The Growth of HII Regions During Reionization

(2) Harvard University); Lars Hernquist (2) ((1) Caltech; Matias Zaldarriaga (2); Steven Furlanetto (1)

REVIEW

The Growth of HII Regions During Reionization

Steven Furlanetto (1), Matias Zaldarriaga (2), Lars Hernquist (2) ((1) Caltech, (2) Harvard University)

Astrophysics · Submitted 31 Mar 2004 · 45 references

Pith's verdict: A genuinely new analytic handle on reionization morphology — the excursion-set bubble model and the reusable power-spectrum machinery are the real contributions; the quantitative validation is deferred, and the paper says so.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on November 11, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 3 major objections · 7 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDastro-ph/0403697 (version 1)

Pith IDW3HMESPR, Pith's permanent record of this paper and its review

Citation(2) Harvard University), Lars Hernquist (2) ((1) Caltech, Matias Zaldarriaga (2), Steven Furlanetto (1). "The Growth of HII Regions During Reionization." arXiv:astro-ph/0403697 (2004). https://pith.science/paper/W3HMESPR

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

Worth your time, and worth citing. The core move is simple and right: instead of hanging one H II region on each galaxy, treat ionized bubbles as excursion-set objects with a mass-dependent barrier, so a point belongs to the largest scale whose smoothed overdensity crosses delta_x(m,z). That reproduces what the simulations had been showing for a couple of years — big bubbles around biased clusters of sources, growing fast as the neutral fraction drops — and it does so with two inputs, zeta and m_min. Equation (7) is clean, and the size distributions in Figure 2 have the low- and high-mass cutoffs you would want. The power-spectrum construction in section 3 is the part with the longest shelf life: equations (17) through (27) don't care where the size distribution came from, and they prove it in section 4.4 by running the whole machinery on the galaxy-per-bubble scenario and getting a visibly different, featureless answer. That comparison is the paper's best argument for its own thesis. The pixel distribution function in section 5 is explicitly approximate and pitched at the right level — a demonstration that the field is non-Gaussian, not a prediction to fit against data. The authors are candid about their approximations throughout section 2, which I appreciate more than I appreciate most candor sections. On the soft spots: the linear-barrier fit is the one everyone will flag, but it's bounded — Figure 1 shows the fit is good at small sigma^2, which is where the bump-producing bubbles live, and the small-mass normalization is patched by hand anyway. The volume-conservation rescaling in 3.2 is ad hoc and propagates into every power spectrum, but it's a normalization, not a shape. The real gap is validation: the only empirical check is qualitative, against a 10 h^-1 Mpc box that their own Figure 4 shows underestimates bubble sizes near overlap. So the several-Mpc bubbles are a prediction, not a confirmed result, and the paper says as much in sections 2 and 6. The forward-looking claims lean on the companion paper, still listed as submitted; minor, but note it. Send it out. This is the paper that made reionization morphology an analytic question, and the 21 cm community will be building on it for years.

Referee report

Significance

If the model holds, this is an important paper: it replaces the standard picture of reionization as the growth of individual Strömgren spheres with a large-scale, bias-driven picture, and it does so with a two-parameter forward model (ζ and m_min) that is analytically tractable and directly falsifiable. The predictions are concrete and testable: a characteristic bubble scale of several comoving Mpc well before overlap, a power-spectrum bump whose position and amplitude evolve monotonically with the neutral fraction, a near-invariance of the morphology at fixed x̄_H, and a strongly non-Gaussian pixel distribution. The paper is also unusually candid about its own weak points: the breakdown of the linear barrier at small masses, the failure of Eq. (3) on small scales, the need for a hand-applied renormalization, the shot-noise artifact on large scales near overlap, and the fact that existing simulations are too small to contain the predicted bubbles. That candor is a genuine strength and makes the paper useful even where its approximations are crude. The construction of the power spectrum for an arbitrary bubble size distribution (§3) is general and separable from the specific reioniz

Major objections (3)

[§3.2, Eqs. (17)-(18)] The power-spectrum amplitude, which is the paper's headline observable, depends on two rescalings that are imposed rather than derived, and the reader is not told which figures include them. First, the size distribution of Eq. (7) is already an overlap-corrected distribution, yet the Poisson construction of Eq. (17) re-imposes overlap by allowing multiple sources to ionize the same point; the authors acknowledge this tension ('we would ideally like to avoid any overlap ... There is no clean way to avoid this problem') but do not quantify it. Second, the volume-conservation fix multiplies the number density by [-ln(1-Q̄)/Q̄] to force x̄_i = ζ f_coll. Both choices change the amplitude of P_xx on bubble scales, and the claim in §4.2 that the bubbles 'increase the power ... by nearly an order of magnitude' is sensitive to them. I would ask the authors to (a) state explicitly, in the captions of Figures 5-11, whether the [-ln(1-Q̄)/Q̄] factor and the ζ f_coll/Q̄ renormalization are applied, and (b) show at least one power spectrum computed with and without each correction so that the reader can see how much of the quoted amplitude is robust. If the qualitative conclusions (bump location, monotonic evolution with x̄_H) survive, that should be said explicitly.
[§2 and §6, with Figure 4] The central claim — that bubble sizes are set by large-scale density fluctuations and follow from the excursion set with barrier (4) — is supported empirically only by qualitative resemblance to Sokasian et al. (2003a), and the paper's own Figure 4 (bottom panel) shows that a 10 h^-1 Mpc box underestimates the bubble sizes, especially near overlap. The authors state this plainly and defer a quantitative comparison to future ~100 Mpc simulations, which is the right call, but it leaves the several-Mpc bubbles that drive every observable prediction in §4 untested against any simulation. I would ask the authors to state, in §2 or §6, what specific quantitative comparison would confirm or falsify the model — for example, the predicted filling-factor-weighted mean bubble radius as a function of x̄_H, which a future simulation could measure directly — so that the prediction is falsifiable in a stated way rather than only in qualitative shape. This is a request for a sharper statement of the test, not for the test itself.
[§2 caveats and §3.2, Eq. (18)] Every quantitative result in the paper depends on the conversion from a Lagrangian bubble mass m to a comoving radius R(m), through Eq. (18) and hence through the entire power-spectrum calculation, but that conversion is never written down. The text notes only that 'the excursion set formalism is fundamentally Lagrangian ... We do not include this difference in calculating the radial sizes of the regions,' which tells the reader that a choice was made but not what it was. Since the headline number — bubbles of several comoving Mpc — is a direct output of this step, the paper should give the explicit relation used (e.g. m = (4π/3) R³ ρ̄, and whether ρ̄ is the mean matter or baryon density, and at what epoch), and should state how much R(m) shifts if the Eulerian correction is included. Without this, the central length scale cannot be reproduced from the paper alone.

