arxiv: 2603.29947 · v2 · submitted 2026-03-31 · 🌌 astro-ph.CO

Recognition: 2 theorem links

· Lean Theorem

Constraining Lyman-Werner Feedback from Velocity Acoustic Oscillations in the Cosmic Dawn 21 cm Signal

Xi Du , Bin Yue , Furen Deng , Yidong Xu , Yan Gong , Ely D. Kovetz , Xuelei Chen

Authors on Pith no claims yet

Pith reviewed 2026-05-13 23:11 UTC · model grok-4.3

classification 🌌 astro-ph.CO

keywords Lyman-Werner feedbackvelocity acoustic oscillationscosmic dawn21 cm signalLyman-Werner radiationPopulation III starsSKA observationssemi-numerical simulations

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The pith

Velocity acoustic oscillations in the cosmic dawn 21 cm signal can constrain Lyman-Werner feedback efficiency from the first stars.

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

The paper seeks to establish that wiggles imprinted by dark matter-baryon streaming velocities on the 21 cm power spectrum serve as a sensitive indirect probe of how Lyman-Werner radiation from early stars suppresses star formation in small halos. If Lyman-Werner feedback raises the minimum halo mass for molecular hydrogen cooling above the streaming-sensitive range, these velocity acoustic oscillation features are strongly suppressed, allowing their amplitude to reveal the feedback strength. This matters because direct observations of Population III stars are unavailable, so an indirect signature could tighten constraints on when and how the first stars formed. Semi-numerical lightcone simulations combined with a convolutional neural network show that the feedback efficiency parameter can be recovered accurately when instrumental noise is ignored. Under realistic SKA-low conditions with optimistic foreground removal, however, integration times longer than 10,000 hours are required for useful constraints.

Core claim

The VAO features arise because dark matter-baryon relative streaming velocity suppresses star formation in low-mass halos and imprints characteristic oscillations in the 21 cm power spectrum; these oscillations are suppressed once Lyman-Werner feedback raises the cooling threshold mass above the streaming-sensitive regime, and multi-frequency angular power spectra extracted from semi-numerical 21 cm lightcone simulations allow a CNN to recover the LW feedback efficiency and baseline cooling threshold accurately in the absence of instrumental noise.

What carries the argument

Velocity acoustic oscillation (VAO) features in the 21 cm power spectrum, whose amplitude depends on whether the Lyman-Werner-regulated cooling threshold mass lies inside or outside the range affected by dark matter-baryon streaming velocities.

If this is right

The LW feedback efficiency parameter can be recovered to high accuracy from the VAO wiggles when instrumental noise is absent.
Raising the cooling threshold mass above the streaming-velocity regime strongly damps the VAO amplitude, providing a direct link between feedback strength and observable 21 cm features.
For the SKA-low AA* configuration, meaningful constraints on LW feedback require integration times exceeding 10,000 hours under optimistic foreground-removal assumptions.
The VAO wiggles constitute a physically motivated signature that is robust to many modeling uncertainties in the underlying star-formation physics.

Where Pith is reading between the lines

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

Combining VAO-based constraints with other 21 cm statistics could help break degeneracies between feedback strength and the timing of reionization.
If the method works, it would supply an independent check on models of Population III star formation that currently rely only on theoretical cooling curves.
Future instruments with lower noise floors could shorten the required integration time and make the probe practical for SKA-era observations.

Load-bearing premise

The semi-numerical 21 cm lightcone simulations correctly capture how Lyman-Werner feedback changes the halo cooling threshold and thereby suppresses the VAO features.

What would settle it

A measurement of the 21 cm power spectrum at cosmic dawn frequencies that shows the expected VAO wiggles persisting at full strength even when independent probes indicate strong Lyman-Werner feedback, or conversely shows complete suppression when feedback is expected to be weak.

Figures

Figures reproduced from arXiv: 2603.29947 by Bin Yue, Ely D. Kovetz, Furen Deng, Xi Du, Xuelei Chen, Yan Gong, Yidong Xu.

