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Can supermassive stars form in protogalaxies due to internal Lyman-Werner feedback?

T0 review · 2 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Adding a nearby star's Lyman-Werner radiation suppresses, rather than enables, supermassive-star formation in atomic-cooling halos.

desk verdict Clean, well-executed negative result: internal Lyman-Werner feedback suppresses accretion in the one halo they simulate, but the single-halo generalization to all atomic-cooling halos is the real soft spot. read the letter →

arxiv 2501.12986 v1 pith:6P47WB2K submitted 2025-01-22 astro-ph.GA astro-ph.CO

James Sullivan , Zoltan Haiman , Mihir Kulkarni , Eli Visbal This is my paper · ORCID
classification astro-ph.GAastro-ph.CO
keywords PopulationIIIstarssupermassivestarformationdirect-collapseblackholeseedsLyman-Wernerfeedbackatomic-coolinghalosmolecularhydrogendissociationprotostellaraccretioncosmologicalzoom-insimulations
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks whether the Lyman-Werner (LW) ultraviolet light emitted by the first star born inside a protogalactic gas halo can strip molecular hydrogen from a neighboring clump of collapsing gas, letting that second clump collapse into a supermassive star, a proposed seed for supermassive black holes. The authors test the idea with hydrodynamical simulations of a massive halo containing two adjacent collapsing clumps about $20$ pc apart, adding an internal LW flux of $10^4 J_{21}$ ($J_{21}=10^{-21}$ erg s$^{-1}$ cm$^{-2}$ Hz$^{-1}$ sr$^{-1}$ is the standard LW intensity unit) either $20{,}000$ or $250{,}000$ years after the first protostar forms. In every case the extra radiation lowers the protostars' accretion rates and final masses rather than raising them: the second clump's star ends at $250$--$1000 M_\odot$ versus about $2000 M_\odot$ without the extra flux, and even a run with molecular hydrogen fully destroyed stalls at about $1200$ K, far below the about $10^4$ K atomic-cooling threshold needed for the supermassive route. The paper concludes that this internal LW feedback inside atomic-cooling halos is unlikely to form supermassive stars or massive black hole seeds.

What carries the argument

The machinery is a set of four ENZO adaptive-mesh-refinement simulations of a single $3.2\times 10^8 M_\odot$ atomic-cooling halo, Halo C, in which two protostellar clumps (A and B, about $20$ pc apart) collapse nearly simultaneously; protostars are represented by sink particles, and the runs differ only in the added internal Lyman-Werner flux and its turn-on time (none; $10^4 J_{21}$ at $20{,}000$ yr; $10^4 J_{21}$ at $250{,}000$ yr; and $10^{10} J_{21}$ with all H$_2$ cooling removed). Two analytic tools carry the interpretation: a front-propagation balance (equation 2) that compares H$_2$ dissociation by LW photons with H$_2$ re-formation through the H$^-$ bottleneck reaction, giving an H$_2$ `survival density' above which molecules survive, and a virial-temperature profile that shows the halo's shallow inner potential well can only support gas at about $1200$ K rather than the about $10^4$ K needed for atomic cooling. Together they show why the added LW flux heats the low-density envelope but not the dense core, and why even full H$_2$ dissociation cannot drive the collapse to supermassive-star conditions within the halo's dynamical time.

What would settle it

Run the same experiment on a grid of halos with deeper potential wells and clump separations from $2$ to $40$ pc, and check whether any configuration sustains accretion above $0.01 M_\odot$ yr$^{-1}$ for longer than $10^5$ yr after H$_2$ is fully dissociated; the paper's estimate implies the threshold lies near $6$ pc separation or a first star more massive than about $150 M_\odot$, where the H$_2$ survival density exceeds $10^6$ cm$^{-3}$. A positive result would show the negative conclusion is specific to Halo C, not general.

Watch

Extended reading notes

Core claim

Using a suite of ENZO adaptive-mesh-refinement simulations of a $3.2\times 10^8 M_\odot$ atomic-cooling halo with two nearby collapsing cores (clumps A and B), the authors show that adding an internal Lyman-Werner flux after the first protostar forms reduces the gas density and H$_2$ abundance in the accretion regions, raises the average gas temperature to several hundred kelvin but not above about $1000$ K, and cuts the accretion rate below the critical $0.01$--$0.04 M_\odot$ yr$^{-1}$ needed to avoid main-sequence contraction. The short-delay and long-delay runs produce second-clump protostars of about $250$ and $1000 M_\odot$, compared with about $2000 M_\odot$ in the background-only run; the first clump falls from about $7000$ to $4600$--$6000 M_\odot$. In an extreme `no-cooling' run with a $10^{10} J_{21}$ flux that fully dissociates H$_2$, the gas heats to about $1200$ K, reaches quasi-hydrostatic equilibrium near the local virial temperature, and accretion shuts off, leaving a $23 M_\odot$ star. Because the already-collapsed core has no reservoir of infall energy left to convert into heat, the dynamical time for about $10^4$ K gas at about $100$ pc is about $50$ Myr, far longer than the protostar's Kelvin-Helmholtz contraction time of $10^4$--$10^5$ yr. The paper therefore concludes that adjacent protostellar cores do not help form a supermassive star and that this route is unlikely to produce massive black hole seeds.

