sign in

REVIEW 4 major objections 5 minor 1 cited by

The paper claims that a neural-network emulator trained on ultra-high-resolution radiative-transfer simulations of 2 comoving Mpc/h boxes predicts the ionizing photon mean free path with 1.6% median relative error, and that the observed mea

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-03 04:48 UTC pith:DQUPS3PV

load-bearing objection A genuinely useful MFP emulator and a plausible late-reionization case, but the headline neutral fraction rests on an unvalidated neutral-island approximation that needs a quantitative check. the 4 major comments →

arxiv 2602.03923 v3 pith:DQUPS3PV submitted 2026-02-03 astro-ph.CO

An emulator for the ionizing photon mean free path in ultra-high resolution simulations: the implications of mean free path measurements for the reionization history

Hurum Maksora Tohfa , Christopher Cain , Matthew McQuinn , Anson D'Aloisio This is my paper
classification astro-ph.CO
keywords cosmic reionizationmean free pathintergalactic mediummachine learning emulatorradiative transfer simulationsneural networkionizing backgroundreionization history
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper sets out to make the ionizing photon mean free path (MFP) a fast, accurate probe of cosmic reionization, despite the fact that the MFP is controlled by gas clumping on the kiloparsec scale—unresolvable in large-volume simulations. It trains a residual neural network on 126 ultra-high-resolution radiative-transfer simulations of 2 h⁻¹ cMpc boxes (2 h⁻¹ kpc resolution) that are each instantaneously reionized at a chosen z_re with constant photoionization rate, and the network predicts the MFP at any z≤z_re from z, z_re, Γ, box-scale overdensity, and photon energy with a median relative error of 1.6% over nearly four decades in MFP. Averaging the emulator's opacity over the reionization history via P(z_re)=−dQ/dz and over large-scale density modes via three-point Gauss-Hermite quadrature, the paper finds that the observed MFP at z≈5–6 is only matched by reionization histories with midpoint z_re≈6.8–7.0 and duration Δz≈2.33—histories in which the universe is still ~30% neutral at z=6—and that reionization completing by z≈8 overpredicts the MFP by factors of 2–3. From the same emulator the paper derives a frequency-integrated ionizing emissivity that drops by a factor 2–3 between z=6 and z=4.8 without power-law opacity assumptions, and argues only 15–20% of that drop can be ascribed to an evolving column-density distribution. The paper itself flags its main simplifications—constant-Γ histories (Appendix A bounds the induced bias at ~20%), and the neglect of neutral-island opacity and of correlations between z_re, Γ, and density (Appendix B)—and positions the emulator as a subgrid opacity prescription for larger simulations.

Core claim

The central claim is that the MFP of ionizing photons can be learned from small boxes: a residual multi-layer perceptron trained on log-transformed MFP values from 2 h⁻¹ cMpc radiative-transfer runs reproduces the MFP from (z, z_re, Γ, δ/σ, photon energy) with 1.6% median relative error (R²=0.95) on a held-out test set, and the same accuracy holds for a validation simulation at an untrained z_re. When the emulator's opacity is convolved with a reionization history (P(z_re)=−dQ/dz) and integrated over box-scale density, the resulting global MFP matches the z≈5–6 quasar measurements only if reionization is late and extended—best-fit tanh model z_re≈6.8–7.0, Δz≈2.33, with ~30% neutral fraction

What carries the argument

The residual multi-layer perceptron—a feed-forward network with skip connections, layer normalization, and a log-transformed target—is the computational engine: it maps the five inputs (z, z_re, Γ−12, δ/σ, photon energy) to log10 λ_mfp, having been trained on sight-line-averaged MFP values from 126 small-box simulations that resolve the Jeans scale and self-shielding. The physical bridge to observations is the opacity integral ⟨κ⟩ = ∫ P(z_re) κ(z_re) dz_re with P = −dQ/dz, plus three-point Gauss-Hermite quadrature over box-scale overdensity to account for modes larger than the 2 Mpc box; the same machinery, integrated over photon frequency, gives the emissivity via Γ = (1+z)²∫ dν Ṅ(ν)σ(ν)λ(

Load-bearing premise

The load-bearing premise is that a 2 h⁻¹ cMpc box whose gas is ionized instantly at one redshift with a constant photoionization rate, and then stacked via P(z_re)=−dQ/dz and a three-point density quadrature, is an adequate stand-in for the real, patchy intergalactic medium—in particular that correlations among z_re, Γ, and large-scale density are negligible and that neutral islands contribute no opacity.