**Figure 2.** Figure 2: The Mcool1 as a function of z, in three models with Mcool0 = 5 × 105 M⊙, αLW = 0; Mcool0 = 105 M⊙ and αLW = 0.9; and Mcool0 = 5 × 104 M⊙ and αLW = 2.0. We mark the range where VAO features appear, from z ∼ 21 to ∼ 17, by two vertical dashed lines. before analyzing the 21 cm signal, in [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: Top: A slice of the 21 cm lightcone, for Mcool0 = 105 M⊙ and αLW = 0. Bottom: The 21 cm global spectrum corresponding to the lightcone. distinguish between a smooth component relevant to the VAO and a smooth component irrelevant to the VAO, as they are both smooth. (3) Compared with the smooth component, the locations of the wiggles are purely determined by cosmology and fundamental physics (Munoz 2019b; S… view at source ↗

**Figure 4.** Figure 4: The MAPS map calculated from the lightcone of Fig. 3. [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗

**Figure 5.** Figure 5: Top lef column: The VAO wiggles in the MAPS maps, for Mcool0 = 105 M⊙ and αLW = 0. Top right column: Similar to the first column but with the noise of the SKA-low AA* with 104 hour integration time. Bottom left column: Similar to the first column, but for Mcool0 = 105 M⊙ and αLW = 4.0. Bottom right column: noise of the SKA-low AA* with 104 integration hour is added to the third column. One simulation produ… view at source ↗

**Figure 6.** Figure 6: The VAO features for Mcool0 = 105 M⊙ and various αLW, as labeled in each panel. For displaying purpose, we only show the frequency range where the VAO features are visible. has the advantage that it does not need to assume the explicit likelihood function, therefore is applicable for non-Gaussian likelihood (Sun et al. 2025; Ting 2025; Marx et al. 2025; Binnie et al. 2025). We adopt the Convolutional Neura… view at source ↗

**Figure 7.** Figure 7: The VAO wiggles for various Mcool0 and αLW values. For displaying purpose, we shift the curves according to the their frequency along the y-axis. The curve is colored by the Mcool1 value. We use the loss function (mean squared error, MSE), mean absolute error (MAE) and the standard recovery performance R2 to estimate the goodness of the parameter inference. For a normalized parameter the loss function is a… view at source ↗

**Figure 8.** Figure 8: An illustration of our CNN model. We have two convolutional layers (Conv2D-BatchNorm-ReLU [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗

**Figure 9.** Figure 9: The training and validation curves of Case A. [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗

**Figure 10.** Figure 10: The recovered αLW against the true values for Case A. Filled patches are minimum and maximum ranges of the recovered parameters for same true values, while the points and errorars are mean and standard deviation of them. To guide the eye, we plot the y = x relation by a dashed line. We run 1000 simulations with Mcool0 uniformly distributed between 5×104 M⊙ and 5×105 M⊙, and αLW uniformly distributed betwe… view at source ↗

**Figure 11.** Figure 11: The training and validation curves of Case B. [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗

**Figure 12.** Figure 12: Top: The recovered αLW against the true values. Bottom: Same to the top panel, however for the parameter Mcool0. In all panels, filled patches are minimum and maximum ranges of the recovered parameters for same true values, points and errorbars are mean and standard deviation of them. The dashed curve is the y = x relation for the purpose of guiding the eye [PITH_FULL_IMAGE:figures/full_fig_p017_12.png] view at source ↗

**Figure 13.** Figure 13: The joint probability density distribution of the predicted [PITH_FULL_IMAGE:figures/full_fig_p018_13.png] view at source ↗

**Figure 14.** Figure 14: Training and validation curves of Case C. [PITH_FULL_IMAGE:figures/full_fig_p019_14.png] view at source ↗

**Figure 15.** Figure 15: Similar to Fig.12, however here the noise for SKA-low AA* is added to the mock samples. [PITH_FULL_IMAGE:figures/full_fig_p021_15.png] view at source ↗

**Figure 16.** Figure 16: The local R2 in αLW − Mcool0 plane, for case C. Top: local R2 αLW . Bottom: local R2 Mcool0 . . derived from simulations involving both the LW feedback and the relative streaming motion, for example Kulkarni et al. (2021); Schauer et al. (2021). Incorporating such refinements would increase the dimensionality of parameter space and likely enhance degeneracies. Importantly, our results suggest that VAO fe… view at source ↗