Load-bearing premise

The negative result rests on a single very massive, late-forming halo (which the authors argue is the easy case for making a supermassive star); if more typical halos have steeper-density cores, more closely spaced clumps, or heavier first stars, the internal ultraviolet flux and the depth of the gas's potential well would both be larger, and the outcome could change.

Editorial extensions

If this is right

  • Internal LW feedback from a first protostar suppresses rather than promotes growth of a nearby second protostar, lowering final stellar masses by factors of 2--8 in the simulated halo.
  • Even complete H$_2$ dissociation does not enable a supermassive star in this halo: the gas settles at about $1200$ K and accretion stops, because the dynamical time at the atomic-cooling radius exceeds the protostar's contraction time.
  • The accretion rates in all runs stay below the $0.01$--$0.04 M_\odot$ yr$^{-1}$ threshold, so the resulting protostars join the main sequence as ordinary-mass Population III stars rather than growing to $10^5$--$10^6 M_\odot$.
  • Consequently, sequential star formation within individual atomic-cooling halos is unlikely to be a major source of the massive black hole seeds that later grow into supermassive black holes.
  • A scenario in which a normal Population III star forms inside a region of warm gas that collapses tens of Myr later remains possible, and the paper identifies it as a follow-up study.

Reading between the lines

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

  • The negative result is demonstrated for one halo; scaling the clump separation down to about $6$ pc or raising the first star's mass would push the H$_2$ survival density above about $10^6$ cm$^{-3}$, and the paper does not simulate such configurations, so the conclusion is strongest for roughly $20$ pc separations and roughly $150 M_\odot$ first stars.
  • The no-cooling run isolates a timing bottleneck that any in-situ warm-atomic-gas mechanism must beat: gas at the atomic-cooling threshold about $100$ pc away has a $50$--Myr dynamical time, while the protostar contracts to the main sequence in $10^4$--$10^5$ yr; this suggests the limiting factor is the halo's potential well, not the LW flux alone.
  • If typical higher-redshift atomic-cooling halos have cuspier inner density profiles or more tightly packed cores, the internal-LW route could be reactivated; a systematic parameter sweep over halo mass, clump separation, and first-star mass would test the paper's conservative-generalization claim.
  • The paper's estimate that a roughly $150 M_\odot$ star at about $20$ pc gives $10^4 J_{21}$ implies that only a modest boost in LW luminosity or proximity is needed to cross the H$_2$ survival threshold, so the mechanism is not ruled out everywhere, only in the simulated configuration.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. This paper uses ENZO adaptive-mesh-refinement simulations of Halo C, an atomic-cooling halo at z~6.56 taken from Kulkarni et al. (2019), to test whether Lyman-Werner (LW) radiation from a first Population III star can dissociate H2 around a nearby protostellar clump and thereby promote the formation of a second, supermassive star. Four runs are compared: a background-only run, two runs with an additional internal LW flux of 1e4 J21 added after either a short (20 kyr) or long (250 kyr) delay, and an extreme no-cooling run with a uniform 1e10 J21 flux that fully dissociates H2. The simulations show that the additional LW flux reduces the accretion rates and final sink masses in both clumps relative to the background-only run (e.g., sink B1 reaches ~2000 Msun in the background-only run but only ~250 Msun and ~1000 Msun in the short- and long-delay runs). The no-cooling run raises the gas temperature to only ~1200 K, well below the atomic-cooling threshold, and the sink stalls at ~23 Msun. The paper concludes that internal LW feedback inside atomic-cooling halos is unlikely to facilitate the formation of supermassive stars or massive BH seeds.

