Pith. sign in

REVIEW 1 major objections 8 minor 108 references

Lyα radiation forces need a three-tier convergence test, not one

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 · glm-5.2

2026-07-10 02:08 UTC pith:5ZOVS7OE

load-bearing objection A practical three-tier convergence framework for Lyα MCRT force estimators, with new analytic benchmarks and a clear demonstration that core-skipping biases internal forces. the 1 major comments →

arxiv 2607.08726 v1 pith:5ZOVS7OE submitted 2026-07-09 astro-ph.GA

Force convergence in Monte Carlo Lyman-alpha radiative transfer

Joshua Kasiri (1) , Aaron Smith (1) , Kevin Lorinc (1) , Olof Nebrin (2) , Kazutaka Kimura (3) ((1) UT Dallas (2) Stockholm (3) Tohoku) This is my paper
classification astro-ph.GA
keywords Lyman-alpha radiative transferMonte Carlo convergenceradiation pressureforce multipliercore skippingmomentum transfer estimatordiffusion limitcoefficient of variation of variance
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.

The paper argues that checking whether a Monte Carlo Lyman-alpha radiative transfer simulation has converged its internal radiation forces requires answering three separate questions in sequence: Does the estimator land on the correct mean value? How large is its sampling noise at finite photon count? And is the estimated noise itself stable under resampling? The authors formalise this as a zeroth-, first-, and second-order hierarchy built from the statistical moments of per-photon contribution distributions. They then apply it to three force estimators—a direct scattering tally, a gradient-of-energy-density reconstruction, and a divergence-of-radiation-pressure reconstruction—across static spherical clouds with both central point-source and uniform-source emission. The central finding is that these three tiers fail independently: an estimator can be precise yet biased, unbiased yet expensive, or apparently smooth while its error bar is unstable. Core-skipping acceleration schemes, which are standard for speeding up Lyα transport, are shown to systematically lower the internal momentum budget rather than merely reducing convergence time. The paper also derives new closed-form diffusion-limit benchmarks for radial acceleration profiles in spherical clouds, against which numerical estimators can be tested for physical bias.

Core claim

The convergence of internal Lyα Monte Carlo radiation-force calculations cannot be captured by a single criterion. It requires a three-tier hierarchy—mean correctness, finite-sampling precision, and variance stability—and these tiers fail independently across different estimators and acceleration schemes. Core-skipping algorithms, while computationally efficient, introduce systematic downward bias in the internal momentum budget because they skip scatterings that contribute real momentum deposition inside the gas.

What carries the argument

The framework treats each completed photon packet's contribution to the force estimator as a single Monte Carlo sample drawn from an unknown distribution P(Y). The raw moments S_k = Σ Y_p^k of these per-packet contributions generate all convergence diagnostics: the first moment gives the signal, the second gives the sampling noise (via fractional error FE = sqrt(Var(S_1))/E[S_1] = CV/sqrt(N_ph)), and the fourth moment governs the stability of the variance estimate itself (via the coefficient of variation of variance, CVoV ≈ sqrt(β_2 - 1)/sqrt(N), where β_2 is the kurtosis). A scaling argument based on the telescoping property of correlated momentum kicks—where the incoming direction of one散射

Load-bearing premise

The scaling argument that predicts optical-depth-independent convergence metrics rests on a heuristic picture of telescoping momentum kicks: the incoming direction of one scattering event is the outgoing direction of the previous one, so intermediate terms partially cancel and the final variance is set by the escape scale rather than the raw number of scatterings. This telescoping picture is stated as an ansatz, not derived from first principles, and the detailed covariance分解

What would settle it

If, in a wider range of optical depths or geometries, the coefficient of variation CV = σ_Y/⟨Y⟩ develops a clear dependence on τ₀ (contradicting Eq. 30), or if the three estimators' fractional errors diverge by orders of magnitude rather than clustering in the same range, the scaling argument based on telescoping covariance would be revealed as an artifact of the limited parameter space tested rather than a fundamental property of the estimator.

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

If this is right

  • Any future Lyα MCRT calculation claiming converged internal forces should report all three tiers: bias against a benchmark, fractional error at the run's photon count, and CVoV to confirm the error bar is trustworthy.
  • Core-skipping schemes used in production galaxy-formation simulations may be systematically underestimating Lyα radiation pressure feedback in optically thick gas, with consequences for predictions of early star formation, black hole growth, and galactic winds.
  • The moment-based hierarchy is estimator-agnostic and could be applied to any Monte Carlo radiative transfer quantity where internal field properties—not just emergent spectra—matter, such as non-LTE level populations or ionization rates.
  • The finding that path-based and event-based estimators have comparable fractional error, despite very different raw variances, suggests that covariance structure—not raw event count—is the primary controller of estimator efficiency, pointing toward covariance-aware importance sampling as an optimisation strategy.
  • The new closed-form radial acceleration profiles for both point-source and uniform-source geometries provide the first spatially resolved benchmarks for validating Lyα force calculations beyond the integrated force multiplier.