**Figure 17.** Figure 17: Top 7 panels: The net VAO wiggles obtained by using polynomials with different degrees to fit the smooth component in the MAPS, for the model with Mcool0 = 105 M⊙ and αLW = 0.0. Bottom panel: the wiggles at νobs = 70 MHz. Errorbars are standard deviations of the wiggles among the 36 realizations. 4.4 Noise and Observational Requirements Including instrumental noise corresponding to the SKA-low AA* configu… view at source ↗

**Figure 18.** Figure 18: The VAO features if we remove all modes with [PITH_FULL_IMAGE:figures/full_fig_p025_18.png] view at source ↗

**Figure 19.** Figure 19: Top: The cylinder power spectrum ∆2 21(k⊥, k∥) of the lightcones from the simulation with Mcool0 = 105 M⊙ and αLW = 0. Here is the mean result of 36 realizations. Bottom: the VAO wiggles ∆2 21,wiggles(k⊥, k∥) in the above panel. To guide eyes we mark the locations of the first and second VAO peaks at q k 2 ⊥ + k 2 ∥ ≈ 0.05 and 0.09 Mpc−1 by solid curves [PITH_FULL_IMAGE:figures/full_fig_p027_19.png] view at source ↗

read the original abstract

During Cosmic Dawn, Pop III stars could be formed in minihalos through molecular hydrogen (H$_2$) cooling. The minimum halo mass required for H$_2$ cooling is highly sensitive to Lyman-Werner (LW) radiation, which dissociates H$_2$ and regulates star formation. However, the efficiency of LW feedback remains poorly constrained due to the lack of direct observations of Pop III stars. The dark matter-baryon relative streaming velocity suppresses star formation in low-mass halos and imprints characteristic Velocity Acoustic Oscillation (VAO) features in the 21 cm power spectrum. These features are particularly sensitive to the cooling threshold mass: if LW feedback raises the minimum halo mass above the streaming-sensitive regime, the VAO signal is strongly suppressed. This makes the VAO wiggles a promising indirect probe of LW feedback during Cosmic Dawn. We investigate the feasibility of constraining LW feedback parameters using semi-numerical 21 cm lightcone simulations. We compute the multi-frequency angular power spectrum (MAPS) to isolate the VAO features and train a Convolutional Neural Network (CNN) to infer the LW feedback efficiency and the baseline cooling threshold. We find that in the absence of instrumental noise, the LW feedback efficiency can be accurately recovered from the VAO features. However, for the SKA-low AA* configuration, meaningful constraints require integration times exceeding $10^4$ hours under optimistic foreground assumptions. Nonetheless, our results demonstrate that VAO features provide a physically robust and potentially powerful probe of LW feedback at Cosmic Dawn.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The abstract sketches a plausible new probe of LW feedback via VAO wiggles isolated in MAPS and inverted with a CNN, but the recovery is shown only in the noise-free limit inside the same semi-numerical model.

read the letter

The main takeaway is that this paper links the suppression of velocity acoustic oscillations in the 21 cm signal to Lyman-Werner feedback raising the halo cooling threshold, then uses MAPS to isolate those wiggles and a CNN to recover the feedback efficiency and baseline threshold from lightcone simulations. In the zero-noise case the abstract states the parameters come back accurately. That connection is physically direct: streaming velocities matter only for low-mass halos, so pushing the minimum mass higher erases the oscillatory signature. The choice to work with multi-frequency angular power spectra is a reasonable way to pull out the scale-dependent features without mixing in other 21 cm contributions. The work is new in applying this specific combination to LW constraints rather than just forecasting the VAO signal itself. The simulations are semi-numerical and the training data comes from the same framework, so the reported accuracy mainly shows that the network can read the inputs it was given. No details appear on validation against independent codes, added instrumental noise beyond the SKA case, or foreground robustness beyond optimistic assumptions. The SKA requirement of more than 10,000 hours integration time is a clear practical limit even if the math holds. Because only the abstract is available, the CNN architecture, training set size, and any error propagation steps cannot be checked. This is aimed at the subset of 21 cm cosmologists already working on Cosmic Dawn and streaming-velocity effects. A reader familiar with those tools would see the motivation and could test the idea further. The argument is internally consistent on its own terms and shows clear thinking about the physics, so it qualifies as serious work despite the limited evidence. I would bring it to a reading group if the group covers 21 cm methods, but I would not cite it until the full validation is visible. It should go to peer review rather than desk rejection because the proposed observable is fresh and worth checking in detail.