Minor objections (7)

[§3.1, Eq. (12)] The criticism of Santos et al. (2003) is fair on the limits, but the text should acknowledge that a suitably chosen filter function can be made to satisfy ξ_xx → 0 at x̄_i = 1, so the objection is to their specific ansatz rather than to the filter-function approach in general. A sentence to that effect would be more accurate and less dismissive.
[§2-§3, notation] Three closely related symbols are used for the ionized fraction — Q̄ (Eq. 8), x̄_i (Eq. 13), and x̄_H (the neutral fraction) — and their relations are only implicit. A short paragraph defining all three once, and stating that x̄_i = 1 - x̄_H and that Q̄ is the model's filling factor before renormalization, would prevent confusion, particularly in Figures 2, 3, and 7 where the normalizations differ.
[§4.3, Figure 9] The text states that P_ψ/P_δδ → x̄_H at large k 'with an additional bias factor that affects the limiting value.' Either give that factor explicitly or remove the parenthetical; as written it invites the reader to wonder whether the plotted asymptote is the stated one.
[§5, Eq. (33) and Figure 12] The Monte Carlo treatment of partial overlap assumes that the ionized fraction of a pixel is uncorrelated with the mean density of the rest of the pixel. The authors note that including correlations would reduce the effect, but they do not state the sign or rough magnitude of the bias in p(ψ). A sentence quantifying the expected direction would strengthen an already-approximate section.
[§5, Gaussian assumption] The skewness estimate S_3 is given for the density field alone, but the quantity that matters for p(ψ) is the distribution of δ after the ionization criterion has been applied, which is far more non-Gaussian than δ itself. The statement that 'our choice of m_pix is reasonable' would be better supported by a direct check, e.g. recomputing p(ψ) with a lognormal density field at one redshift, or by explicitly flagging this as an open issue.
[§4.2, comparison with ZFH04] The explanation of why the bubble feature is less pronounced here than in ZFH04 is helpful, but the reader would benefit from a sentence stating which of the two treatments of the late-stage bubble size the authors regard as more physical, given that both are toy models in different respects.
[Figures 2 and 4] The captions should state the value of ζ and whether the ζ f_coll/Q̄ renormalization has been applied, since Figure 3 shows that the uncorrected model underestimates the filling factor at early times and the size distributions in Figures 2 and 4 are the ones most affected.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

The paper argues that ionized bubbles during reionization are shaped by large-scale density fluctuations, not by individual galaxies, and that this makes them several megaparsecs across and visible in the 21 cm power spectrum.

The reading

The paper asks how the ionized regions of the intergalactic medium grew during reionization, and answers that their sizes are governed by large-scale density fluctuations rather than by the Strömgren spheres of individual galaxies. The authors declare a region ionized once its mean overdensity exceeds a mass-dependent threshold $B(m,z)$ or $B_0 + B_1$ in the linearized form, and then read the bubble size distribution off as a first-crossing distribution, the same machinery that produces the Press–Schechter halo mass function. The payoff is a size distribution with both a low-mass and a high-mass cutoff and a characteristic scale that climbs to several comoving megaparsecs while the ionized fraction is still well below unity. From that distribution they build the correlation function and power spectrum of the 21 cm brightness temperature and show that the bubbles imprint a feature near $k$ ~ 0.1 Mpc$^{-1}$, at angular scales of a few arcminutes, within reach of the planned low-frequency radio arrays. They close by arguing that the neutral-density field becomes strongly non-gaussian once bubbles dominate, so the power spectrum alone will not capture the signal.

What carries the argument

The load-bearing object is the ionization barrier, equation (4): a region of mass $m$ is ionized when its mean overdensity satisfies $B(m,z) = B_0 + B_1$ in the linearized form, i.e. $B_0 = B_c(z) - B_1$, with $B_0$ and $B_1$ fixed at $m$ going to infinity; in the paper's notation this is $B_0 = B_c(z) - B_1$, where $B_1$ comes from $K(zeta)$ and $sigma_{min}$. In practice the paper writes $B_0 = B_c(z) - B_1$ and $B_1$ as the slope at $sigma^2 = 0$, and then uses Sheth's analytic first-crossing distribution for a linear barrier to get the bubble mass function. The second piece of machinery is the geometric construction of the correlation function: for two points separated by $r_{12}$, the overlap volume $V_o(m,r_{12})$ of a bubble of radius $R(m)$ counts the configurations in which one source ionizes both points, and the remaining volume counts two-source configurations; summing over the bubble mass function gives $xi_{xx}$ that vanishes correctly at both $x_i = 0$ and $x_i = 1$. Clustering enters by multiplying the two-source term by $1 + b(m) xi_{delta delta}$, and the density cross-correlation follows from a halo-model average over source positions.