Where Pith is reading between the lines

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

  • If the telescoping-covariance scaling (σ²_Y ~ (aτ₀)^{2/3}, yielding optical-depth-independent CV) holds across a wider τ₀ range than tested, one could predict the photon budget for any Lyα force calculation from a single pilot run, regardless of cloud opacity. If it breaks down at extreme optical depths, the convergence cost could grow steeply in ways the current τ₀ ≤ 10⁸ tests would not reveal.
  • The observation that path-based estimators reinforce variance through coherent over-contribution of long-lived photons suggests a natural target for variance reduction: splitting or Russian-roulette strategies that break the coherent path-length correlation without altering the physical mean.
  • If the uniform-source geometric-core undersampling problem is fundamentally a volume-weighted launching issue, then adaptive source-function decomposition—launching photons from coarse spatial strata with compensating weights—might repair the central-region noise without the weight-dispersion penalty that defeated simple volume boosting.

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

1 major / 8 minor

Summary. This paper develops a three-tier convergence hierarchy (zeroth-order mean correctness, first-order finite-sampling precision, second-order variance stability) for internal Lyman-alpha (Lyα) Monte Carlo radiative transfer (MCRT) force calculations. The authors derive new diffusion-limit analytic benchmarks for radial acceleration profiles in static spherical clouds for both central point-source and uniform-source emission (Eqs. 6–17), validate them against MCRT simulations (Fig. 2), and then apply the convergence hierarchy to three force estimators: direct event-based scattering, gradient-of-energy-density, and divergence-of-radiation-pressure. The key practical findings are: (1) core-skipping algorithms systematically bias internal momentum deposition downward (Figs. 3–5), (2) path-based estimators carry additional reconstruction bias for point-source geometries that worsens at coarse spatial resolution (Fig. 6), (3) all three estimators have comparable fractional error despite different raw variance structures, which the authors attribute to intra-history covariance effects, and (4) the three estimators are not interchangeable and must be evaluated separately for bias, variance, and cost. The paper is well-structured, the analytic benchmarks are a useful contribution, and the convergence framework is practically relevant for the Lyα MCRT community.

Significance. The paper makes a solid contribution to the methodology of Lyα radiative transfer. The new closed-form diffusion-limit radial acceleration profiles (Eqs. 6, 12) and cumulative force-multiplier expressions (Eqs. 7, 13) are a genuine addition to the analytic literature and are validated against independent MCRT simulations. The three-tier convergence hierarchy is standard statistical practice (bias, variance, variance-of-variance) but its systematic application to internal Lyα force estimators—including the distinction between physical accuracy and statistical precision—is practically useful and not previously codified in this form. The empirical demonstration that core-skipping biases internal forces (not just spectra) is important for the community. The scaling argument in §2.4 is honestly flagged as heuristic and deferred to a companion paper, which is appropriate. The framework is falsifiable: the CV~constant prediction (Eq. 30) and the bias trends with τ₀ are testable against future simulations at higher optical depth or in different geometries.

major comments (1)
  1. §2.4, Eqs. (29)–(30): The ansatz σ²_Y ~ (aτ₀)^{2/3} is the critical step producing the optical-depth-independent CV prediction (Eq. 30). It rests on the 'telescoping' argument (Eq. 26) that intra-history covariance suppresses raw kick variance down to the escape scale, but this is asserted heuristically, not derived. The empirical test spans τ₀ = 10⁵–10⁸ (three decades), and the prediction CV ~ constant is a weak claim: many functional forms (e.g., CV ~ τ₀^α with |α| ≲ 0.1) would be indistinguishable from constant over this range. This concern is load-bearing for the interpretation that all three estimators share comparable FE for fundamental reasons (§4.2.1) rather than as a coincidence of the tested range. The authors should either (a) add a quantitative test of the CV~constant prediction (e.g., a power-law fit to CV vs. τ₀ with the exponent and its uncertainty reported) or (b) more谨慎地
minor comments (8)
  1. §2.4, Eq. (22): The independent-kick expectation CV ~ a^{-1/3} τ₀^{1/6} is presented as a contrast to the final ansatz, but the reader would benefit from a one-sentence explanation of why the τ₀^{1/6} scaling arises from N_scat ~ τ₀ and σ_Y ~ τ₀^{1/2}.
  2. Fig. 3: The violin distributions are informative but the color coding for no-core-skipping vs. dynamical core-skipping is not clearly distinguished in the caption. A brief note on how to read the violin widths would help the reader.
  3. Fig. 5, bottom row: The path-based estimator bias is defined relative to the matching x_crit scattering estimator, which is a different baseline than the top row. This is stated in the text but could be made more prominent in the figure caption to avoid confusion.
  4. §4.1.5, Fig. 7: The relative error curves deviate from N^{-1/2} at the largest group sizes due to small group counts. The caption notes this, but adding a shaded region or vertical line indicating where the number of independent groups drops below ~10 would clarify the reliable range.
  5. Appendix B: The volume-boosted tests are a useful supplement. The conclusion that volume boosting is not effective is clear, but a brief note on whether alternative importance-sampling strategies (e.g., source-position biasing with optimized weights) might work would be a helpful pointer for readers facing this issue.
  6. §4.2.3, Fig. 10: The runtime scaling exponents (τ₀^{0.961} and τ₀^{0.959}) are quoted to three significant figures. Given the likely scatter in timing measurements, reporting two significant figures would be more appropriate.
  7. The paper uses 'force multiplier' notation M_F inconsistently: sometimes as M_F (Eq. 4), sometimes as M^scat_F, M^{∇u}_F, M^{∇·P}_F (Fig. 5). A brief notation summary would improve readability.
  8. References: Several arXiv preprints are cited (e.g., Byrohl & Nelson 2025, Li & Zheng 2026, Menon & Smith 2026, Nebrin et al. 2026). If any have been published since submission, the references should be updated.