Referee Report

2 major / 1 minor

Summary. The paper claims that Velocity Acoustic Oscillation (VAO) features imprinted by dark matter-baryon streaming velocities in the Cosmic Dawn 21 cm signal can be used to constrain Lyman-Werner (LW) feedback efficiency. Semi-numerical 21 cm lightcone simulations are used to compute the multi-frequency angular power spectrum (MAPS), isolating the VAO wiggles; a Convolutional Neural Network (CNN) is then trained to recover the LW feedback efficiency and baseline cooling threshold. The abstract reports accurate recovery of the LW feedback efficiency in the zero-noise limit, while SKA-low observations would require integration times exceeding 10^4 hours under optimistic foreground assumptions.

Significance. If the central result holds, the work identifies a physically motivated, indirect probe of LW feedback during Cosmic Dawn that exploits the sensitivity of the cooling threshold mass to the suppression of VAO features. This could provide a new observational handle on Pop III star formation efficiency in the absence of direct detections.

major comments (2)

[Abstract] Abstract: the claim that the CNN recovers LW feedback efficiency accurately in the noise-free case is unsupported by any description of the training/validation sets, error propagation, robustness tests against simulation variations, or comparison to full-physics runs, leaving the central inference claim without load-bearing evidence.
[Abstract] Abstract: training and testing the CNN exclusively on data generated from the same semi-numerical model whose parameters are being inferred creates a circularity risk; the reported recovery demonstrates sensitivity within the assumed framework rather than independent validation of the LW feedback modeling.

minor comments (1)

The abstract refers to 'optimistic foreground assumptions' for SKA-low without defining the specific foreground removal model or residual levels assumed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive comments on our manuscript. We address each major comment point by point below.

read point-by-point responses

Referee: [Abstract] Abstract: the claim that the CNN recovers LW feedback efficiency accurately in the noise-free case is unsupported by any description of the training/validation sets, error propagation, robustness tests against simulation variations, or comparison to full-physics runs, leaving the central inference claim without load-bearing evidence.

Authors: Abstracts are concise by design and do not contain the full methodological details. The main text describes the semi-numerical lightcone simulations, the generation of training and validation sets from multiple realizations, the CNN architecture and training protocol, quantitative recovery metrics in the zero-noise limit, and robustness checks against variations in streaming velocity and cooling threshold. Parameter uncertainties are obtained from the network output distributions. Direct comparison to full-physics runs is not performed here, as the work focuses on the semi-numerical framework; this modeling limitation is discussed explicitly. We will revise the abstract to include a brief reference to the validation procedure. revision: yes
Referee: [Abstract] Abstract: training and testing the CNN exclusively on data generated from the same semi-numerical model whose parameters are being inferred creates a circularity risk; the reported recovery demonstrates sensitivity within the assumed framework rather than independent validation of the LW feedback modeling.

Authors: We agree that this constitutes a demonstration of information content and sensitivity within the adopted modeling framework rather than an external validation. Such simulation-based inference is standard for establishing the constraining power of a new observable before real-data application. The manuscript discusses the underlying assumptions and potential biases of the semi-numerical model. We will clarify this scope in the revised abstract and discussion to avoid any implication of model-independent validation. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The abstract describes a standard simulation-based feasibility study: semi-numerical 21 cm lightcone simulations generate MAPS containing VAO features, a CNN is trained on those simulations to recover LW feedback efficiency, and recovery is demonstrated in the zero-noise limit. This shows information content within the model rather than any derivation that reduces by construction to its inputs. No equations, self-citations, or load-bearing steps are present in the available text that match the enumerated circularity patterns; the result is not equivalent to the inputs by definition and remains a self-contained demonstration against the internal benchmarks of the simulations.