What would settle it

A resolved large-volume run (≥100 cMpc with ≤2 ckpc cells, or zoom-in equivalents) through the same ionization histories would directly test the stacking: if its global MFP deviates from the emulator by more than ~20%, the method fails. A cheaper test: a 10%-accurate MFP measurement at z≈5.5—if it lands near the early-reionization prediction (a factor ~2 above the best-fit late curve), the paper's central historical conclusion is wrong.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • MFP observations at z≈5–6 are already informative: the emulator shows they rule out early (z≈8) completion of reionization at roughly 2σ, favoring a late, extended history.
  • The emulator can serve as a subgrid prescription for ionizing opacity inside large-volume reionization simulations, replacing cruder interpolation schemes with a physically fitted mapping.
  • The frequency-integrated emulator yields an ionizing emissivity that declines by a factor of 2–3 between z=6 and z=4.8 without power-law opacity assumptions; this decline is not explained by evolution in the absorber column density distribution and so points to evolving ionizing sources.
  • The inferred reionization midpoint and duration overlap CMB plus kinetic Sunyaev-Zeldovich constraints at 1σ, so the MFP-based and CMB-based pictures of reionization can be made consistent.
  • Because the emulator evaluates in milliseconds, large grid searches (tens of thousands of parameter combinations) become tractable, something infeasible with direct simulations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the stacking approximation holds, large-volume simulations that ignore kiloparsec-scale clumping may systematically mispredict the opacity evolution; a fair test would be to plug this emulator into one such simulation and see whether the MFP field changes its predictions.
  • The same architecture could be retrained (or augmented) to include time-evolving Γ histories and He II photoionization, extending the MFP probe to higher redshift and to the helium reionization epoch; the paper's appendix suggests Γ-evolution effects are ~20% and only modestly shift constraints.
  • A testable consequence: if future 21-cm or Lyman-α damping-wing observations find the neutral fraction at z=6 is far below 30%, the late-reionization conclusion would need revision; conversely, a neutral fraction near 30% would corroborate it.
  • The inferred factor 2–3 emissivity decline, if due to sources, implies the escape fraction of ionizing photons must fall or the source population must fade between z=6 and z≈5; upcoming deep galaxy surveys could measure this directly.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper presents a deep-learning emulator for the ionizing photon mean free path (MFP), trained on 126 high-resolution radiative-transfer simulations of 2 h^-1 cMpc boxes that are reionized instantaneously at various z_re with constant photoionization rates. The emulator predicts MFP as a function of z, z_re, Γ, box-scale overdensity, and photon energy, reporting 1.6% median relative error on a held-out test set and 1.7% error for an independent z_re=6.5 validation simulation. The authors integrate this emulator over box-scale density and over a global reionization history P(z_re)=-dQ/dz, compare the resulting global MFP to z≈4.5-6 quasar measurements, and derive constraints: a tanh ionization history with z_re≈6.8-7.0 and Δz≈2.3, a neutral fraction ≈30% at z=6, disfavoring of early-completion reionization histories, and an ionizing emissivity that declines by a factor 2-3 from z=6 to 4.8. The paper argues that MFP measurements therefore favor late reionization with substantial neutral fractions persisting below z≈6.

Significance. If the central approximation is valid, this is a valuable methodological contribution: the emulator's interpolation accuracy is demonstrated on held-out data and an independent validation simulation, and its millisecond evaluation time enables parameter searches that would otherwise be prohibitive. The forward-modeling approach is clear, and the qualitative conclusion that MFP measurements favor late reionization is physically interesting and consistent with several independent constraints. However, the bridge from the small-box emulator to the global MFP relies on an unvalidated two-phase-medium approximation, and the treatment of evolving Γ is systematic rather than fully quantified. These issues must be resolved before the headline z_re and neutral-fraction claims can be accepted.

major comments (4)
  1. [§3.4, Eq. (3.5)] Equation (3.5) computes λ^{-1}(z) = Q(z)^{-1} ∫_z^∞ P(z_re) κ(z_re) dz_re, which averages the opacity of already-reionized gas and entirely neglects absorption by neutral islands. At the best-fit history Q(z=6)≈0.7, the neutral volume fraction is 30%. In a two-phase medium the effective opacity along an observed sightline contains an additional term ∼(1−Q)/ℓ_island; whether this is negligible depends on the size and clustering of neutral islands, which the paper does not quantify. The statement that Q≳0.7 and the exponential transmission profile make the bias small is an assertion, not a calculation. Because Eq. (3.5) is the link between the emulator and all observational constraints in §§3.3–3.5, a two-phase radiative-transfer test or an explicit bound on ℓ_island is required before the headline z_re and neutral-fraction constraints can be considered robust.
  2. [Appendix A, Figs. 7–8] The 20% correction for neglecting Γ evolution is applied as a one-sided reduction of the emulator MFP, described as the 'maximum potential bias.' Figure 7 shows scatter between the evolving-Γ simulations and the emulator, not a well-defined systematic; the sign of the correction is not established, and no two-sided bracket is given. This correction shifts the tanh fit from (z_end, Δz)=(4.64, 2.33) to (5.54, 1.17)—i.e., Δz changes by roughly a factor of two. That shift is comparable to the quoted statistical precision and should be propagated as a systematic uncertainty in the final constraints, not only as a robustness check. As written, the claim that the conclusions are unaffected is not quantitatively supported.
  3. [§3.4 and §4] The best-fit reionization midpoint is reported inconsistently: the Fig. 5 caption states z_re=6.84, Section 4 states z_re=6.97, and the abstract states 6.8±1.2. If these refer to different quantities (e.g., the midpoint before versus after the Appendix A correction, or the midpoint of a slightly different best-fit), that is not explained. Since this is the paper's central numerical result, the value needs to be harmonized and clearly defined.
  4. [§3.1, Fig. 2; §3.3] The emulator's largest residuals are reported for extremely large MFP values, which is exactly the regime populated by the early-early reionization models that the paper later disfavors by factors of 2–3. The magnitude and direction of this bias in that regime are not quantified. An additional validation simulation at high z_re (e.g., z_re=15) or a statement of the test-set error restricted to large-MFP predictions is needed to ensure that the disfavoring of early reionization is not an artifact of the emulator rather than a robust conclusion from the data.
minor comments (5)
  1. [Abstract vs. §3.1] The abstract gives a median relative error of 1.3% while §3.1 and Fig. 2 report 1.6%. These need to be reconciled.
  2. [§3.2 vs. §4] The instantaneous-reionization fit is quoted as z_re=5.82±0.573 in §3.2 but as z_re=5.82±0.07 in §4; the former appears consistent with Fig. 3, and the latter is likely a typo. Similarly, Γ−12 is 0.36±0.10 in §3.2 and 0.36±0.08 in §4.
  3. [§3.4] The MFP data compilation used for the tanh fit is not fully specified. The text cites [20,54,56,57] but does not list the individual points, redshifts, or uncertainties; a table or explicit enumeration would aid reproducibility.
  4. [§3.5, Eq. (3.6)] The footnote about the distant-photon correction is appropriate, but since the correction is order 20% at z≈5 and the paper's emissivity decline is a factor 2–3, it should be either included or explicitly shown not to change the comparison.
  5. [Throughout] Minor typos and infelicities: 'sucessfull' in Appendix B; 'the emulator does only has learned' in §4; duplicated reference entries (e.g., D'Aloisio et al. 2018 appears multiple times with different numbers).