Circularity Check

0 steps flagged

No significant circularity; the framework is self-contained against external benchmarks and the heuristic scaling argument is honestly flagged as non-load-bearing.

full rationale

The paper's central practical claims—the three-tier convergence hierarchy, the core-skipping bias, and the estimator non-interchangeability—are established empirically and through standard statistical definitions, not through circular derivation. The analytic benchmarks (Eqs. 6–17) derive from Lao & Smith (2020), which shares author A. Smith with this paper, but those are parameter-free diffusion-limit solutions validated against independent MCRT simulations in Fig. 2, satisfying the non-circularity criterion. The bias truth values use the no-core-skipping scattering estimator as reference (zero by construction in Fig. 5), but this is explicitly stated as a relative comparison, not a physical truth claim. The §2.4 scaling argument (σ²_Y ~ (aτ₀)^{2/3}, Eq. 29) is the only potentially weak link: it produces the optical-depth-independent CV prediction (Eq. 30) via a heuristic 'telescoping' argument (Eq. 26) that is asserted, not derived. However, the authors explicitly label this as 'only intended as a scaling argument, not a closed-form statistical theory' and defer detailed covariance analysis to a companion paper. Crucially, this ansatz supports the interpretation of why estimators share comparable FE, but it is not load-bearing for the central framework or the bias result, which stand on empirical evidence (Figs. 3–5, 8–11) independent of the scaling argument. No prediction or first-principles result reduces to its inputs by construction. The one minor self-citation (Lao & Smith 2020) is not load-bearing because it is independently validated here. Score 1 reflects this minor self-citation with no circularity in the central claims.

Axiom & Free-Parameter Ledger

2 free parameters · 4 axioms · 0 invented entities

No new physical entities are introduced. The free parameters are algorithmic choices (core-skipping thresholds, diagnostic group sizes) rather than physically fitted constants. The key ad hoc element is the variance-scaling ansatz in §2.4, which is honestly flagged as heuristic.

free parameters (2)
  • Core-skipping threshold x_crit = 0, 1, 2, 3, dynamical
    Swept as a parameter; not fitted to data but chosen as algorithmic prescriptions to test.
  • Group size N for convergence diagnostics = varied from ~10^2 to ~10^5
    Diagnostic partition parameter for computing group-level statistics; not a physical parameter.
axioms (4)
  • domain assumption Diffusion approximation valid when aτ₀ ≫ 10³ (Nebrin et al. 2025)
    Invoked in §2 to derive analytic benchmarks; validated numerically in Fig. 2 for τ₀=10⁸.
  • domain assumption Photon packets are independent Monte Carlo samples (Cov(Y_p, Y_q) ≈ Var(Y_p)δ_pq)
    Stated in Eq. 27, §2.4; underpins the N^{-1/2} scaling of fractional error and the group-based diagnostics.
  • ad hoc to paper Intra-history covariance suppresses raw kick variance via telescoping (σ²_Y ~ R·σ²_kick with R < 1)
    Introduced in §2.4 as heuristic; the specific scaling σ²_Y ~ (aτ₀)^{2/3} (Eq. 29) is an ansatz, not derived. Detailed analysis deferred to Kasiri et al. (in prep.).
  • domain assumption Fick's Law closure: F ≈ -c∇u/(3k) for diffusive radiation
    Used in Eq. 4 to connect force multiplier to energy density gradient; standard in diffusion-limit radiative transfer.

pith-pipeline@v1.1.0-glm · 32603 in / 2244 out tokens · 369148 ms · 2026-07-10T02:08:42.810822+00:00 · methodology

0 comments
read the original abstract

Monte Carlo radiative transfer (MCRT) is widely used to model Lyman-alpha (Lya) resonant-line transport, but convergence is difficult to assess in optically thick media where photons undergo many scatterings before escape. This is especially important for internal quantities such as radiative acceleration and the force multiplier, which depend on momentum deposition throughout the gas rather than only on emergent spectra. We study the convergence of Lya MCRT momentum-transfer estimators in static spherical clouds. We first establish diffusion-limit benchmarks for radial acceleration profiles and integrated force multipliers, then develop a moment-based framework for diagnosing convergence from the photon-packet contribution distribution. This framework separates three distinct questions: whether the estimator converges to the correct mean, how large its finite-sampling uncertainty is, and whether the estimated uncertainty is itself stable. We apply this hierarchy to the direct event-based scattering estimator, a gradient-of-energy-density estimator, and a divergence-of-radiation-pressure estimator. Zeroth-order convergence is assessed with profile comparisons, integrated force-multiplier bias, and finite-group relative error. First-order convergence is quantified with fractional error, the photon number required to reach a target precision, and the corresponding runtime requirement. Second-order convergence is tested with the coefficient of variation of variance, which measures the reliability of the variance estimate used in the first-order diagnostics. Core-skipping prescriptions, source geometry, estimator construction, and spatial resolution enter this hierarchy in different ways. Our results provide a practical convergence framework for internal Lya MCRT force calculations and show why statistical precision, computational cost, and physical accuracy must be evaluated separately.