Axiom & Free-Parameter Ledger

2 free parameters · 3 axioms · 0 invented entities

The central claim rests on the accuracy of the semi-numerical simulation framework linking LW feedback to the H2 cooling threshold and VAO suppression, plus optimistic foreground assumptions for SKA.

free parameters (2)

Lyman-Werner feedback efficiency
Primary parameter the CNN is trained to infer from the simulated VAO signal.
baseline cooling threshold
Minimum halo mass for H2 cooling in the absence of LW feedback, also inferred by the network.

axioms (3)

domain assumption The minimum halo mass required for H2 cooling is highly sensitive to LW radiation.
Stated as the physical basis for the sensitivity of star formation to feedback.
domain assumption VAO features are strongly suppressed if LW feedback raises the minimum halo mass above the streaming-sensitive regime.
Core premise making VAO a probe of LW feedback.
domain assumption Semi-numerical lightcone simulations accurately model the 21 cm signal including streaming velocity and LW effects.
Invoked to generate the training data for the CNN.

pith-pipeline@v0.9.0 · 5574 in / 1539 out tokens · 71835 ms · 2026-05-13T23:11:30.160096+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We employ a two-parameter formula ... Mcool1 = Mcool0 [1 + α_LW (4π J_LW)^0.47] ... train a Convolutional Neural Network (CNN) to infer the LW feedback efficiency and the baseline cooling threshold.
IndisputableMonolith/Foundation/DimensionForcing.lean alexander_duality_circle_linking unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We compute the multi-frequency angular power spectrum (MAPS) to isolate the VAO features

What do these tags mean?

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supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

75 extracted references · 75 canonical work pages · 2 internal anchors

[1]

L., & Norman, M

Abel, T., Bryan, G. L., & Norman, M. L. 2000, The Astrophysical Journal, 540, 39 4 Ali-Ha¨ımoud, Y ., Meerburg, P. D., & Yuan, S. 2014, Physical Review D, 89, 083506 2

work page 2000
[2]

2001, Physics Reports, 349, 125 2, 4

Barkana, R., & Loeb, A. 2001, Physics Reports, 349, 125 2, 4

work page 2001
[3]

K., & Samui, S

Bera, A., Ghara, R., Chatterjee, A., Datta, K. K., & Samui, S. 2023, Journal of Astrophysics and Astronomy, 44, 10 7

work page 2023
[4]

Bevins, H. T. J., Fialkov, A., De Lera Acedo, E., et al. 2022, Nature Astronomy, 6, 1473 2

work page 2022
[5]

R., & Mao, Y

Binnie, T., Zhao, X., Pritchard, J. R., & Mao, Y . 2025, arXiv e-prints, arXiv:2502.08152 11

work page arXiv 2025
[6]

Bromm, V ., Yoshida, N., Hernquist, L., & McKee, C. F. 2009, Nature, 459, 49 2

work page 2009
[7]

2008, The Astrophysical Journal, 684, 18 2

Chen, X., & Miralda-Escud´e, J. 2008, The Astrophysical Journal, 684, 18 2

work page 2008
[8]

Fisher Matrices and Confidence Ellipses: A Quick-Start Guide and Software

Coe, D. 2009, arXiv e-prints, arXiv:0906.4123 29

work page internal anchor Pith review Pith/arXiv arXiv 2009
[9]

Cohen, A., Fialkov, A., Barkana, R., & Monsalve, R. A. 2020, Monthly Notices of the Royal Astronomical Society, 495, 4845 7

work page 2020
[10]

Cruz, H. A. G., Mu˜noz, J. B., Sabti, N., & Kamionkowski, M. 2025, Physical Review D, 111, 083503 2

work page 2025
[11]

2010, Journal of Cosmology and Astroparticle Physics, 2010, 007 2

Dalal, N., Pen, U.-L., & Seljak, U. 2010, Journal of Cosmology and Astroparticle Physics, 2010, 007 2

work page 2010
[12]

D., & Carilli, C

Datta, A., Bowman, J. D., & Carilli, C. L. 2010, The Astrophysical Journal, 724, 526 23

work page 2010
[13]

K., Choudhury, T

Datta, K. K., Choudhury, T. R., & Bharadwaj, S. 2007, Monthly Notices of the Royal Astronomical Society, 378, 119 7

work page 2007
[14]

K., Mellema, G., Mao, Y ., et al

Datta, K. K., Mellema, G., Mao, Y ., et al. 2012, Monthly Notices of the Royal Astronomical Society, 424, 1877 7

work page 2012
[15]

E., Mesinger, A., & Murray, S

Davies, J. E., Mesinger, A., & Murray, S. G. 2025, Astronomy & Astrophysics, 701, A236 3

work page 2025
[16]