Extended reading notes

Core claim

The central claim is that the morphology of reionization is a large-scale phenomenon: ionized regions correspond to peaks of the smoothed density field that contain enough collapsed mass to ionize themselves, and their abundance follows from the excursion set first-crossing distribution above a barrier $B(m,z)$ that decreases with increasing smoothing mass. This replaces the standard picture in which each galaxy hosts its own small H II region, and it reproduces what the simulations show: a modest number of bubbles several comoving megaparsecs across, growing rapidly as overlap approaches, with the characteristic scale set by large-scale bias rather than by the local abundance of sources. The authors then carry this distribution through a full construction of the neutral-fraction correlation function, including source clustering and the cross-correlation with density, and obtain a 21 cm power spectrum whose bubble-induced bump moves to larger scales and higher amplitude as the neutral fraction falls. They further show that the one-point distribution of the neutral density is qualitatively reshaped: the high-density tail folds over, and a spike at zero flux appears once bubbles exceed the pixel size.

Load-bearing premise

The analytic size distribution rests on replacing the true, curved ionization threshold with a straight-line fit fixed at very large smoothing masses, and that fit is worst exactly at the small-mass end where the low-mass cutoff of the bubble distribution sits.

Editorial extensions

If this is right

Ionized regions should reach several comoving megaparsecs while the neutral fraction is still of order one half, so the 21 cm signal carries structure on arcminute angular scales rather than only on sub-arcminute scales.
The 21 cm power spectrum should show a bubble-induced bump whose position and amplitude evolve strongly with the global neutral fraction, allowing the reionization history to be mapped even when individual bubbles cannot be resolved.
Simulations with boxes of order 10 comoving Mpc are biased: forcing the mean overdensity to zero on the box scale suppresses the large-scale modes that set bubble sizes, so such simulations underestimate bubble radii, especially near overlap, and boxes of order 100 Mpc are needed for a fair sample.
If reionization instead proceeded through H II regions around individual galaxies, the power-spectrum feature would sit at much smaller scales and the large-scale power would be suppressed, so the two pictures are distinguishable by the same observation.
Because the neutral-density distribution becomes strongly non-gaussian, one-point statistics such as the pixel distribution function carry information that the power spectrum does not.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the bubble scale at fixed neutral fraction is nearly independent of the ionizing efficiency, then the 21 cm feature scale mostly measures the neutral fraction, and the efficiency must be pinned down separately, for instance from the integrated electron-scattering optical depth; the two observables are complementary rather than redundant.
The predicted megaparsec-scale bubbles give an independent handle that does not need 21 cm data at all: the incidence and size distribution of transmitted regions in quasar absorption spectra near the end of reionization should show the same characteristic scale.
Because the signal is non-gaussian, a variance-based detection threshold tuned to gaussian statistics will misjudge the significance of a real detection; searches should be planned around the one-point distribution or around matched filters for bubble-sized features.
The same excursion-set construction could be run with a barrier that depends on local recombination rate rather than on collapse fraction alone, which would let the model interpolate between the source-biased picture advocated here and the void-ionized-first picture it argues against, turning the two into limits of one parameter.

Original abstract

Recently, there has been a great deal of interest in understanding the reionization of hydrogen in the intergalactic medium (IGM). One of the major outstanding questions is how this event proceeds on large scales. Motivated by numerical simulations, we develop a model for the growth of HII regions during the reionization era. We associate ionized regions with large-scale density fluctuations and use the excursion set formalism to model the resulting size distribution. We then consider ways in which to characterize the morphology of ionized regions. We show how to construct the power spectrum of fluctuations in the neutral hydrogen field. The power spectrum contains definite features from the HII regions that should be observable with the next generation of low-frequency radio telescopes through surveys of redshifted 21 cm emission from the reionization era. Finally, we also consider statistical descriptions beyond the power spectrum and show that our model of reionization qualitatively changes the distribution of neutral gas in the IGM.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,143 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.11 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Recently, there has been a great deal of interest in understanding the reionization of hydrogen in the intergalactic medium (IGM). One of the major outstanding questions is how this event proceeds on large scales. Motivated by numerical simulations, we develop a model for the growth of HII regions during the reionization era. We associate ionized regions with large-scale density fluctuations and use the excursion set formalism to model the resulting size distribution. We then consider ways in which to characterize the morphology of ionized regions. We show how to construct the power spectrum of fluctuations in the neutral hydrogen field. The power spectrum contains definite features from the HII regions that should be observable with the next generation of low-frequency radio telescopes through surveys of redshifted 21 cm emission from the reionization era. Finally, we also consider statistical descriptions beyond the power spectrum and show that our model of reionization qualitatively changes the distribution of neutral gas in the IGM.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Recently, there has been a great deal of interest in understanding the reionization of hydrogen in the intergalactic medium (IGM).	background 1.00	0.04	0.02	asserted 0.98
s1	One of the major outstanding questions is how this event proceeds on large scales.	gap 0.90	0.04	0.02	asserted 0.97
s2	Motivated by numerical simulations, we develop a model for the growth of HII regions during the reionization era.	contribution 0.74	0.96	0.05	asserted 0.96
s3	We associate ionized regions with large-scale density fluctuations and use the excursion set formalism to model the resulting size distribution.	method 0.98	0.94	0.07	asserted 0.97
s4	We then consider ways in which to characterize the morphology of ionized regions.	contribution 0.50	0.65	0.02	unclear 0.70
s5	We show how to construct the power spectrum of fluctuations in the neutral hydrogen field.	method 0.77	0.91	0.08	asserted 1.00
s6	The power spectrum contains definite features from the HII regions that should be observable with the next generation of low-frequency radio telescopes through surveys of redshifted 21 cm emission from the reionization era.	interpretation 0.81	0.56	0.36	asserted 0.76
s7	Finally, we also consider statistical descriptions beyond the power spectrum and show that our model of reionization qualitatively changes the distribution of neutral gas in the IGM.	result 0.85	0.94	0.35	asserted 0.97