Significance. If the conclusion holds, this is a useful negative result: it challenges an appealing mechanism for producing direct-collapse black hole seeds through sequential Population III star formation within a single atomic-cooling halo, complementing earlier work on external LW backgrounds. The paper's strengths are the clean controlled comparison of four runs, the explicit no-cooling diagnostic, the identification of a plausible physical explanation (dense-core H2 survives while outer gas heats and expands, and the shallow inner potential cannot raise the temperature to ~1e4 K), and the quantitative discussion of cooling vs. dynamical times. The simulations are internally consistent, and the negative trend is robust across two clumps and two flux turn-on delays. The main weakness is that the population-level conclusion is extrapolated from a single, already-collapsed halo, as discussed below.

major comments (2)
  1. [Section 6] The generalization from Halo C to the broader ACH population is not supported by the simulations. The text states that Halo C is conservative because it is massive and late-forming ('We therefore regard our result as conservative, and expect our conclusions to hold for higher-redshift ACHs'), but the failure mode identified in the no-cooling run (Sec 5.2, Figs 12-13, 15) is set by the shallow inner potential at r < 1 pc, where the gas has already collapsed and is pressure-supported at T~1200 K. This is an evolutionary-state property, not a total-halo-mass property. A higher-redshift ACH with a cuspier inner density profile, or one in which H2 is dissociated before/during the initial collapse, could have deeper inner potential and residual infall energy to shock the gas to ~1e4 K. To support the headline conclusion, the authors should either test additional halos or idealized density-profile variations, or explicitly restrict the conclusion to already-collapsed massive halos like Halo C.
  2. [Section 5.2] The no-cooling experiment is not a clean test of whether internal LW feedback can prevent H2 cooling in a typical ACH, because the extreme 1e10 J21 flux is switched on after Halo C's gas has already undergone H2-cooling collapse and assembled a dense, quasi-static core. The authors themselves note that gas at ~100 pc has T~8000 K but a dynamical time of ~50 Myr; the simulation shows quasi-hydrostatic settling at ~1200 K, demonstrating that this particular core cannot be re-heated by residual infall within the simulated time. This does not exclude the possibility that in a less-evolved halo, dissociating H2 before the initial collapse would allow infalling gas to shock to ~1e4 K and maintain high accretion. A simulation with the extreme flux applied before/at the onset of H2 cooling, or an idealized halo with a deeper inner potential, is needed to separate these two interpretations.
minor comments (4)
  1. [Section 3] The hydrogen number density normalization in the unnumbered equation is printed as n0 = 1.04e-6 cm^-3; this appears to be a typo for 1.04e6 cm^-3, since the electron-density fit and the protostellar-core densities in Figs 5 and 9 imply values near 1e6 cm^-3 at r < 0.1 pc. As written, the analytic dissociation-timescale estimate of ~150 yr is computed for a medium many orders of magnitude less dense than the simulated core and should be corrected.
  2. [Section 3] The first paragraph of Section 3 states that the second protostar is forming ~20 kpc away; this should be ~20 pc, consistent with the rest of the paper and with the quoted 1e4 J21 flux normalization.
  3. [Section 4.2.3] The text refers to 'snapshot #50' when discussing the central XH2 values in the short- and long-delay runs, but Figure 5 shows columns for snapshots #17, #35, and #60 only; please clarify whether the values refer to snapshot #60 or to an additional plotted/unplotted snapshot.
  4. [Table 1 / Section 5.2] The no-cooling run is listed in Table 1 with t_delay = 0, but Section 5.2 says the 1e10 J21 flux is added 'beginning at dynamic collapse (z = 6.5618)', which is slightly later than the simulation restart at z = 6.5648; the time normalization should be made consistent.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the negative conclusion is produced by direct controlled simulations; inherited initial conditions and self-citations are data and validation checks, not assumptions of the result.

full rationale

I find no step in which a result is assumed by construction or a fitted parameter is renamed a prediction. The initial conditions are taken from Kulkarni et al. (2019), a paper whose authors overlap with the present work, but that prior paper supplies only the zoom-in halo, the radiation backgrounds, and the sink-particle method; the paper's negative conclusion (Secs. 4-5) is obtained from new ENZO runs that compare otherwise identical simulations with and without added LW flux. The sink method is additionally cross-checked against the independent Regan & Downes (2018) algorithm, so the self-citation is not the load-bearing evidence. The analytical estimates in Sec. 3 use density, electron-density, and temperature profiles fitted from the simulation (Eqs. 3-4), but these are diagnostic scalings for front propagation, and the paper explicitly qualifies them: 'This analytical result does not fully take into account self-shielding or the progression of this front at different speeds.' The headline result rests on the direct numerical experiments: the 10^4 J21 runs (Sec. 4) and the artificial 10^10 J21 no-cooling run (Sec. 5.2), whose outcome (gas settles around 1200 K, accretion stalls at 23 M_sun) is not enforced by any input parameter. The 'H2 survival density' calculation is a rate balance, not a fit. The main weakness is generality, not circularity: the paper extrapolates from one already collapsed, late-forming halo, and itself flags that 'The likelihood of scenarios such as forming clumps at much closer distances would need to be assessed' and asserts 'We therefore regard our result as conservative, and expect our conclusions to hold for higher-redshift ACHs.' That is an untested transferability claim, and the abstract's 'too shallow to promptly heat the gas to ≳1000 K' wording sits awkwardly with the no-cooling run's ~1200 K plateau, but neither issue reduces the derivation to its own inputs. No equation is equivalent to its input by construction, and no fitted value is presented as a prediction.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new particles, forces, or entities. The central claim rests on inherited simulation inputs (halo, backgrounds), modeling choices (uniform LW field, sink particles), and a single-halo generalization argument. The free parameters are simulation controls, not fitted constants, but they shape the result and are listed for transparency.