G., Swart, G., et al

Dewdney, P., Labate, M. G., Swart, G., et al. 2022, SKA1 Design Baseline Description, Tech. rep., SKAO 7

work page 2022
[17]

2025, Monthly Notices of the Royal Astronomical Society, 542, 2292 2

Dhandha, J., Fialkov, A., Gessey-Jones, T., et al. 2025, Monthly Notices of the Royal Astronomical Society, 542, 2292 2

work page 2025
[18]

Fialkov, A., Barkana, R., Tseliakhovich, D., & Hirata, C. M. 2012, Monthly Notices of the Royal Astronomical Society, 424, 1335 2, 4, 20

work page 2012
[19]

Fialkov, A., Barkana, R., Visbal, E., Tseliakhovich, D., & Hirata, C. M. 2013, Monthly Notices of the Royal Astronomical Society, 432, 2909 3, 4

work page 2013
[20]

B., Somerville, W

Field, G. B., Somerville, W. B., & Dressler, K. 1966, Annual Review of Astronomy and Astrophysics, 4, 207 2

work page 1966
[21]

R., Peng Oh, S., & Briggs, F

Furlanetto, S. R., Peng Oh, S., & Briggs, F. H. 2006, Physics Reports, 433, 181 2

work page 2006
[22]

S., Bevins, H

Gessey-Jones, T., Sartorio, N. S., Bevins, H. T. J., et al. 2025, Nature Astronomy, 9, 1268 2

work page 2025
[23]

2024, Monthly Notices of the Royal Astronomical Society, 530, 191 7

Ghara, R., Bag, S., Zaroubi, S., & Majumdar, S. 2024, Monthly Notices of the Royal Astronomical Society, 530, 191 7

work page 2024
[24]

K., & Choudhury, T

Ghara, R., Datta, K. K., & Choudhury, T. R. 2015, Monthly Notices of the Royal Astronomical Society, 453, 3144 7

work page 2015
[25]

2013, in Astrophysics and Space Science Library, V ol

Glover, S. 2013, in Astrophysics and Space Science Library, V ol. 396, The First Galaxies, ed. T. Wiklind, B. Mobasher, & V . Bromm, 103 2, 3 32 Du et al

work page 2013
[26]

Glover, S. C. O., Clark, P. C., Greif, T. H., et al. 2008, Proceedings of the International Astronomical Union, 4, 3 2

work page 2008
[27]

H., White, S

Greif, T. H., White, S. D. M., Klessen, R. S., & Springel, V . 2011, The Astrophysical Journal, 736, 147 2

work page 2011
[28]

2018, Monthly Notices of the Royal Astronomical Society, 477, 3217 7

Greig, B., & Mesinger, A. 2018, Monthly Notices of the Royal Astronomical Society, 477, 3217 7

work page 2018
[29]

C., Binnie, T., Mu˜noz, J

Hotinli, S. C., Binnie, T., Mu˜noz, J. B., Dinda, B. R., & Kamionkowski, M. 2021, Physical Review D, 104, 063536 2

work page 2021
[30]

C., Marsh, D

Hotinli, S. C., Marsh, D. J. E., & Kamionkowski, M. 2022, Physical Review D, 106, 043529 2

work page 2022
[31]

2016, Monthly Notices of the Royal Astronomical Society, 456, 66 23

Jensen, H., Majumdar, S., Mellema, G., et al. 2016, Monthly Notices of the Royal Astronomical Society, 456, 66 23

work page 2016
[32]

Kashlinsky, A., & Rees, M. J. 1983, Monthly Notices of the Royal Astronomical Society, 205, 955 3

work page 1983
[33]

S., & Glover, S

Klessen, R. S., & Glover, S. C. 2023, Annual Review of Astronomy and Astrophysics, 61, 65 2

work page 2023
[34]

Kulkarni, M., Visbal, E., & Bryan, G. L. 2021, The Astrophysical Journal, 917, 40 2, 3, 22

work page 2021
[35]

R., & Trott, C

Liu, A., Parsons, A. R., & Trott, C. M. 2014, Physical Review D, 90, 023018 23

work page 2014
[36]

E., Bryan, G

Machacek, M. E., Bryan, G. L., & Abel, T. 2001, The Astrophysical Journal, 548, 509 3, 4, 20

work page 2001
[37]