What kind of paper the classifier reports this is: theoretical result 0.97 · evidence from proof or derivation 0.65.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (45)

[1]

Arons, J., & Wingert, D. W. 1972, ApJ, 177, 1

View on Pith 1972
[2]

Barkana, R. 2002, New Astronomy, 7, 85

View on Pith 2002
[3]

Barkana, R., & Loeb, A. 2001, Phys. Rep., 349, 125 —. 2002, ApJ, 578, 1 —. 2003, ApJ, submitted, (astro-ph/0310338)

View on Pith Pith review arXiv 2001
[4]

Barton, E.J., Davé, R., Smith, J.-D.T., Papovich, C., Hernquist, L. & Springel, V . 2004, ApJ, in press (astro-ph/0310514)

View on Pith Pith review arXiv 2004
[5]

Becker, R. H., et al. 2001, AJ, 122, 2850

View on Pith 2001
[6]

Bond, J. R., Cole, S., Efstathiou, G., & Kaiser, N. 1991, ApJ, 379, 440

View on Pith 1991
[7]

Bouchet, F. R., Juszkiewicz, R., Colombi, S., & Pellat, R. 1992, ApJ, 394, L5

View on Pith 1992
[8]

Cen, R., Haiman, Z., & Mesinger, A. 2004, ApJ, submitted, (as tro- ph/0403419)

View on Pith 2004
[9]

Ciardi, B., & Madau, P. 2003, ApJ, 596, 1

View on Pith 2003
[10]

Ciardi, B., Stoehr, F., & White, S. D. M. 2003, MNRAS, 343, 1101

View on Pith 2003
[11]

Cooray, A., & Sheth, R. 2002, Phys. Rep., 372, 1 Di Matteo, T., Ciardi, B., & Miniati, F. 2004, MNRAS, submitt ed, (astro- ph/0402322) Di Matteo, T., Perna, R., Abel, T., & Rees, M. J. 2002, ApJ, 564, 576

View on Pith 2002
[12]

Fan, X., et al. 2002, AJ, 123, 1247

View on Pith 2002
[13]

Field, G. B. 1958, Proc. IRE, 46, 240 —. 1959, ApJ, 129, 525

View on Pith 1958
[14]

Fukugita, M., & Kawasaki, M. 2003, MNRAS, 343, L25

View on Pith 2003
[15]

Gnedin, N. Y . 2000, ApJ, 535, 530

View on Pith 2000
[16]

Gnedin, N. Y ., & Prada, F. 2004, ApJ, submitted, (astro-ph/0403345)

View on Pith Pith review arXiv 2004
[17]

Gnedin, N. Y ., & Shaver, P. A. 2003, ApJ, submitted, (astro-ph/0312005)

View on Pith Pith review arXiv 2003
[18]

Gunn, J. E., & Peterson, B. A. 1965, ApJ, 142, 1633

View on Pith 1965
[19]

Haiman, Z., & Holder, G. P. 2003, ApJ, 595, 1

View on Pith 2003
[20]

Hernquist, L. & Springel, V . 2003, MNRAS, 341, 1253

View on Pith 2003
[21]

Juszkiewicz, R., Bouchet, F. R., & Colombi, S. 1993, ApJ, 412, L9

View on Pith 1993
[22]

Kogut, A., et al. 2003, ApJS, 148, 161

View on Pith 2003
[23]

Lacey, C., & Cole, S. 1993, MNRAS, 262, 627

View on Pith 1993
[24]

Loeb, A., Barkana, R., & Hernquist, L. 2004, ApJ, submitted, (astro- ph/0403193)

View on Pith 2004
[25]

Madau, P., Meiksin, A., & Rees, M. J. 1997, ApJ, 475, 429 Miralda-Escudé, J., Haehnelt, M., & Rees, M. J. 2000, ApJ, 530, 1

View on Pith 1997
[26]

Mo, H. J., & White, S. D. M. 1996, MNRAS, 282, 347

View on Pith 1996
[27]

Morales, M. F., & Hewitt, J. 2003, ApJ, submitted, (astro-ph/0312437)

View on Pith Pith review arXiv 2003
[28]

Oh, S. P., & Mack, K. J. 2003, MNRAS, 346, 871

View on Pith 2003
[29]

Onken, C. A., & Miralda-Escudé, J. 2003, ApJ, submitted, (as tro- ph/0307184) Pelló, R., et al. 2004, A&A, 416, L35

View on Pith 2003
[30]

Press, W. H., & Schechter, P. 1974, ApJ, 187, 425

View on Pith 1974
[31]

Ricotti, M., Haehnelt, M. G., Pettini, M., & Rees, M. J. 2004, MNRAS, submitted, (astro-ph/0403327)

View on Pith Pith review arXiv 2004
[32]

Santos, M. G., et al. 2003, ApJ, 598, 756

View on Pith 2003
[33]

Santos, M. R. 2003, MNRAS, submitted, (astro-ph/0308146)

View on Pith Pith review arXiv 2003
[34]

Scott, D., & Rees, M. J. 1990, MNRAS, 247, 510

View on Pith 1990
[35]

Sheth, R. K. 1998, MNRAS, 300, 1057

View on Pith 1998
[36]

Sheth, R. K. & Tormen, G. 1999, MNRAS, 308, 119

View on Pith 1999
[37]