Circularity Check

0 steps flagged

No significant circularity: the emulator is validated internally and the reionization constraints are forward-model fits to external data, with self-citations only for simulation methodology.

full rationale

The paper's derivation chain is a standard forward model that is not defined in terms of its conclusions. The emulator is trained on MFP values measured from the authors' high-resolution RT simulations (Sec. 2) and validated on a held-out test set plus a deliberately omitted z_re=6.5 simulation ('the emulator predicts this case with 1.7% error at 13.6 eV'), so the claimed 1.6% accuracy is an empirical performance claim, not a restatement of an input. The global MFP is obtained by integrating the emulated opacity over P(z_re)=-dQ/dz and over three box-scale densities using Gauss-Hermite quadrature (Eqs. 3.2-3.5); this is an assumed mixing model, not a quantity fitted to the MFP observations. The tanh parameters z_re and Δz are obtained by chi^2 grid search against observed MFP values from Becker, Worseck, and Zhu (Eq. 3.1, Fig. 5), so the inferred z_re≈6.8-7.0 and Δz≈2.33 are fitted outputs, not inputs disguised as predictions. The paper explicitly flags the neutral-island opacity omission in Eq. 3.5 and argues Q≳0.7 makes it small; this is a model limitation that could bias results, but it is not circularity because the approximation does not assume the headline neutral fraction. Self-citations ([22], [103], [50], [49,104]) provide simulation methodology and prior context, but the central constraint is not forced by those references; it is checked against independent data (Planck+kSZ, dark-gap constraints, and the MFP measurements). Thus no step reduces by construction to its own input.

Axiom & Free-Parameter Ledger

5 free parameters · 6 axioms · 0 invented entities

No new physical entities are introduced. The free parameters are the fitted reionization-history variables and a few hand-set training choices; the main physical assumptions are the small-box/instantaneous-reionization model, the neglect of correlations, and the neglect of neutral-island opacity.

free parameters (5)
  • z_re (tanh midpoint) = best fit 6.97 (Section 4); abstract says 6.58; Fig. 5 caption says 6.84
    Fitted to z=4.5–6 MFP observations in the tanh model, Eq. 3.4.
  • Δz (tanh duration) = 2.33
    Fitted together with z_re in Section 3.4.
  • Γ (instantaneous-reionization model) = 0.36 × 10^-12 s^-1
    Grid-search fit to MFP in Section 3.2; not used in the extended-history analysis.
  • z_re (instantaneous model) = 5.82 (errors quoted as ±0.573 in §3.2 and ±0.07 in §4)
    Grid-search fit to MFP in Section 3.2.
  • Neural network loss weight for z_re sensitivity = 2.5
    Hand-set in Section 3.1; affects training but not a physical parameter.
axioms (6)
  • standard math Radiative transfer and hydrodynamics are governed by the standard equations and solved with the existing RadHydro code (Trac et al. 2007; D'Aloisio et al. 2020).
    The simulation suite is taken as a validated numerical experiment; not re-derived here.
  • domain assumption A box reionized instantaneously at z_re with constant Γ can be combined with P(z_re)=−dQ/dz to represent a patchy global reionization history.
    Used in Eqs. 3.2–3.4; the paper treats this as an approximation and examines Γ-evolution effects in Appendix A.
  • domain assumption Large-scale density modes are captured by three separate-universe simulations at δ/σ=0, ±√3 with three-point Gauss-Hermite quadrature.
    Section 2 footnote and Eq. 3.3; exact only if the integrand is a polynomial of degree ≤5.
  • domain assumption Correlations between z_re, Γ, and box-scale overdensity are negligible.
    Appendix B argues they are small but does not compute them.
  • domain assumption Neutral islands contribute no transmission, so λ_mfp^-1 = Q^-1 ∫κ; the resulting overestimate of MFP is small for Q≳0.7.
    Eq. 3.5 and surrounding text; this enters the tanh fit and the reported neutral fractions.
  • ad hoc to paper The adopted tanh form Q(z)=1/2[1+tanh((z_re−z)/Δz)] is a sufficient parameterization of the ionization history.
    Eq. 3.4; no physical derivation, used for the grid fit.