free parameters (5)
  • Internal LW flux amplitude (short/long-delay runs) = 10^4 J21
    Chosen to represent a roughly 150 solar mass Pop III star at about 20 pc separation between clumps. Not derived from the simulation; if the actual flux is larger, H2 in the dense cores could be dissociated.
  • Turn-on delay for internal LW flux = 20,000 yr (short-delay) and 250,000 yr (long-delay)
    Chosen to bracket early versus late appearance of the first star's LW radiation. Both delays suppress accretion, so the result is insensitive to this choice.
  • Artificial no-cooling LW flux = 10^10 J21
    A deliberately extreme flux used to fully dissociate H2 and isolate the effect of removing molecular cooling. Far above any realistic stellar flux, but serves as a numerical control.
  • Background LW flux = 100+75*(F/F0) J21 with F=0.1 F0, about 107.5 J21
    Adopted from Kulkarni et al. 2019 as representative of an overdense region; sets the baseline level of H2 suppression.
  • Background ionizing flux = 0.1 F0 = 6.7e5 photons/s/cm^2
    Adopted from Kulkarni et al. 2019 to delay the collapse of the halo and shape its mass and formation time.
assumptions (5)
  • domain assumption ENZO's nine-species primordial chemistry and associated cooling rates are adequate, and HD/deuterium cooling is negligible.
    Stated in Sec 2 with reference to McGreer & Bryan 2008 and Kulkarni et al. 2019. If HD cooling were significant, fragmentation and cooling would differ.
  • domain assumption The internal LW radiation field can be approximated as a uniform, isotropic background rather than a point source with radial falloff.
    Sec 2 states that all radiation is treated as isotropic and uniform. This overestimates the flux far from the source but is a conservative choice for H2 destruction near the clump.
  • domain assumption The sink particle method (maximum refinement level 18, merging within 10 cell widths) adequately captures protostar formation and accretion.
    Sec 2 describes the method and cites agreement with Regan & Downes 2018. Sink accretion prescriptions can affect final masses, and no convergence test is provided.
  • domain assumption The halo's prior evolution inherited from Kulkarni et al. 2019 produces an atomic-cooling halo representative of SMS host candidates.
    Sec 2 selects Halo C from prior work, and Sec 6 argues it is conservative, but this is a qualitative argument rather than a demonstrated one.
  • standard math Standard analytic rates for H2 dissociation and formation (Shang et al. 2010; Galli & Palla 1998) apply in the simulated density and temperature regime.
    Used in Sec 3 and Sec 5.1 for order-of-magnitude estimates; these are standard fits from the literature.

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Cite this review

Pith. "Pith review of Can supermassive stars form in protogalaxies due to internal Lyman-Werner feedback?." pith.science (2026). https://pith.science/paper/6P47WB2K

@misc{pith2026250112986,
  author       = {Pith},
  title        = {Pith review of: Can supermassive stars form in protogalaxies due to internal Lyman-Werner feedback?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6P47WB2K}},
  note         = {Machine review of arXiv:2501.12986}
}
abstract