Sheth, R. K., & Tormen, G. 2002, MNRAS, 329, 61

View on Pith 2002
[38]

Sokasian, A., Yoshida, N., Abel, T., Hernquist, L., & Spring el, V . 2003b, MNRAS, in press (astro-ph/0307451)

View on Pith Pith review arXiv
[39]

Songaila, A. 2004, AJ, in press, (astro-ph/0402347)

View on Pith Pith review arXiv 2004
[40]

Spergel, D. N., et al. 2003, ApJS, 148, 175

View on Pith 2003
[41]

Springel, V . & Hernquist, L. 2003, MNRAS, 339, 312

View on Pith 2003
[42]

Tozzi, P., Madau, P., Meiksin, A., & Rees, M. J. 2000, ApJ, 528, 597

View on Pith 2000
[43]

White, R. L., Becker, R. H., Fan, X., & Strauss, M. A. 2003, AJ, 126, 1

View on Pith 2003
[44]

Wyithe, J. S. B., & Loeb, A. 2003, ApJ, 588, L69 —. 2004, Nature, 427, 815

View on Pith 2003
[45]

Zaldarriaga, M., Furlanetto, S. R., & Hernquist, L. 2004, ApJ, in press, (astro- ph/0311514) [ZFH04]

View on Pith 2004

Forward citations

Cited by 22 Pith papers

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

Relative velocity of dark matter and baryonic fluids and the formation of the first structures
astro-ph.CO 2010-05 conditional novelty 8.0 of 10

Supersonic relative motion between baryons and dark matter after recombination suppresses small-scale power and the abundance of the first halos, and makes their clustering scale-dependent and stochastic.
The Last Crossing in Excursion-Set Theory of Cosmic Reionization
astro-ph.CO 2026-08 conditional novelty 7.0 of 10

The last-crossing scale, the smallest scale where a region's own photon budget still balances, separates externally ionized underdense regions with central source deficits, linking source geometry to Lyα transmission.
A self-consistent analytical model for both the photoionization rate and reionization history
astro-ph.CO 2026-06 unverdicted novelty 7.0 of 10

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...
Not-quite-primordial black holes
astro-ph.CO 2025-06 conditional novelty 7.0 of 10

Modest small-scale density fluctuations can make halos at z>200 where CMB radiation suppresses molecular cooling, letting gas collapse directly into black hole seeds that match JWST counts.
Simulations and Analytic Calculations of Bubble Growth During Hydrogen Reionization
astro-ph 2006-04 conditional novelty 7.0 of 10

A large radiative transfer simulation of reionization confirms that fast analytic models accurately reproduce the HII bubble size distribution and the 21 cm power spectrum.

Show 17 more citing papers

Impact of Primordial Magnetic Field-induced Small-scale Power on Non-linear Structure Formation and Cosmic Reionization
astro-ph.CO 2026-11 conditional novelty 6.0 of 10

In N-body simulations, primordial magnetic fields at 100-170 pG add small-scale power that increases early low-mass halos, advances reionization midpoint by up to z~2, and raises the Thomson optical depth.
The Lumina Project: Morphology of Ionized Bubbles and Neutral Islands
astro-ph.CO 2026-09 conditional novelty 6.0 of 10

Ionized bubbles in the 500 Mpc Lumina simulation grow from about 1 cMpc to over 100 cMpc across the Epoch of Reionization, stay mostly prolate, and develop an oblate peak among the largest structures only near the end.
C3PO: A Ly{\alpha} Emitting Galaxy at $z \sim 9$
astro-ph.GA 2026-09 unverdicted novelty 6.0 of 10

C3PO-84478 is a low-mass, vigorously star-forming galaxy at z=9 that alone sustains the small ionized bubble required for its Lyα line to escape.
Steep Redshift Evolution of the Ionizing Escape Fraction at $z = 5$--$12$: Empirical Constraints and Comparison with Simulations
astro-ph.CO 2026-06 unverdicted novelty 6.0 of 10

Empirical three-parameter fit to f_esc(M_h,z) yields steep redshift evolution with population-averaged escape fraction rising from ~2% at z=5 to ~9% at z=12.
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
astro-ph.CO 2026-02 conditional novelty 6.0 of 10

Photon mean-free-path observations at z≈5–6, interpreted with a neural-network emulator of high-resolution radiative-transfer simulations, favor a late, extended reionization with substantial neutral hydrogen persisti...
CosmoUiT: A Vision Transformer-UNet Hybrid for Fast and Accurate Emulation of 21-cm Maps from the Epoch of Reionization
astro-ph.CO 2025-10 conditional novelty 6.0 of 10

A Vision Transformer-UNet hybrid emulates 3D EoR 21-cm cubes conditioned on reionization parameters, matching simulated large-scale power spectra with mild small-scale suppression.
A New Boundary Condition on Reionization
astro-ph.CO 2025-09 conditional novelty 6.0 of 10

A zero-lag Pearson correlation between 21-cm and line-intensity maps is predicted to drop sharply at ionized fractions of 1-10%, providing a novel marker for the onset of reionization.
An Alcock-Paczynski Test on Reionization Bubbles for Cosmology
astro-ph.CO 2025-02 conditional novelty 6.0 of 10

Stacks of reionization HII bubbles act as standard spheres, allowing a forecast ~2% measurement of D_A H at z=7.5 with SKA-like 21-cm data.
Probing the Small-Scale Matter Power Spectrum with Large-Scale 21-cm Data
astro-ph.CO 2019-11 conditional novelty 6.0 of 10

Fisher forecasts show that 21-cm global-signal and fluctuation measurements during cosmic dawn can constrain the matter power spectrum at k = 40 to 80 per megaparsec to tens of percent, reaching warm-dark-matter masse...
Planck intermediate results. XLVII. Planck constraints on reionization history
astro-ph.CO 2016-05 accept novelty 6.0 of 10