pith-pipeline@v1.3.0-alltime-deepseek · 21795 in / 14049 out tokens · 131359 ms · 2026-08-03T04:48:25.179556+00:00 · methodology

0 comments
read the original abstract

Measurements of the mean free path of ionizing photons from high-redshift quasar spectra at $z \sim 5$-$6$ constrain the reionization history, but interpreting them requires modeling the kiloparsec-scale clumping that large-volume reionization simulations cannot resolve. We present a deep learning emulator for the mean free path (MFP) trained on high-resolution cosmological radiative transfer simulations of ionization fronts sweeping through small 2 comoving Mpc/h volumes. Using a residual multi-layer perceptron neural network, we predict the MFP at a given redshift as a function of the reionization redshift, photoionization rate, wavelength, and box-scale density, achieving a median relative error of 1.3\% across nearly four orders of magnitude in MFP. Integrating its predictions over box-scale overdensity and an extended reionization history allows the emulator to predict the global MFP. We apply the emulator to extended reionization histories constrained by observed photoionization rates, finding that models prefer late reionization with substantial neutral fractions persisting at $z \lesssim 6$. Fitting a parametric ionization history yields a midpoint of reionization of $z_{\rm re} = 6.58\pm 1.2$ for reionization durations consistent with Planck and kinetic Sunyaev-Zeldovich constraints, and the universe being $10\%$ neutral still at $z < 5.8 ~(6.3)$ at 1~(2)$\sigma$. Global ionizing emissivity inferences using measurements of the photoionization rate and MFP plus our emulator, which avoids common power-law assumptions, suggest a factor of $2-3$ decline between $z = 6$ and $4.8$, in agreement with previous studies. Our method provides an efficient (and more converged) alternative to large-volume radiative-hydrodynamic simulations of reionization for interpreting MFP measurements, and can also serve as a subgrid prescription for the ionizing opacity within such simulations.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. A self-consistent analytical model for both the photoionization rate and reionization history

    astro-ph.CO 2026-06 unverdicted novelty 7.0

    A new analytical formalism self-consistently predicts both the ionized fraction x_i(z) and photoionization rate Gamma_HI(z), achieving percent-level accuracy in x_i and 20-30% accuracy in Gamma_HI versus radiative tra...

Reference graph

Works this paper leans on

105 extracted references · 67 linked inside Pith · cited by 1 Pith paper

  1. [1]

    Furlanetto, S. R. et al.,Taxing the rich: recombinations and bubble growth during reionization, Mon. Not. Roy. Astron. Soc.363(2005) 1031-1048

    2005

  2. [2]

    Alvarez, M. A. et al.,Quasar HII regions during cosmic reionization, Astrophys. J.747(2012) 126

    2012

  3. [3]

    et al.,Inhomogeneous recombinations during cosmic reionization, Mon

    Sobacchi, E. et al.,Inhomogeneous recombinations during cosmic reionization, Mon. Not. Roy. Astron. Soc.440(2014) 1662-1673

    2014

  4. [4]

    et al.,Large fluctuations in the hydrogen-ionizing background and mean free path following the epoch of reionization, Mon

    D’Aloisio, A. et al.,Large fluctuations in the hydrogen-ionizing background and mean free path following the epoch of reionization, Mon. Not. Roy. Astron. Soc.473(2018) 560-575

    2018

  5. [5]

    et al.,Damping wing absorption associated with a giant Lyαtrough atz <6: direct evidence for late-ending reionization, Mon

    Becker, George D. et al.,Damping wing absorption associated with a giant Lyαtrough atz <6: direct evidence for late-ending reionization, Mon. Not. Roy. Astron. Soc.533(2024) 1525–1540 [arXiv:2405.08885]

    Pith/arXiv arXiv 2024

  6. [8]

    Kingma et al.,Adam: A Method for Stochastic Optimization, arXiv:1412.6980

    Diederik P. Kingma et al.,Adam: A Method for Stochastic Optimization, arXiv:1412.6980. – 20 –

    Pith/arXiv arXiv

  7. [9]

    Kaiming He et al.,Deep Residual Learning for Image Recognition, arXiv:1512.03385

    Pith/arXiv arXiv

  8. [10]

    Stuart B

    Wyithe, J. Stuart B. et al.,Near-zone sizes and the rest-frame extreme ultraviolet spectral index of the highest redshift quasars, Mon. Not. Roy. Astron. Soc.412(2011) 1926-1936 [arXiv:1008.1107]

    Pith/arXiv arXiv 2011

  9. [11]

    et al.,Measurements of the ultraviolet background at 4.6 ¡ z ¡ 6.4 using the quasar proximity effect, Mon

    Calverley, Alexander P. et al.,Measurements of the ultraviolet background at 4.6 ¡ z ¡ 6.4 using the quasar proximity effect, Mon. Not. Roy. Astron. Soc.412(2011) 2543-2562 [arXiv:1011.5850]