Figures

Figures reproduced from arXiv: 2607.08726 by Aaron Smith (1), Joshua Kasiri (1), Kazutaka Kimura (3) ((1) UT Dallas (2) Stockholm (3) Tohoku), Kevin Lorinc (1), Olof Nebrin (2).

Figure 1
Figure 1. Figure 1: Schematic picture of Lyα photon transport in an optically thick, static neutral hydrogen cloud. Near line centre, photons undergo many short mean-free￾path core scatterings, resulting in approximately isotropic momentum kicks with little net radial drift but significant nonzero variance. During rare wing excursions, the propagation distances are larger and photons can make coherent radially outward progres… view at source ↗
Figure 2
Figure 2. Figure 2: Numerical validation of the analytic diffusion-limit solutions for a static spherical cloud with τ0 = 108 , xcrit = 0, and Nph = 106 . Left: Point-source radial profiles, normalised as R 3ρa(r)/(L /c) and cR2u(r)/L for acceleration and energy density respectively, as given by Eqs. (6) and (8). Right: Uniform-source radial profiles, normalised the same as point-source, as given by Eqs. (12) and (14). The da… view at source ↗
Figure 3
Figure 3. Figure 3: Integrated force multiplier distributions for central point-source and uniform-source emission as a function of line-centre optical depth. Violin distributions show the packet-level contributions to MF for the direct scattering estimator, with colours indicating the no-core-skipping and dynamical core-skipping cases. Gray dashed and dotted curves show the corresponding path-based reconstructions from ∇u an… view at source ↗
Figure 4
Figure 4. Figure 4: Radial acceleration profiles for point-source and uniform-source emission. The top row shows the direct scattering estimator a scat and the bottom two rows show the gradient-of-energy-density a ∇u and radiation-pressure-divergence a ∇·P reconstruction relative to the direct scattering case. Colours indicate line-centre optical depth, while line styles indicate the core-skipping prescription xcrit. Black cu… view at source ↗
Figure 5
Figure 5. Figure 5: Integrated force-multiplier bias as a function of optical depth for the three force constructions. The top row bias is computed relative to the no-core-skipping direct scattering estimator at each optical depth, so the xcrit = 0 scattering curve is zero by construction. The bottom row shows M∇u F and M∇·P F relative to Mscat F of the corresponding optical depth and core skipping prescription. Columns show … view at source ↗
Figure 6
Figure 6. Figure 6: Resolution bias of the path-based force reconstructions at τ0 = 108 . The horizontal axis gives the maximum radial cell width normalised by the cloud radius (near 0 represents native bin count and 1 represents single bin count), and the vertical axis gives the integrated force-multiplier bias relative to the high-resolution reference calculation. Curves with filled circles show the finite-volume stencil, w… view at source ↗
Figure 7
Figure 7. Figure 7: Finite-group relative error as a function of photon count per group. Top row shows the direct scattering estimator, while the bottom row displays the gradient-of￾energy-density reconstruction relative to scattering estimator; columns show point-source and uniform-source emission. The lower axis gives the photon count in each group, while the upper axis gives the corresponding number of independent groups. … view at source ↗
Figure 8
Figure 8. Figure 8: Radial profiles of the fractional error for the three force constructions. Rows show FE(a scat), FE(a ∇u ), and FE(a ∇·P ); columns show point-source and uniform￾source emission. Colours indicate optical depth and line styles indicate the core-skipping prescription. For point-source emission, the fractional errors are small across most of the domain, with localised features appearing most clearly in the ∇ … view at source ↗
Figure 9
Figure 9. Figure 9: Photon number required to reach a target integrated fractional error of 1%. Rows correspond to the three force constructions, and columns show point-source and uniform-source emission. The required photon count is inferred from the measured fractional error using the expected N −1/2 Monte Carlo scaling. Point-source calculations typically require only ∼ 103–104 photons for the integrated force metrics show… view at source ↗
Figure 10
Figure 10. Figure 10: Estimated normalised runtime required to reach a target integrated fractional error of 1% for the direct scattering estimator. The required photon number is converted to a wall-clock time using the measured time per photon for each run and then multiplied by the number of ranks and threads utilized. Colours show the integrated force-multiplier bias of each core-skipping prescription, and line styles indic… view at source ↗
Figure 11
Figure 11. Figure 11: Coefficient of variation of variance as a function of photon count per group. Rows show the direct scattering estimator and the gradient-of-energy-density reconstruction relative to the scattering estimator; columns show point-source and uniform-source emission. The lower axis gives the photon count per group, while the upper axis gives the corresponding number of independent groups. Colours indicate opti… view at source ↗

discussion (0)

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

Reference graph

Works this paper leans on

108 extracted references · 108 canonical work pages · 62 internal anchors

  1. [1]

    Planck 2018 results. VI. Cosmological parameters. , keywords =. doi:10.1051/0004-6361/201833910 , archivePrefix =. 1807.06209 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201833910 2018

  2. [2]

    , year = 1967, month = mar, volume =

    Are Young Galaxies Visible?. , year = "1967", month = "Mar", volume =. doi:10.1086/149079 , adsurl =

    work page doi:10.1086/149079 1967

  3. [3]