2025, arXiv e-prints, arXiv:2509.22561 11

Marx, E., Chatterjee, D., Desai, M., et al. 2025, arXiv e-prints, arXiv:2509.22561 11

work page arXiv 2025
[38]

McQuinn, M., & O’Leary, R. M. 2012, The Astrophysical Journal, 760, 3 2

work page 2012
[39]

2011, Monthly Notices of the Royal Astronomical Society, 411, 955 3

Mesinger, A., Furlanetto, S., & Cen, R. 2011, Monthly Notices of the Royal Astronomical Society, 411, 955 3

work page 2011
[40]

H., Furlanetto, S

Mirocha, J., Mebane, R. H., Furlanetto, S. R., Singal, K., & Trinh, D. 2018, Monthly Notices of the Royal Astronomical Society, 478, 5591 2

work page 2018
[41]

G., & Greig, B

Mondal, R., Mellema, G., Murray, S. G., & Greig, B. 2022, Monthly Notices of the Royal Astronomical Society: Letters, 514, L31 7

work page 2022
[42]

K., Iliev, I

Mondal, R., Shaw, A. K., Iliev, I. T., et al. 2020, Monthly Notices of the Royal Astronomical Society, 494, 4043 7

work page 2020
[43]

F., Hazelton, B., Sullivan, I., & Beardsley, A

Morales, M. F., Hazelton, B., Sullivan, I., & Beardsley, A. 2012, The Astrophysical Journal, 752, 137 23 Mu˜noz, J. B. 2019a, Physical Review D, 100, 063538 2, 8 Mu˜noz, J. B. 2019b, Physical Review Letters 2, 7, 8 Mu˜noz, J. B., Qin, Y ., Mesinger, A., et al. 2022, Monthly Notices of the Royal Astronomical Society, 511, 3657 7

work page 2012
[44]

2020, The Journal of Open Source Software, 5, 2582 3

Murray, S., Greig, B., Mesinger, A., et al. 2020, The Journal of Open Source Software, 5, 2582 3

work page 2020
[45]

2024, The Journal of Open Source Software, 9, 6501 23 O’Shea, B

Murray, S., Pober, J., & Kolopanis, M. 2024, The Journal of Open Source Software, 9, 6501 23 O’Shea, B. W., & Norman, M. L. 2008, The Astrophysical Journal, 673, 14 3 Planck Collaboration, Ade, P. A. R., Aghanim, N., et al. 2016, Astronomy & Astrophysics, 594, A13 3

work page 2024
[46]

C., Parsons, A

Pober, J. C., Parsons, A. R., DeBoer, D. R., et al. 2013, The Astronomical Journal, 145, 65 23

work page 2013
[47]

C., Liu, A., Dillon, J

Pober, J. C., Liu, A., Dillon, J. S., et al. 2014, The Astrophysical Journal, 782, 66 23

work page 2014
[48]

R., Schauer, A

Prole, L. R., Schauer, A. T. P., Clark, P. C., et al. 2023, Monthly Notices of the Royal Astronomical Society, 520, 2081 2

work page 2023
[49]

2012, Monthly Notices of the Royal Astronomical Society, 426, 1159 2 LW feedback & V AO 33

Safranek-Shrader, C., Agarwal, M., Federrath, C., et al. 2012, Monthly Notices of the Royal Astronomical Society, 426, 1159 2 LW feedback & V AO 33

work page 2012
[50]

G., Cooray, A., & Knox, L

Santos, M. G., Cooray, A., & Knox, L. 2005, The Astrophysical Journal, 625, 575 7

work page 2005
[51]

Sarkar, D., & Kovetz, E. D. 2023, Physical Review D, 107, 023524 2, 7, 8

work page 2023
[52]

Schauer, A. T. P., Boylan-Kolchin, M., Colston, K., et al. 2023, The Astrophysical Journal, 950, 20 2

work page 2023
[53]

Schauer, A. T. P., Glover, S. C. O., Klessen, R. S., & Clark, P. 2021, Monthly Notices of the Royal Astronomical Society, 507, 1775 3, 22

work page 2021
[54]

K., Ghara, R., Zaroubi, S., et al

Shaw, A. K., Ghara, R., Zaroubi, S., et al. 2023, Monthly Notices of the Royal Astronomical Society, 522, 2188 7

work page 2023
[55]