    Pith/arXiv arXiv 2011

  10. [12]

    J.728(2011) 23 [arXiv:1004.3347]

    Worseck, G´ abor et al.,GALEX Far-ultraviolet Color Selection of UV-bright High-redshift Quasars, Astrophys. J.728(2011) 23 [arXiv:1004.3347]

    Pith/arXiv arXiv 2011

  11. [13]

    J.630(2005) 643-656 [arXiv:astro-ph/0504189]

    McQuinn, Matthew et al.,The Kinetic Sunyaev-Zel’dovich Effect from Reionization, Astrophys. J.630(2005) 643-656 [arXiv:astro-ph/0504189]

    Pith/arXiv arXiv 2005

  12. [14]

    J.654(2007) 12-26 [arXiv:astro-ph/0604177]

    Zahn, Oliver et al.,Simulations and Analytic Calculations of Bubble Growth during Hydrogen Reionization, Astrophys. J.654(2007) 12-26 [arXiv:astro-ph/0604177]

    Pith/arXiv arXiv 2007

  13. [15]

    et al.,The Growth of H II Regions During Reionization, Astrophys

    Furlanetto, Steven R. et al.,The Growth of H II Regions During Reionization, Astrophys. J. 613(2004) 1-15 [arXiv:astro-ph/0403697]

    Pith/arXiv arXiv 2004

  14. [18]

    J.743(2011) 82 [arXiv:1101.1964]

    McQuinn, Matthew et al.,On Lyman-limit Systems and the Evolution of the Intergalactic Ionizing Background, Astrophys. J.743(2011) 82 [arXiv:1101.1964]

    Pith/arXiv arXiv 2011

  15. [19]

    Pontzen, Andrew,Scale-dependent bias in the baryonic-acoustic-oscillation-scale intergalactic neutral hydrogen, Phys. Rev. D89(2014) 083010 [arXiv:1402.0506]

    Pith/arXiv arXiv 2014

  16. [20]

    Becker, George D. et al.,The mean free path of ionizing photons at 5 ¡ z ¡ 6: evidence for rapid evolution near reionization, Monthly Notices of the Royal Astronomical Society508(2021) 1853-1869 [arXiv:2103.16610]

    Pith/arXiv arXiv 2021

  17. [21]

    et al.,Lyman alpha forest constraints on the mass of warm dark matter and the shape of the linear power spectrum, Monthly Notices of the Royal Astronomical Society398 (2009) L26

    Bolton, James S. et al.,Lyman alpha forest constraints on the mass of warm dark matter and the shape of the linear power spectrum, Monthly Notices of the Royal Astronomical Society398 (2009) L26

    2009

  18. [22]

    Cain, Christopher et al.,The hydrodynamic response of small-scale structure to reionization drives large IGM temperature fluctuations that persist to z = 4, Monthly Notices of the Royal Astronomical Society (2024) [arXiv:2405.02397]

    Pith/arXiv arXiv 2024

  19. [23]

    Cain, Christopher et al.,New constraints on the galactic ionizing efficiency and escape fraction at 2.5 ¡ z ¡ 6 based on quasar absorption spectra, Cambridge Large Two (2025) 1-22 [arXiv:2503.08778]

    Pith/arXiv arXiv 2025

  20. [24]

    Chan, T. K. et al.,Photoevaporation of Jeans-unstable molecular clouds, arXiv e-prints (2023) arXiv:2305.04959 [arXiv:2305.04959]

    Pith/arXiv arXiv 2023

  21. [25]

    Chardin, Jonathan et al.,Calibrating cosmological simulations with implicit likelihood inference using galaxy growth observables, Monthly Notices of the Royal Astronomical Society478 (2018) 4785-4805

    2018

  22. [26]

    et al.,Simulating intergalactic medium reionization, Monthly Notices of the Royal Astronomical Society366(2006) 689-696

    Ciardi, B. et al.,Simulating intergalactic medium reionization, Monthly Notices of the Royal Astronomical Society366(2006) 689-696

    2006

  23. [27]

    D’Aloisio, Anson et al.,Large fluctuations in the high-redshift metagalactic ionizing background, Mon. Not. Roy. Astron. Soc.473(2018) 560-575 [arXiv:1611.02711]. – 21 –

    Pith/arXiv arXiv 2018

  24. [28]

    J.874(2019) 154 [arXiv:1807.09282]

    D’Aloisio, Anson et al.,Heating of the Intergalactic Medium by Hydrogen Reionization, Astrophys. J.874(2019) 154 [arXiv:1807.09282]

    Pith/arXiv arXiv 2019

  25. [29]

    9(2004) 443-465 [arXiv:astro-ph/0309599]

    Trac, Hy et al.,A moving frame algorithm for high Mach number hydrodynamics, New Astron. 9(2004) 443-465 [arXiv:astro-ph/0309599]

    Pith/arXiv arXiv 2004

  26. [30]

    Trac, Hy et al.,Radiative Transfer Simulations of Cosmic Reionization. I. Methodology and Initial Results, Astrophys. J.671(2007) 1-13 [arXiv:astro-ph/0612406]

    Pith/arXiv arXiv 2007

  27. [31]