    Lyman Alpha Emitting Galaxies as a Probe of Reionization

    Ly Emitting Galaxies as a Probe of Reionisation. , keywords =. 2014. doi:10.1017/pasa.2014.33 , archivePrefix =. 1406.7292 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1017/pasa.2014.33 2014

  4. [4]

    1973", month =

    The scattering of resonance-line radiation in the limit of large optical depth. , year = "1973", month = "Jan", volume =. doi:10.1093/mnras/162.1.43 , adsurl =

    work page doi:10.1093/mnras/162.1.43 1973

  5. [5]

    , keywords =

    The Transfer of Resonance-Line Radiation in Static Astrophysical Media. , keywords =. 1990. doi:10.1086/168375 , adsurl =

    work page doi:10.1086/168375 1990

  6. [6]

    Scattered Lyman-alpha Radiation Around Sources Before Cosmological Reionization

    Scattered Ly Radiation around Sources before Cosmological Reionization. , keywords =. 1999. doi:10.1086/307844 , archivePrefix =. astro-ph/9902180 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/307844 1999

  7. [7]

    Ly Radiation from Collapsing Protogalaxies. I. Characteristics of the Emergent Spectrum. , keywords =. 2006. doi:10.1086/506243 , archivePrefix =. astro-ph/0510407 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/506243 2006

  8. [8]

    Auer, Lawrence H. , doi =. ApJ , month =

    work page

  9. [9]

    ApJ , keywords =

    Ahn, Sang-Hyeon and Lee, Hee-Won and Lee, Hyung Mok , doi =. ApJ , keywords =

    work page

  10. [10]

    ApJ , keywords =

    Zheng, Zheng and Miralda-Escud\'. ApJ , keywords =. doi:10.1086/342400 , issn =

    work page doi:10.1086/342400

  11. [11]

    Osterbrock, Donald E. , doi =. ApJ , month =

    work page

  12. [12]

    , year = 1972, month = jun, volume =

    The Escape of Resonance-Line Radiation from Extremely Opaque Media. , year = 1972, month = jun, volume =. doi:10.1086/151503 , adsurl =

    work page doi:10.1086/151503 1972

  13. [13]

    Adams, Thomas F. , doi =. ApJ , month =

    work page

  14. [14]

    and Piedipalumbo, E

    Lyman radiative transfer in a multiphase medium. , keywords =. 2006. doi:10.1111/j.1365-2966.2005.09870.x , archivePrefix =. astro-ph/0507586 , primaryClass =

    work page doi:10.1111/j.1365-2966.2005.09870.x 2006

  15. [15]

    , issn =

    Unno, W. , issn =. PASJ , pages =

    work page

  16. [16]

    Hummer, D. G. , doi =. MNRAS , pages =

    work page

  17. [17]

    and Dell'Antonio, Ian P

    Rybicki, George B. and Dell'Antonio, Ian P. , doi =. ApJ , keywords =

    work page

  18. [18]

    ApJ , keywords =

    Tasitsiomi, Argyro , doi =. ApJ , keywords =

    work page

  19. [19]

    On the transfer of resonant-line radiation in mesh simulations

    On the Transfer of Resonant-Line Radiation in Mesh Simulations. , keywords =. doi:10.1086/505682 , archivePrefix =. astro-ph/0601562 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/505682

  20. [20]

    , keywords =

    The scattering of Ly radiation in the intergalactic medium: numerical methods and solutions. , keywords =. doi:10.1111/j.1365-2966.2012.21917.x , archivePrefix =. 1206.6759 , primaryClass =

    work page doi:10.1111/j.1365-2966.2012.21917.x 2012

  21. [21]

    and Dubois, Y

    Verhamme, A. and Dubois, Y. and Blaizot, J. and Garel, T. and Bacon, R. and Devriendt, J. and Guiderdoni, B. and Slyz, A. , doi =. A&A , keywords =

    work page

  22. [22]

    and Sommer-Larsen, Jesper , doi =

    Laursen, Peter and Razoumov, Alexei O. and Sommer-Larsen, Jesper , doi =. ApJ , keywords =

    work page

  23. [23]

    Discrete diffusion Lyman-alpha radiative transfer

    Discrete diffusion Lyman radiative transfer. , keywords =. 2018. doi:10.1093/mnras/sty1509 , archivePrefix =. 1709.10187 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/sty1509 2018

  24. [24]

    The Lyman-alpha signature of the first galaxies

    The Lyman signature of the first galaxies. , keywords =. 2015. doi:10.1093/mnras/stv565 , archivePrefix =. 1409.4480 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stv565 2015

  25. [25]

    Radiative processes in astrophysics. 1979

    work page 1979

  26. [26]

    1975", month =

    Uniform asymptotic expansions in transport theory with small mean free paths, and the diffusion approximation. Journal of Mathematical Physics , year = "1975", month = "Apr", volume =. doi:10.1063/1.522618 , adsurl =

    work page doi:10.1063/1.522618 1975

  27. [27]

    , keywords =

    Bipolar reflection nebulae : Monte Carlo simulations. , keywords =. doi:10.1086/161780 , adsurl =

    work page doi:10.1086/161780

  28. [28]