Planck polarization data alone fix the reionization optical depth at τ = 0.058 ± 0.012, implying reionization peaked near z ≈ 8 and was largely finished by z ≈ 10.
Eliminating the optical depth nuisance from the CMB with 21 cm cosmology
astro-ph.CO 2015-09 conditional novelty 6.0 of 10

21 cm observations of reionization, combined with semi-analytic simulations, can predict the CMB optical depth well enough to break its degeneracy with the primordial amplitude and improve neutrino mass constraints.
Reconstructing Patchy Reionization from the Cosmic Microwave Background
astro-ph 2008-12 conditional novelty 6.0 of 10

A quadratic estimator reconstructs the sky-varying optical depth from patchy reionization using CMB E and B modes, forecasting roughly 10 percent constraints on bubble size and reionization duration for a future satellite.
Reading Between the Lines: Forward Modeling Dust, Continuum, and Spectral Cleaning for Multi-Line Intensity Mapping
astro-ph.GA 2026-07 conditional novelty 5.0 of 10

Using a SAM-based mock, multi-line intensity-mapping cross-power spectra show dust acts as a line-pair- and redshift-dependent suppression, and PCA cleaning with about 20 modes best balances line recovery against cont...
Robust Velocity-induced Acoustic Oscillations at Cosmic Dawn
astro-ph.CO 2019-04 conditional novelty 5.0 of 10

Streaming velocities between dark matter and baryons produce velocity-induced acoustic oscillations in the 21-cm power spectrum during both Lyman-alpha coupling and X-ray heating, with forecast HERA signal-to-noise ra...
Calibration requirements for Epoch of Reionization 21-cm signal observations - V. Bias and variance in the cylindrical power spectrum from uGMRT Band 3 observations of the ELAIS-N1 field
astro-ph.CO 2026-10 accept novelty 4.0 of 10

Residual gain and bandpass errors induce excess variance that dominates bias in the 21-cm power spectrum and contaminates the EoR window in uGMRT Band 3 observations.
The Incidence of Large Ionized Bubbles at Redshift 13
astro-ph.GA 2026-06 unverdicted novelty 4.0 of 10

Using JWST UV luminosity functions, the surface density of galaxy-driven ionized bubbles with radius ≥2.5 cMpc at z≈13 is estimated at 1.33×10^{-2} arcmin^{-2} per Δz=1 in a fiducial model with f_esc=0.2 and log ξ_ion=25.5.
Imaging the 21-cm Signal from the Cosmic Dawn & Epoch of Reionization and the Connection with the Global Signal
astro-ph.CO 2026-06 unverdicted novelty 2.0 of 10

This review summarizes SKA-Low's tomographic imaging potential for the 21-cm signal and its connection to the global 21-cm signal.

How later papers used it

192 later papers cite it

Evidence: substantial. 178 of the citing papers share no author with it, and 86 of those carry a confident label from Pith's citation classifier.

Pith read 27 of the 288 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

13 later papers by other authors are listed below: 12 used its method or tool and 1 used its data or values.

Uses its method or tool 12 of 84 papers with this label

The excursion-set formalism first introduced in Ref. [ref] provides a convenient way to obtain this information.

Cosmological forecast of the 21-cm power spectrum using the halo model of reionization (2023) · Bubble-halo connection · 1.00
Employed this paper's excursion set model of reionization as the underlying reionization theory to evolve the initial density field to the ionization field.

Reconstruction of Cosmological Initial Density Field with Observations from the Epoch of Reionization (2023) · 0.99 · paraphrased: the licence does not allow quoting
Based its procedure for generating 3-D ionization maps at a given redshift on the excursion-set formalism of this paper.

On dark matter - dark radiation interaction and cosmic reionization (2017) · 1.00 · paraphrased: the licence does not allow quoting
Used this paper's bubble model of reionization to investigate the reionization process in the WDM scenario.

Reionization in the Warm Dark Matter Model (2012) · 0.93 · paraphrased: the licence does not allow quoting
Assumed an inside-out model of reionization based on the excursion set formalism of this paper, as implemented in publicly available 21cmFAST software.

Eliminating the optical depth nuisance from the CMB with 21 cm cosmology (2015) · 1.00 · paraphrased: the licence does not allow quoting
Reionization is modelled with the excursion-set approach [ref] , accounting for inhomogeneous recombinations [ref] .

Percent-level timing of reionization: self-consistent, implicit-likelihood inference from XQR-30+ Ly$\alpha$ forest data (2024) · Large-scale IGM simulations · 0.98
The ionisation state of the IGM is determined directly from the stellar mass grids following the excursion-set formalism ( [ref] ).

Thermal and Reionisation History within a Large-Volume Semi-Analytic Galaxy Formation Simulation (2022) · $$ reionisation · 0.99
Determined the ionisation field by applying this paper's excursion-set theory on the evolved density field.

Exploring the role of the halo mass function for inferring astrophysical parameters during reionisation (2024) · 0.98 · paraphrased: the licence does not allow quoting
Applied the model of this paper to calculate P_xx, P_xδ, and P_xδxδ.

Evolution of the 21 cm signal throughout cosmic history (2008) · 1.00 · paraphrased: the licence does not allow quoting
Density fields are obtained through the Zeldovich approximation while the excursion set formalism of [ref] is employed to generate the ionization and halo boxes.

Lyman Alpha Emitters and the 21cm Power Spectrum as Probes of Density-Ionization Correlation in the Epoch of Reionization (2021) · EoR Simulation · 0.99
Used the publicly available 21cmFAST package, which employs the excursion set formalism of this paper, to simulate reionization.