K., Mo, H

Sheth, R. K., Mo, H. J., & Tormen, G. 2001, Monthly Notices of the Royal Astronomical Society, 323, 1 5

work page 2001
[56]

P., & Williams, D

Stecher, T. P., & Williams, D. A. 1967, The Astrophysical Journal, 149, L29 2

work page 1967
[57]

2025, Communications Physics, 8, 220 11

Sun, T.-Y ., Shao, Y ., Li, Y ., et al. 2025, Communications Physics, 8, 220 11

work page 2025
[58]

2021, Monthly Notices of the Royal Astronomical Society, 502, 463 2

Tanaka, T., & Hasegawa, K. 2021, Monthly Notices of the Royal Astronomical Society, 502, 463 2

work page 2021
[59]

L., Li, M., & Haiman, Z

Tanaka, T. L., Li, M., & Haiman, Z. 2013, Monthly Notices of the Royal Astronomical Society, 435, 3559 2

work page 2013
[60]

J., et al

Tegmark, M., Silk, J., Rees, M. J., et al. 1997, The Astrophysical Journal, 474, 1 4

work page 1997
[61]

Deep Learning in Astrophysics

Ting, Y .-S. 2025, arXiv e-prints, arXiv:2510.10713 11

work page internal anchor Pith review Pith/arXiv arXiv 2025
[62]

2024, SKA-Low Substation Templates, Tech

Trott, C., Breen, s., Green, J., & Pearcey, S. 2024, SKA-Low Substation Templates, Tech. rep., SKAO 7

work page 2024
[63]

M., Mondal, R., Mellema, G., et al

Trott, C. M., Mondal, R., Mellema, G., et al. 2022, Astronomy & Astrophysics, 666, A106 7

work page 2022
[64]

Tseliakhovich, D., Barkana, R., & Hirata, C. M. 2011, Monthly Notices of the Royal Astronomical Society, 418, 906 2

work page 2011
[65]

2010, Physical Review D, 82, 083520 2, 3

Tseliakhovich, D., & Hirata, C. 2010, Physical Review D, 82, 083520 2, 3

work page 2010
[66]

M., Qin, Y ., Balu, S., & Wyithe, J

Ventura, E. M., Qin, Y ., Balu, S., & Wyithe, J. S. B. 2025, Monthly Notices of the Royal Astronomical Society, 540, 483 2

work page 2025
[67]

M., Trinca, A., Schneider, R., et al

Ventura, E. M., Trinca, A., Schneider, R., et al. 2023, Monthly Notices of the Royal Astronomical Society, 520, 3609 2

work page 2023
[68]

Visbal, E., Barkana, R., Fialkov, A., Tseliakhovich, D., & Hirata, C. M. 2012, Nature, 487, 70 7

work page 2012
[69]

L., & Barkana, R

Visbal, E., Haiman, Z., Terrazas, B., Bryan, G. L., & Barkana, R. 2014, Monthly Notices of the Royal Astronomical Society, 445, 107 3, 4, 5, 20

work page 2014
[70]

E., Naoz, S., Yoshida, N., et al

Williams, C. E., Naoz, S., Yoshida, N., et al. 2026, The Astrophysical Journal, 997, 202 2

work page 2026
[71]

H., & Abel, T

Wise, J. H., & Abel, T. 2007, The Astrophysical Journal, 671, 1559 3

work page 2007
[72]

L., O’Shea, B

Xu, H., Norman, M. L., O’Shea, B. W., & Wise, J. H. 2016, The Astrophysical Journal, 823, 140 2

work page 2016
[73]

2003, The Astrophysical Journal, 592, 645 4

Yoshida, N., Abel, T., Hernquist, L., & Sugiyama, N. 2003, The Astrophysical Journal, 592, 645 4

work page 2003
[74]

2024, The Astrophysical Journal, 964, 62 2, 3, 5, 7

Zhang, X., Lin, H., Zhang, M., et al. 2024, The Astrophysical Journal, 964, 62 2, 3, 5, 7

work page 2024
[75]

Zhao, X., Mao, Y ., Cheng, C., & Wandelt, B. D. 2022, The Astrophysical Journal, 926, 151 11

work page 2022