    Chasing Lyman alpha-emitting galaxies at z = 8.8

    Lyman -emitting galaxies in the epoch of reionization. , keywords =. doi:10.1051/0004-6361/201833645 , archivePrefix =. 1806.07392 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201833645

  29. [29]

    The physics of Lyman-alpha escape from high-redshift galaxies

    The physics of Lyman escape from high-redshift galaxies. , keywords =. doi:10.1093/mnras/sty3483 , archivePrefix =. 1810.08185 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/sty3483

  30. [30]

    Ly{\alpha} emission from galaxies in the Epoch of Reionization

    Ly emission from galaxies in the Epoch of Reionization. , keywords =. doi:10.1093/mnras/stz980 , archivePrefix =. 1903.06185 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stz980 1903

  31. [31]

    RASCAS: RAdiation SCattering in Astrophysical Simulations

    RASCAS: RAdiation SCattering in Astrophysical Simulations. , keywords =. doi:10.1051/0004-6361/201834961 , archivePrefix =. 2001.11252 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201834961 2001

  32. [32]

    ART$^2$: A 3D Parallel Multi-wavelength Radiative Transfer Code for Continuum and Atomic and Molecular Lines

    ART ^ 2 : A 3D Parallel Multi-wavelength Radiative Transfer Code for Continuum and Atomic and Molecular Lines. , keywords =. doi:10.1093/mnras/staa733 , archivePrefix =. 2001.11146 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/staa733 2001

  33. [33]

    On the effect of Lyman alpha trapping during the initial collapse of massive black hole seeds

    On the effect of Lyman trapping during the initial collapse of massive black hole seeds. , keywords =. doi:10.1093/mnras/stx2074 , archivePrefix =. 1706.01467 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stx2074

  34. [34]

    Lyman-alpha radiation hydrodynamics of galactic winds before cosmic reionization

    Lyman radiation hydrodynamics of galactic winds before cosmic reionization. , keywords =. doi:10.1093/mnras/stw2591 , archivePrefix =. 1607.07166 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stw2591

  35. [35]

    Ly-alpha Radiative Transfer: Monte-Carlo Simulation of the Wouthuysen-Field Effect

    Ly Radiative Transfer: Monte Carlo Simulation of the Wouthuysen-Field Effect. , keywords =. doi:10.3847/1538-4365/aba2d6 , archivePrefix =. 2005.00238 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4365/aba2d6 2005

  36. [36]

    Lyman-alpha radiation pressure: an analytical exploration

    Lyman-alpha radiation pressure: an analytical exploration. , keywords =. doi:10.1093/mnras/stab876 , archivePrefix =. 2103.14655 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stab876

  37. [37]

    The impact of gas bulk rotation on the lyman-alpha line

    The Impact of Gas Bulk Rotation on the Ly Line. , keywords =. doi:10.1088/0004-637X/795/2/120 , archivePrefix =. 1408.2561 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/795/2/120

  38. [38]

    Lyman-$\alpha$ photons through rotating outflows

    Lyman photons through rotating outflows. , keywords =. doi:10.1093/mnras/sty3009 , archivePrefix =. 1811.01266 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/sty3009

  39. [39]

    , keywords =

    Line transfer through clumpy, large-scale outflows: Ly absorption and haloes around star-forming galaxies. , keywords =. doi:10.1111/j.1365-2966.2012.21131.x , archivePrefix =. 1203.3803 , primaryClass =

    work page doi:10.1111/j.1365-2966.2012.21131.x 2012

  40. [40]

    Radiation Hydrodynamics

    work page

  41. [41]

    Resonant-line radiative transfer within power-law density profiles

    Resonant-line radiative transfer within power-law density profiles. , keywords =. doi:10.1093/mnras/staa2198 , archivePrefix =. 2005.09692 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/staa2198 2005

  42. [42]

    The Radiative Equilibrium of an Expanding Planetary Nebula. I. Radiation Pressure in Lyman-. , year = 1945, month = nov, volume =. doi:10.1086/144771 , adsurl =

    work page doi:10.1086/144771 1945

  43. [43]

    , keywords =

    Fermi Acceleration of Lyman-Alpha Photons by Shocks. , keywords =. doi:10.1086/185241 , adsurl =

    work page doi:10.1086/185241

  44. [44]

    Blue Wings and Bumps via Fermi-like Acceleration of Lyman-alpha photons across Shocks

    Blue wings and bumps via Fermi-like acceleration of Ly photons across shocks. , keywords =. doi:10.1093/mnras/stv2340 , archivePrefix =. 1509.07364 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stv2340

  45. [45]

    Astrophysics , year = 1981, month = jan, volume =

    Thermalization Length of Resonance Radiation in the Case of Partial Frequency Redistribution. Astrophysics , year = 1981, month = jan, volume =. doi:10.1007/BF01014298 , adsurl =

    work page doi:10.1007/bf01014298 1981

  46. [46]

    Improved Fokker-Planck Equation for Resonance Line Scattering

    Improved Fokker-Planck Equation for Resonance-Line Scattering. , keywords =. doi:10.1086/505327 , archivePrefix =. astro-ph/0603047 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/505327

  47. [47]

    , year = 1959, month = may, volume =

    The Time Relaxation of a Resonance-Line Profile. , year = 1959, month = may, volume =. doi:10.1086/146654 , adsurl =

    work page doi:10.1086/146654 1959

  48. [48]