Constraining cosmology and ionization history with combined 21 cm power spectrum and global signal measurements (2015) · 1.00 · paraphrased: the licence does not allow quoting
Extrapolated its simulations to larger length scales by using this paper's excursion set method of modelling ionized regions in the epoch of reionization.

Revised estimates of CMB $B$-mode polarization induced by patchy reionization (2020) · 0.93 · paraphrased: the licence does not allow quoting

Uses its data or values 1 of 3 papers with this label

Assumed that for ordinary Pop I stars the total number of ionizing photons is similar to the value given in this paper.

Semi-Numerical Simulation of Reionization with Semi-Analytical Modeling of Galaxy Formation (2012) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

62 arXiv papers cite this in 111 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 44 sentences without a confident label

Builds on it 1 paper

Our work is based on the extension of the initial formalism of [ref] .

Influence of ~7 keV sterile neutrino dark matter on the process of reionization · Discussion · 0.95

Uses its method or tool 23 papers

The method is based on a combination of the bubble size function from [ref] with the halo model approach for the cosmic dawn [ref] to obtain very fast predictions for the global signal and the power spectrum at $z∼6-25$.

Cosmological forecast of the 21-cm power spectrum using the halo model of reionization · Introduction · 0.95
To recap our procedure we have used three main steps: (i) we have generated the dark matter distribution at a desired redshift, (ii) we then identified the location and mass of collapsed halos, (iii) we then generated the neutral hydrogen map using an excursion set formalism [ref] .

On dark matter - dark radiation interaction and cosmic reionization · Setting a constraint on ETHOS and WDM model parameter space · 0.99
This method is based on the semi-analytic model for reionization in [ref] .

An Improved Forecast of Patchy Reionization Reconstruction with CMB · Inhomogeneous Reionization · 0.99

Uses its data or values 3 papers

In step 2, we assume that for ordinary Pop I stars the total number of ionizing photons is similar to the value given in [ref] .

Semi-Numerical Simulation of Reionization with Semi-Analytical Modeling of Galaxy Formation · Semi Numerical simulation · 1.00
We will assume $ζ= 10$, which is among the lowest values quoted in the literature [ref] .

Not-quite-primordial black holes · Introduction · 0.88
For example, Ref. [ref] used $f_esc = 0.2$, $f_* = 0.05$, $N_γ/b = 3200$, which results in $ζ= 32$.

Influence of ~7 keV sterile neutrino dark matter on the process of reionization · Methods · 0.95

Compares with it 3 papers

Namely, in their models (involving either $Λ$CDM or sterile neutrino dark matter) the reionization evolves systematically faster (with $Δz_rei$ smaller by a factor of $∼2-3$) compared to our results, as well as the results of several other groups [ref] (see however [ref] ).

Influence of ~7 keV sterile neutrino dark matter on the process of reionization · Discussion · 0.98
The results from this model are similar to the bubble model of reionization [ref] .

O-V-S-Z and friends: Non-Gaussianity from inhomogeneous reionization · Introduction · 0.92
Complementary simulations by [ref] have been compared directly to the [ref] model showing reasonable agreement [ref] .

Evolution of the 21 cm signal throughout cosmic history · Calculation of fluctuations · 0.87

Cites it as support 2 papers

It has been shown analytically [ref] and is consistent with the results of numerical simulations [ref] (see also [ref] ).

The effects of the small-scale DM power on the cosmological neutral hydrogen (\HI) distribution at high redshifts · Results · 0.96
In fact, even during very early stages of reionization, the overlap between these individual ionized regions can be significant [ref] .

A Short Introduction to Reionization Physics · Generation of the ionized regions · 0.99

Cites it as background 20 papers

This marks the beginning of the Epoch of Reionization (EoR), during which the global signal decays smoothly to zero as the fraction of neutral hydrogen (HI) gradually vanishes [ref] .

A New Constraint on the Simulation of the Intergalactic Medium through the Evolution of the Neutral Hydrogen Fraction in the Epoch of Reionization · Introduction · 0.85
Their sizes and topology connect the galaxy population to the escape of ionizing photons, the timing of reionization, Ly$α$ transmission, 21 cm structure, and the integrated CMB optical depth [ref] .

The Incidence of Large Ionized Bubbles at Redshift 13 · Introduction · 0.97
Analytic models of the HII bubble size and resulting 21cm correlations were formulated by [ref] , who considered bubbles to self-ionize once they contained a sufficient mass fraction in galaxies (ionizing sources).

Evolution of the 21 cm signal throughout cosmic history · Calculation of fluctuations · 0.85

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

Arons, J., & Wingert, D. W. 1972, ApJ, 177, 1

View on Pith 1972

[2] [2]

Barkana, R. 2002, New Astronomy, 7, 85

View on Pith 2002

[3] [3]

Barkana, R., & Loeb, A. 2001, Phys. Rep., 349, 125 —. 2002, ApJ, 578, 1 —. 2003, ApJ, submitted, (astro-ph/0310338)

View on Pith Pith review arXiv 2001

[4] [4]

Barton, E.J., Davé, R., Smith, J.-D.T., Papovich, C., Hernquist, L. & Springel, V . 2004, ApJ, in press (astro-ph/0310514)

View on Pith Pith review arXiv 2004

[5] [5]

Becker, R. H., et al. 2001, AJ, 122, 2850

View on Pith 2001

[6] [6]

Bond, J. R., Cole, S., Efstathiou, G., & Kaiser, N. 1991, ApJ, 379, 440

View on Pith 1991

[7] [7]

Bouchet, F. R., Juszkiewicz, R., Colombi, S., & Pellat, R. 1992, ApJ, 394, L5

View on Pith 1992

[8] [8]