    Hirata, Christopher M.,Small-scale structure and the Lyman-αforest baryon acoustic oscillation feature, Mon. Not. Roy. Astron. Soc.474(2018) 2173-2193 [arXiv:1707.03358]

    Pith/arXiv arXiv 2018

  28. [32]

    D’Aloisio, Anson et al.,Modeling cosmic reionization, The Astrophysical Journal898(2020) 149

    2020

  29. [33]

    Doughty, C. C. et al.,Modeling the Lyman-alpha forest in collisionless simulations, arXiv e-prints (2023) arXiv:2305.16200 [arXiv:2305.16200]

    Pith/arXiv arXiv 2023

  30. [34]

    Fan, Xiaohui et al.,Observational constraints on cosmic reionization, Annual Review of Astronomy and Astrophysics44(2006) 415-462

    2006

  31. [35]

    Faucher-Gigu` ere, Claude-Andr´ e et al.,Evolution of the intergalactic opacity: implications for the ionizing background, cosmic star formation, and quasar activity, The Astrophysical Journal 673(2008) 39-50

    2008

  32. [36]

    Faucher-Gigu` ere, Claude-Andr´ e et al.,A new calculation of the ionizing background spectrum and the effects of He II reionization, The Astrophysical Journal681(2009) 831-855

    2009

  33. [37]

    Gnedin, Nickolay Y.,Effect of reionization on structure formation in the universe, The Astrophysical Journal542(2000) 535-541

    2000

  34. [38]

    Haardt, Francesco et al.,Radiative transfer in a clumpy universe. IV. New synthesis models of the cosmic UV/X-ray background, The Astrophysical Journal746(2012) 125

    2012

  35. [39]

    Hui, Lam et al.,Equation of state of the photoionized intergalactic medium, Monthly Notices of the Royal Astronomical Society292(1997) 27-42

    1997

  36. [40]

    et al.,The impact of small-scale structure on cosmological ionization fronts and reionization, The Astrophysical Journal624(2005) 491-504

    Iliev, Ilian T. et al.,The impact of small-scale structure on cosmological ionization fronts and reionization, The Astrophysical Journal624(2005) 491-504

    2005

  37. [41]

    et al.,Lyman-alpha forest power spectrum analysis using wavelets, Monthly Notices of the Royal Astronomical Society477(2018) 5501-5514

    Keating, Laura C. et al.,Lyman-alpha forest power spectrum analysis using wavelets, Monthly Notices of the Royal Astronomical Society477(2018) 5501-5514

    2018

  38. [42]

    Kim, Tae-Sun et al.,The column density distribution and cosmological mass density of the Ly-alpha forest and Lyman-limit systems from the VLT/UVES advanced data products quasar sample, Astronomy & Astrophysics552(2013) A77

    2013

  39. [43]

    Kulkarni, Girish et al.,Model-independent evidence for dark-matter particles with mass below 10 keV from the abundance of small dark matter haloes, The Astrophysical Journal812(2015) 30

    2015

  40. [44]

    McQuinn, Matthew et al.,The evolution of the intergalactic medium, Monthly Notices of the Royal Astronomical Society456(2016) 47-65

    2016

  41. [45]

    Cain, Christopher et al.,The morphology of reionization in a dynamically clumpy universe, Mon. Not. Roy. Astron. Soc.522(2023) 2047-2064 [arXiv:2207.11266]

    Pith/arXiv arXiv 2023

  42. [46]

    J.530 (2000) 1-16 [arXiv:astro-ph/9812306]

    Miralda-Escud´ e, Jordi et al.,Reionization of the Inhomogeneous Universe, Astrophys. J.530 (2000) 1-16 [arXiv:astro-ph/9812306]

    Pith/arXiv arXiv 2000

  43. [48]

    Satyavolu, Sindhu et al.,Robustness of direct measurements of the mean free path of ionizing photons in the epoch of reionization, Mon. Not. Roy. Astron. Soc.533(2024) 676-686 [arXiv:2311.06344]

    Pith/arXiv arXiv 2024

  44. [49]

    J.l917(2021) L37 [arXiv:2105.10511]

    Cain, Christopher et al.,A Short Mean Free Path at z = 6 Favors Late and Rapid Reionization by Faint Galaxies, Astrophys. J.l917(2021) L37 [arXiv:2105.10511]

    Pith/arXiv arXiv 2021

  45. [50]

    J.898(2020) 149 [arXiv:2002.02467]

    D’Aloisio, Anson et al.,Hydrodynamic Response of the Intergalactic Medium to Reionization, Astrophys. J.898(2020) 149 [arXiv:2002.02467]

    Pith/arXiv arXiv 2020

  46. [51]

    Nasir, Fahad et al.,Hydrodynamic response of the intergalactic medium to reionization II: Physical characteristics and dynamics of ionizing photon sinks, The Astrophysical Journal923 (2021) 161

    2021

  47. [53]

    Xavier et al.,A Direct Measurement of the Intergalactic Medium Opacity to H I Ionizing Photons, Astrophys

    Prochaska, J. Xavier et al.,A Direct Measurement of the Intergalactic Medium Opacity to H I Ionizing Photons, Astrophys. J.l705(2009) L113-L117 [arXiv:0910.0009]