    , year = 1973, month = sep, volume =

    On the Existence of Classical Microturbulence. , year = 1973, month = sep, volume =. doi:10.1086/152344 , adsurl =

    work page doi:10.1086/152344 1973

  49. [49]

    Lyman Radiation Hydrodynamics of Turbulent H II Regions in Molecular Clouds: A Physical Origin of LyC Leakage and the Associated Ly$\alpha$ Spectra

    Radiation Hydrodynamics of Turbulent H II Regions in Molecular Clouds: A Physical Origin of LyC Leakage and the Associated Ly Spectra. , keywords =. doi:10.3847/1538-4357/abc2d9 , archivePrefix =. 1905.02480 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/abc2d9 1905

  50. [50]

    Understanding the escape of LyC and Ly$\alpha$ photons from turbulent clouds

    Understanding the escape of LyC and Ly photons from turbulent clouds. , keywords =. doi:10.1093/mnras/stz989 , archivePrefix =. 1901.05990 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stz989 1901

  51. [51]

    arXiv e-prints , keywords =

    A systematic study of the escape of LyC and Ly photons from star-forming, magnetized turbulent clouds. arXiv e-prints , keywords =

    work page

  52. [52]

    3D Ly radiation transfer. I. Understanding Ly line profile morphologies. , keywords =. doi:10.1051/0004-6361:20065554 , archivePrefix =. astro-ph/0608075 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361:20065554

  53. [53]

    Lyman-alpha radiative transfer during the Epoch of Reionization: contribution to 21-cm signal fluctuations

    Lyman-alpha radiative transfer during the epoch of reionization: contribution to 21-cm signal fluctuations. , keywords =. doi:10.1051/0004-6361:20077965 , archivePrefix =. 0707.2483 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361:20077965

  54. [54]

    , keywords =

    ART ^ 2 : coupling Ly line and multi-wavelength continuum radiative transfer. , keywords =. doi:10.1111/j.1365-2966.2012.21228.x , archivePrefix =. 1109.4891 , primaryClass =

    work page doi:10.1111/j.1365-2966.2012.21228.x 2012

  55. [55]

    A systematic study of Lyman-Alpha transfer through outflowing shells: Model parameter estimation

    A Systematic Study of Lyman- Transfer through Outflowing Shells: Model Parameter Estimation. , keywords =. doi:10.1088/0004-637X/812/2/123 , archivePrefix =. 1506.03836 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/812/2/123

  56. [56]

    Ly$\alpha$ Spectra from Multiphase Outflows, and their Connection to Shell Models

    Lyman- Spectra from Multiphase Outflows, and their Connection to Shell Models. , keywords =. doi:10.3847/0004-637X/826/1/14 , archivePrefix =. 1604.06805 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/0004-637x/826/1/14

  57. [57]

    On the (non-)enhancement of the Lyman \alpha\ equivalent width by a multiphase interstellar medium

    On the (Non-)Enhancement of the Ly Equivalent Width by a Multiphase Interstellar Medium. , keywords =. doi:10.1088/0004-637X/766/2/124 , archivePrefix =. 1211.2833 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/766/2/124

  58. [58]

    Lyman-alpha radiative transfer: Modeling spectrum and surface brightness profile of Lyman-alpha emitting galaxies at z=3-6

    Ly Radiative Transfer: Modeling Spectrum and Surface Brightness Profiles of Ly -emitting Galaxies at Z = 3-6. , keywords =. doi:10.3847/1538-4357/abac02 , archivePrefix =. 2007.08172 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/abac02 2007

  59. [59]

    Beamed Lyman Alpha Emission through Outflow-Driven Cavities

    Beamed Ly emission through outflow-driven cavities. , keywords =. doi:10.1051/0004-6361/201322949 , archivePrefix =. 1401.4860 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201322949

  60. [60]

    Anisotropic Lyman-alpha Emission

    Anisotropic Lyman-alpha Emission. , keywords =. doi:10.1088/0004-637X/794/2/116 , archivePrefix =. 1308.1405 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/794/2/116

  61. [61]

    The<scp>thesan</scp>project: Lyman-α emission and transmission during the Epoch of Reionization , volume=

    Smith, A and Kannan, R and Garaldi, E and Vogelsberger, M and Pakmor, R and Springel, V and Hernquist, L , year=. The<scp>thesan</scp>project: Lyman-α emission and transmission during the Epoch of Reionization , volume=. Monthly Notices of the Royal Astronomical Society , publisher=. doi:10.1093/mnras/stac713 , number=

    work page doi:10.1093/mnras/stac713

  62. [62]

    The physics of Lyman-alpha escape from disc-like galaxies

    The physics of Lyman- escape from disc-like galaxies. , keywords =. doi:10.1093/mnras/stac2641 , archivePrefix =. 2111.13721 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stac2641

  63. [63]

    Lyman-$\alpha$ feedback prevails at Cosmic Dawn: Implications for the first galaxies, stars, and star clusters

    Lyman- feedback prevails at Cosmic Dawn: implications for the first galaxies, stars, and star clusters. , keywords =. doi:10.1093/mnras/staf038 , archivePrefix =. 2409.19288 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/staf038