Population III stars are possible precursors to early massive and supermassive black holes (BHs). The presence of soft UV Lyman Werner (LW) background radiation can suppress Population III star formation in minihalos and allow them to form in pristine atomic cooling halos. In the absence of molecular hydrogen ($\rm H_2$) cooling, atomic-cooling halos enable rapid collapse with suppressed fragmentation. High background LW fluxes from preceding star-formation have been proposed to dissociate $\rm H_2$. This flux can be supplemented by LW radiation from one or more Population III star(s) in the same halo, reducing the necessary background level. Here we consider atomic-cooling halos in which multiple protostellar cores form close to one another nearly simultaneously. We assess whether the first star's LW radiation can dissociate nearby $\rm H_2$, enabling the prompt formation of a second, supermassive star (SMS) from warm, atomically-cooled gas. We use a set of hydrodynamical simulations with the code ENZO, with identical LW backgrounds centered on a halo with two adjacent collapsing gas clumps. When an additional large local LW flux is introduced, we observe immediate reductions in both the accretion rates and the stellar masses that form within these clumps. While the LW flux reduces the $\text{H}_2$ fraction and increases the gas temperature, the halo core's potential well is too shallow to promptly heat the gas to $\gtrsim$ 1000 K and increase the accretion rate onto the second protostar. We conclude that internal LW feedback inside atomic-cooling halos is unlikely to facilitate the formation of SMSs or massive BH seeds.

Figures

Figures reproduced from arXiv: 2501.12986 by the authors.

Figure 1
Figure 1. Left: Gas density centered on clump A’s maximum density gas cell and projected along the x-axis. Both clump A and clump B are circled. Clump B is marked by the white arrow. Right: Slice of gas temperature along the x-axis and centered on clump A’s maximum density gas cell. Both clumps are again circled and an arrow points to clump B. Both the projection and slice are at snapshot #10, 𝑧 = 6.5648. our tests. Finally, … view at source ↗
Figure 2
Figure 2. The top panel displays the sink B1’s mass and the bottom panel displays its accretion rate as a function of time for each run. 𝑡 = 0 is defined as the (re)start of the simulation at 𝑧 = 6.5648. The three solid colored lines represent the three test runs (blue: background only; red: short-delay; black: long-delay). The vertical red and black dashed lines represent when the additional internal LW flux is added in the … view at source ↗
Figure 4
Figure 4. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figures from the paper (9 more)
Figure 5
Figure 5. Figure 5: From top to bottom: radial profiles of temperature, gas number density, 𝑋H2 , and 𝑋e centered about sink B1. From left to right, the columns display the profiles at snapshot #17 (𝑧 = 6.5644, ∼0.06 Myr after sink A1 forms in snapshot #11), 0.18 Myr later at snapshot #35…
Figure 6
Figure 6. Figure 6: The evolution of the sink A1’s accretion rate (bottom panel) and its mass (top panel) in the first three runs. The time is again defined as in Figs. 2-4. The three colors represent the three test runs with the same color scheme as in Figs. 2-5. The additional internal …
Figure 7
Figure 7. Figure 7: Evolution of the temperature (top panel) and density (bottom panel) at sink A1’s location. The sink particle location is defined as the grid cell con￾taining sink A1. Again the blue, red, and black lines represent the background only, short-delay, and long-delay cases …
Figure 9
Figure 9. Figure 9: From top to bottom: radial profiles of temperature, gas number density, 𝑋H2 , and electron density centered on sink A1. We display the region from 0.02 to 2 pc around sink A1. This limits the number of empty cells that the produce vertical spikes seen in the leftmost c…
Figure 10
Figure 10. Figure 10: From left to right, the three panels show radial profiles of the cooling time (𝑡H2 ) and dynamical time (𝑡dyn) at snapshot #17 (𝑧 = 6.5644), 0.18 Myr later at snapshot #35 (𝑧 = 6.5633), and an additional 0.25 Myr later at snapshot #60 (𝑧 = 6.5618). The blue, red, and …
Figure 11
Figure 11. Figure 11: The evolution of sink A1’s accretion rate (bottom panel) and mass (top panel) in the background-only (blue), short-delay (red), and no-cooling (black) runs. In the no-cooling run, the accretion shuts off soon after the flux is added and the mass stalls at 23 M⊙. we fi…
Figure 13
Figure 13. Figure 13: The top and bottom panels show the time evolution of the av￾erage temperature and density respectively within 1 pc of sink A1. Again the blue, red, and black lines represent the background-only, short-delay, and no-cooling runs respectively, as in Figs. 11 and 12. The…
Figure 14
Figure 14. Figure 14: Phase diagrams of temperature, density, and 𝑋H2 surrounding sink A1 at 𝑡 = 0 Myr (top left), 0.25 Myr (top right), 0.50 Myr (bottom left), and 0.75 Myr (bottom right) in the no-cooling run. Each panel shows gas within 1 pc from sink A1. We see the gas temperature rise…
Figure 15
Figure 15. Figure 15: Radial profile of the virial temperature, centered around sink A1 in the no-cooling run. From left to right, the three panels show the profiles at snapshot #10 (z = 6.5648), 0.25 Myr later at snapshot #35 (z = 6.5633), and an additional 0.25 Myr later at snapshot #60 …

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.