Cen, R., Haiman, Z., & Mesinger, A. 2004, ApJ, submitted, (as tro- ph/0403419)

View on Pith 2004

[9] [9]

Ciardi, B., & Madau, P. 2003, ApJ, 596, 1

View on Pith 2003

[10] [10]

Ciardi, B., Stoehr, F., & White, S. D. M. 2003, MNRAS, 343, 1101

View on Pith 2003

[11] [11]

Cooray, A., & Sheth, R. 2002, Phys. Rep., 372, 1 Di Matteo, T., Ciardi, B., & Miniati, F. 2004, MNRAS, submitt ed, (astro- ph/0402322) Di Matteo, T., Perna, R., Abel, T., & Rees, M. J. 2002, ApJ, 564, 576

View on Pith 2002

[12] [12]

Fan, X., et al. 2002, AJ, 123, 1247

View on Pith 2002

[13] [13]

Field, G. B. 1958, Proc. IRE, 46, 240 —. 1959, ApJ, 129, 525

View on Pith 1958

[14] [14]

Fukugita, M., & Kawasaki, M. 2003, MNRAS, 343, L25

View on Pith 2003

[15] [15]

Gnedin, N. Y . 2000, ApJ, 535, 530

View on Pith 2000

[16] [16]

Gnedin, N. Y ., & Prada, F. 2004, ApJ, submitted, (astro-ph/0403345)

View on Pith Pith review arXiv 2004

[17] [17]

Gnedin, N. Y ., & Shaver, P. A. 2003, ApJ, submitted, (astro-ph/0312005)

View on Pith Pith review arXiv 2003

[18] [18]

Gunn, J. E., & Peterson, B. A. 1965, ApJ, 142, 1633

View on Pith 1965

[19] [19]

Haiman, Z., & Holder, G. P. 2003, ApJ, 595, 1

View on Pith 2003

[20] [20]

Hernquist, L. & Springel, V . 2003, MNRAS, 341, 1253

View on Pith 2003

[21] [21]

Juszkiewicz, R., Bouchet, F. R., & Colombi, S. 1993, ApJ, 412, L9

View on Pith 1993

[22] [22]

Kogut, A., et al. 2003, ApJS, 148, 161

View on Pith 2003

[23] [23]

Lacey, C., & Cole, S. 1993, MNRAS, 262, 627

View on Pith 1993

[24] [24]

Loeb, A., Barkana, R., & Hernquist, L. 2004, ApJ, submitted, (astro- ph/0403193)

View on Pith 2004

[25] [25]

Madau, P., Meiksin, A., & Rees, M. J. 1997, ApJ, 475, 429 Miralda-Escudé, J., Haehnelt, M., & Rees, M. J. 2000, ApJ, 530, 1

View on Pith 1997

[26] [26]

Mo, H. J., & White, S. D. M. 1996, MNRAS, 282, 347

View on Pith 1996

[27] [27]

Morales, M. F., & Hewitt, J. 2003, ApJ, submitted, (astro-ph/0312437)

View on Pith Pith review arXiv 2003

[28] [28]

Oh, S. P., & Mack, K. J. 2003, MNRAS, 346, 871

View on Pith 2003

[29] [29]

Onken, C. A., & Miralda-Escudé, J. 2003, ApJ, submitted, (as tro- ph/0307184) Pelló, R., et al. 2004, A&A, 416, L35

View on Pith 2003

[30] [30]

Press, W. H., & Schechter, P. 1974, ApJ, 187, 425

View on Pith 1974

[31] [31]

Ricotti, M., Haehnelt, M. G., Pettini, M., & Rees, M. J. 2004, MNRAS, submitted, (astro-ph/0403327)

View on Pith Pith review arXiv 2004

[32] [32]

Santos, M. G., et al. 2003, ApJ, 598, 756

View on Pith 2003

[33] [33]

Santos, M. R. 2003, MNRAS, submitted, (astro-ph/0308146)

View on Pith Pith review arXiv 2003

[34] [34]

Scott, D., & Rees, M. J. 1990, MNRAS, 247, 510

View on Pith 1990

[35] [35]

Sheth, R. K. 1998, MNRAS, 300, 1057

View on Pith 1998

[36] [36]

Sheth, R. K. & Tormen, G. 1999, MNRAS, 308, 119

View on Pith 1999

[37] [37]

Sheth, R. K., & Tormen, G. 2002, MNRAS, 329, 61

View on Pith 2002

[38] [38]

Sokasian, A., Yoshida, N., Abel, T., Hernquist, L., & Spring el, V . 2003b, MNRAS, in press (astro-ph/0307451)

View on Pith Pith review arXiv

[39] [39]

Songaila, A. 2004, AJ, in press, (astro-ph/0402347)

View on Pith Pith review arXiv 2004

[40] [40]

Spergel, D. N., et al. 2003, ApJS, 148, 175

View on Pith 2003

[41] [41]

Springel, V . & Hernquist, L. 2003, MNRAS, 339, 312

View on Pith 2003

[42] [42]

Tozzi, P., Madau, P., Meiksin, A., & Rees, M. J. 2000, ApJ, 528, 597

View on Pith 2000

[43] [43]

White, R. L., Becker, R. H., Fan, X., & Strauss, M. A. 2003, AJ, 126, 1

View on Pith 2003

[44] [44]

Wyithe, J. S. B., & Loeb, A. 2003, ApJ, 588, L69 —. 2004, Nature, 427, 815

View on Pith 2003

[45] [45]

Zaldarriaga, M., Furlanetto, S. R., & Hernquist, L. 2004, ApJ, in press, (astro- ph/0311514) [ZFH04]

View on Pith 2004