    Pith/arXiv arXiv 2009

  48. [55]

    et al.,Separate universe simulations., Mon

    Wagner, C. et al.,Separate universe simulations., Mon. Not. Roy. Astron. Soc.448(2015) L11-L15 [arXiv:1409.6294]

    Pith/arXiv arXiv 2015

  49. [57]

    Measuring the mean free path across cosmic time, Mon

    Worseck, G´ abor et al.,The Giant Gemini GMOS survey ofz em >4.4quasars - I. Measuring the mean free path across cosmic time, Mon. Not. Roy. Astron. Soc.445(2014) 1745-1760 [arXiv:1402.4154]

    Pith/arXiv arXiv 2014

  50. [58]

    Rahmati, Alireza et al.,On the evolution of the H I column density distribution in cosmological simulations, Monthly Notices of the Royal Astronomical Society430(2013) 2427-2445

    2013

  51. [59]

    et al.,Photoevaporation of cosmological minihaloes during reionization, Monthly Notices of the Royal Astronomical Society348(2004) 753-782

    Shapiro, Paul R. et al.,Photoevaporation of cosmological minihaloes during reionization, Monthly Notices of the Royal Astronomical Society348(2004) 753-782

    2004

  52. [60]

    Kulkarni, Girish et al.,Large Lyαopacity fluctuations and low CMBτin models of late reionization with large islands of neutral hydrogen extending toz <5.5, Mon. Not. Roy. Astron. Soc.485(2019) L24-L28 [arXiv:1809.06374]

    Pith/arXiv arXiv 2019

  53. [61]

    Cain, Christopher et al.,On the rise and fall of galactic ionizing output at the end of reionization, Mon. Not. Roy. Astron. Soc.531(2024) 1951-1970 [arXiv:2311.13638]

    Pith/arXiv arXiv 2024

  54. [62]

    Ocvirk, Pierre et al.,Lyman-alpha opacities at z = 4-6 require low mass, radiatively-suppressed galaxies to drive cosmic reionization, Mon. Not. Roy. Astron. Soc.507(2021) 6108-6117 [arXiv:2105.01663]

    Pith/arXiv arXiv 2021

  55. [63]

    et al.,Long troughs in the Lyman-αforest below redshift 6 due to islands of neutral hydrogen, Mon

    Keating, Laura C. et al.,Long troughs in the Lyman-αforest below redshift 6 due to islands of neutral hydrogen, Mon. Not. Roy. Astron. Soc.491(2020) 1736-1745 [arXiv:1905.12640]

    Pith/arXiv arXiv 2020

  56. [64]

    Nasir, Fahad et al.,Observing the tail of reionization: neutral islands in the z = 5.5 Lyman-α forest, Monthly Notices of the Royal Astronomical Society494(2020) 3080–3094

    2020

  57. [65]

    Qin, Yuxiang et al.,Percent-level timing of reionization: self-consistent, implicit-likelihood inference from XQR-30+ Lyαforest data, arXiv e-prints (2024) arXiv:2412.00799 [arXiv:2412.00799]

    Pith/arXiv arXiv 2024

  58. [66]

    Bosman, Sarah E. I. et al.,Hydrogen reionization ends by z = 5.3: Lyman-αoptical depth measured by the XQR-30 sample, Mon. Not. Roy. Astron. Soc.514(2022) 55-76 [arXiv:2108.03699]. – 23 –

    Pith/arXiv arXiv 2022

  59. [67]

    Zhu, Yongda et al.,Damping wing-like features in the stacked Lyαforest: Potential neutral hydrogen islands at z<6, Mon. Not. Roy. Astron. Soc.533(2024) L49-L56 [arXiv:2405.12275]

    Pith/arXiv arXiv 2024

  60. [68]

    Becker, G. D. et al.,Evidence of patchy hydrogen reionization from an extreme Lyαtrough below redshift 6, MNRAS447(2015) 3402-3419 [arXiv:1407.4850]

    Pith/arXiv arXiv 2015

  61. [69]

    J.955(2023) 115 [arXiv:2308.04614]

    Zhu, Yongda et al.,Probing Ultralate Reionization: Direct Measurements of the Mean Free Path over 5 ¡ z ¡ 6, Astrophys. J.955(2023) 115 [arXiv:2308.04614]

    Pith/arXiv arXiv 2023

  62. [70]

    Davies, Frederick B et al.,Updated dark pixel fraction constraints on reionization ’s end from the Lyman-series forests of XQR-30, Monthly Notices of the Royal Astronomical Society545 (2025)

    2025

  63. [71]

    Gaikwad, Prakash et al.,Measuring the photoionization rate, neutral fraction, and mean free path of H I ionizing photons at 4.9≤z≤6.0 from a large sample of XShooter and ESI spectra, Mon. Not. Roy. Astron. Soc.525(2023) 4093-4120 [arXiv:2304.02038]

    Pith/arXiv arXiv 2023

  64. [72]

    Kakiichi, Koki et al.,JWST ASPIRE: How Did Galaxies Complete Reionization? Evidence for Excess IGM Transmission around [OIII] Emitters during Reionization, arXiv e-prints, arXiv:2503.07074 (2025) [arXiv:2503.07074]

    Pith/arXiv arXiv 2025

  65. [73]