  64. [64]

    Lyman-alpha Pressure Strongly Enhances Pre-Supernova Feedback at Cosmic Dawn: The First Multi-Dimensional Lyman-alpha Radiation Hydrodynamics Simulations

    Lyman-alpha Pressure Strongly Enhances Pre-Supernova Feedback at Cosmic Dawn: The First Multi-Dimensional Lyman-alpha Radiation Hydrodynamics Simulations. arXiv e-prints , keywords =. doi:10.48550/arXiv.2606.02711 , archivePrefix =. 2606.02711 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2606.02711

  65. [65]

    Lyman-alpha Radiation Pressure in Dense Star Clusters: Implications for Star Formation and Winds at Cosmic Dawn

    Lyman-alpha Radiation Pressure in Dense Star Clusters: Implications for Star Formation and Winds at Cosmic Dawn. arXiv e-prints , keywords =. doi:10.48550/arXiv.2605.13982 , archivePrefix =. 2605.13982 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2605.13982

  66. [66]

    A Novel Solution for Resonant Scattering Using Self-Consistent Boundary Conditions

    A Novel Solution for Resonant Scattering Using Self-consistent Boundary Conditions. , keywords =. doi:10.3847/1538-4357/ac7724 , archivePrefix =. 2205.05082 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/ac7724

  67. [67]

    Intergalactic Lyman-$\alpha$ haloes before reionization are detectable with JWST

    Intergalactic Lyman- haloes before reionization are detectable with JWST. , keywords =. doi:10.1088/1475-7516/2024/10/059 , archivePrefix =. 2404.18998 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1475-7516/2024/10/059 2024

  68. [68]

    Impact of Lyman alpha pressure on metal-poor dwarf galaxies

    Impact of Lyman alpha pressure on metal-poor dwarf galaxies. , keywords =. doi:10.1093/mnras/sty126 , archivePrefix =. 1801.04952 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/sty126

  69. [69]

    On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests

    On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests. arXiv e-prints , keywords =. doi:10.48550/arXiv.1509.02237 , archivePrefix =. 1509.02237 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1509.02237

  70. [70]

    Lyman-alpha resonant-line radiative transfer in expanding media

    Lyman- resonant-line radiative transfer in expanding media. , keywords =. doi:10.1093/mnras/staf961 , archivePrefix =. 2501.01928 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/staf961

  71. [71]

    Arepo-MCRT: Monte Carlo Radiation Hydrodynamics on a Moving Mesh

    AREPO-MCRT: Monte Carlo Radiation Hydrodynamics on a Moving Mesh. , keywords =. doi:10.3847/1538-4357/abc47e , archivePrefix =. 2008.01750 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/abc47e 2008

  72. [72]

    The Failure of Monte Carlo Radiative Transfer at Medium to High Optical Depths

    The Failure of Monte Carlo Radiative Transfer at Medium to High Optical Depths. , keywords =. doi:10.3847/1538-4357/aac824 , archivePrefix =. 1805.09502 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/aac824

  73. [73]

    , keywords =

    Energy transfer by the scattering of resonant photons. , keywords =. doi:10.1111/j.1365-2966.2006.10632.x , archivePrefix =. astro-ph/0603855 , primaryClass =

    work page doi:10.1111/j.1365-2966.2006.10632.x 2006

  74. [74]

    and White, S

    Ly -driven outflows around star-forming galaxies. , keywords =. doi:10.1111/j.1365-2966.2008.13920.x , archivePrefix =. 0807.2645 , primaryClass =

    work page doi:10.1111/j.1365-2966.2008.13920.x 2008

  75. [75]

    Suppression of globular cluster formation in metal-poor gas clouds by Lyman-alpha radiation feedback

    Suppression of globular cluster formation in metal-poor gas clouds by Lyman radiation feedback. , keywords =. doi:10.1093/mnrasl/sly018 , archivePrefix =. 1801.10473 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnrasl/sly018

  76. [76]

    Bulletin of the Astronomical Institutes of Czechoslovakia , keywords =

    Derivatives of the Voigt Functions. Bulletin of the Astronomical Institutes of Czechoslovakia , keywords =

    work page

  77. [77]

    Journal of Applied Mechanics , year = 1991, month = jan, volume =

    The Fokker-Planck Equation: Methods of Solution and Application, 2nd ed. Journal of Applied Mechanics , year = 1991, month = jan, volume =. doi:10.1115/1.2897281 , adsurl =

    work page doi:10.1115/1.2897281 1991

  78. [78]

    , keywords =

    Computing radiative equilibria with Monte Carlo techniques. , keywords =

    work page

  79. [79]

    Monte Carlo transition probabilities

    Monte Carlo transition probabilities. , keywords =. doi:10.1051/0004-6361:20011756 , archivePrefix =. astro-ph/0107377 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361:20011756

  80. [80]

    and Hayashi, Eric and Power, Chris and Jenkins, Adrian and Frenk, Carlos S

    A three-dimensional Monte Carlo photoionization code for modelling diffuse ionized gas. , keywords =. doi:10.1111/j.1365-2966.2004.07458.x , archivePrefix =. astro-ph/0311584 , primaryClass =

    work page doi:10.1111/j.1365-2966.2004.07458.x 2004

Showing first 80 references.