    The evolving relationship between galaxies and the intergalactic medium in the final stages of reionization, arXiv e-prints (2025) arXiv:2506.03121 [arXiv:2506.03121]

    Kashino, Daichi et al.,EIGER VII. The evolving relationship between galaxies and the intergalactic medium in the final stages of reionization, arXiv e-prints (2025) arXiv:2506.03121 [arXiv:2506.03121]

    Pith/arXiv arXiv 2025

  66. [74]

    Bosman, Sarah E. I. et al.,A measurement of the escaping ionising efficiency of galaxies at redshift 5, arXiv e-prints (2024) arXiv:2409.08315 [arXiv:2409.08315]

    Pith/arXiv arXiv 2024

  67. [75]

    et al.,Large fluctuations in the hydrogen-ionizing background and mean free path following the epoch of reionization, Mon

    Davies, Frederick B. et al.,Large fluctuations in the hydrogen-ionizing background and mean free path following the epoch of reionization, Mon. Not. Roy. Astron. Soc.460(2016) 1328-1339 [arXiv:1509.07131]

    Pith/arXiv arXiv 2016

  68. [76]

    Anson D’Aloisio et al.,LARGE OPACITY V ARIATIONS IN THE HIGH-REDSHIFT LYα FOREST: THE SIGNATURE OF RELIC TEMPERATURE FLUCTUATIONS FROM PATCHY REIONIZATION, The Astrophysical Journal813(2015) L38

    2015

  69. [77]

    J.906(2021) 124 [arXiv:2007.02940]

    Zeng, Chenxiao et al.,Nonequilibrium Temperature Evolution of Ionization Fronts during the Epoch of Reionization, Astrophys. J.906(2021) 124 [arXiv:2007.02940]

    Pith/arXiv arXiv 2021

  70. [78]

    Pawlik, A. H. et al.,Keeping the Universe Ionised: Photoheating and the High-redshift Clumping Factor of the Intergalactic Gas, (2010)

    2010

  71. [79]

    et al.,Constraints on the Evolution of the Ionizing Background and Ionizing Photon Mean Free Path at the End of Reionization, Astrophys

    Davies, Frederick B. et al.,Constraints on the Evolution of the Ionizing Background and Ionizing Photon Mean Free Path at the End of Reionization, Astrophys. J.965(2024) 134 [arXiv:2312.08464]

    Pith/arXiv arXiv 2024

  72. [80]

    et al.,The Predicament of Absorption-dominated Reionization: Increased Demands on Ionizing Sources, Astrophys

    Davies, Frederick B. et al.,The Predicament of Absorption-dominated Reionization: Increased Demands on Ionizing Sources, Astrophys. J.l918(2021) L35 [arXiv:2105.10518]

    Pith/arXiv arXiv 2021

  73. [81]

    J. D. Emberson et al.,THE OPACITY OF THE INTERGALACTIC MEDIUM DURING REIONIZATION: RESOL VING SMALL-SCALE STRUCTURE, The Astrophysical Journal 763(2013) 146

    2013

  74. [82]

    Matthew McQuinn et al.,ON LYMAN-LIMIT SYSTEMS AND THE EVOLUTION OF THE INTERGALACTIC IONIZING BACKGROUND, The Astrophysical Journal743(2011) 82

    2011

  75. [83]

    J.721(2010) 1448-1466 [arXiv:1007.3262]

    Songaila, Antoinette et al.,The Evolution of Lyman Limit Absorption Systems to Redshift Six, Astrophys. J.721(2010) 1448-1466 [arXiv:1007.3262]

    Pith/arXiv arXiv 2010

  76. [84]

    Xavier et al.,On the (Non)Evolution of H I Gas in Galaxies Over Cosmic Time, Astrophys

    Prochaska, J. Xavier et al.,On the (Non)Evolution of H I Gas in Galaxies Over Cosmic Time, Astrophys. J.696(2009) 1543-1547 [arXiv:0811.2003]. – 24 –

    Pith/arXiv arXiv 2009

  77. [85]

    Puchwein, Ewald et al.,The Sherwood-Relics simulations: overview and impact of patchy reionization and pressure smoothing on the intergalactic medium, Mon. Not. Roy. Astron. Soc. 519(2023) 6162-6183 [arXiv:2207.13098]

    Pith/arXiv arXiv 2023

  78. [86]

    et al.,New measurements of the ionizing ultraviolet background over 2 ¡ z ¡ 5 and implications for hydrogen reionization, Mon

    Becker, George D. et al.,New measurements of the ionizing ultraviolet background over 2 ¡ z ¡ 5 and implications for hydrogen reionization, Mon. Not. Roy. Astron. Soc.436(2013) 1023-1039 [arXiv:1307.2259]

    Pith/arXiv arXiv 2013

  79. [87]

    Madau, Piero et al.,Radiative Transfer in a Clumpy Universe. III. The Nature of Cosmological Ionizing Sources, Astrophys. J.514(1999) 648-659 [arXiv:astro-ph/9809058]

    Pith/arXiv arXiv 1999

  80. [88]

    Kuhlen, Michael et al.,Concordance models of reionization: implications for faint galaxies and escape fraction evolution, Mon. Not. Roy. Astron. Soc.423(2012) 862-876 [arXiv:1201.0757]

    Pith/arXiv arXiv 2012

Showing first 80 references.