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Hawking Radiation from non-evaporating primordial black holes cannot enable the formation of direct collapse black holes

T0 review · 0 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This paper argues that Hawking radiation from non-evaporating primordial black holes cannot supply the Lyman-Werner radiation needed to trigger direct collapse into supermassive black hole seeds in the early Universe.

desk verdict A clean, honest negative result that closes a loophole for non-evaporating PBHs as DCBH seeds, with the extreme-clustering escape hatch explicitly left open. read the letter →

arxiv 2411.09081 v2 pith:6V76IJRU submitted 2024-11-13 astro-ph.GA astro-ph.CO

Jonathan Regan , Marios Kalomenopoulos , Kelly Kosmo O'Neil This is my paper · ORCID
classification astro-ph.GAastro-ph.CO
keywords primordialblackholesHawkingradiationdirectcollapseLyman-Wernersupermassiveholeseedsmolecularhydrogensuppressionhigh-redshiftgalaxyformationcriticalintensity
topics Dark Matter
open problems Dark Matter
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 Hawking radiation from primordial black holes that have not yet evaporated could act as the Lyman-Werner radiation source that suppresses molecular hydrogen cooling and lets a primordial gas cloud collapse directly into a massive black hole seed. The authors derive a narrow mass window, roughly $4\times10^{-13}$ to $7.5\times10^{-12}\,M_\odot$, in which PBH Hawking temperatures are high enough to matter and X-ray feedback is not overwhelming. They then compute the Lyman-Werner specific intensity produced by such PBHs arranged as a point source, a uniform halo distribution, or an isothermal halo distribution, and compare it with the critical intensity $J_{\rm crit}\sim5$ to $1400$ (in units of $10^{-21}\,\mathrm{erg\,s^{-1}\,cm^{-2}\,Hz^{-1}\,sr^{-1}}$) needed for direct collapse. Their conclusion is that in every one of these geometries the delivered intensity falls many orders of magnitude short of critical, so non-evaporating PBHs cannot by themselves seed the supermassive black holes seen at high redshift. The paper leaves open the possibility that extreme central clustering of PBHs, with an internal-to-external density contrast near $10^7$, could change the answer.

What carries the argument

The machinery is the inverse relation between black hole mass and Hawking temperature, $T_{\rm BH}=\hbar c^3/(8\pi k_B G M_{\rm BH})\simeq 6.17\times10^{-8}(M_\odot/M_{\rm BH})\,\mathrm{K}$, combined with a blackbody photon spectrum $B_\nu$ modified by a greybody factor $f_\Gamma=0.24$ and photon fraction $f_{\rm ph}=0.2$. From this the authors build the Lyman-Werner specific intensity at a distance $d$ from a single PBH, $J_{\rm LW}=(B_{\rm LW}/4)(R_S/d)^2$, and integrate it over PBH number density profiles (constant distance, uniform sphere, isothermal sphere) to obtain the total intensity at the halo center. The comparison standard is the temperature-dependent critical intensity $J_{\rm crit}$ of Sugimura et al. (2014), which for the allowed mass window ranges from about 5 to 1400 in units of $J_{21}=10^{-21}\,\mathrm{erg\,s^{-1}\,cm^{-2}\,Hz^{-1}\,sr^{-1}}$. The inverse mass-temperature relation is what selects the narrow mass window, and the $(R_S/d)^2$ geometric dilution is what makes the intensity extremely small.

What would settle it

A simulation of a $\sim10^8\,M_\odot$ atomic-cooling halo at $z\sim20$ that places non-evaporating PBHs near $10^{-12}\,M_\odot$ with a central density contrast $f_{\rm in}/f_{\rm out}\sim10^7$ and computes the Lyman-Werner intensity at the halo center would refute the blanket conclusion if that intensity reached $J_{\rm crit}\sim5$.

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Extended reading notes

Core claim

The central claim is that Hawking radiation from non-evaporating primordial black holes cannot serve as the irradiating mechanism that enables direct collapse black hole formation. For PBH masses in the window $4\times10^{-13}\lesssim M_{\rm PBH}/M_\odot\lesssim 7.5\times10^{-12}$, the Hawking temperature lies in the range able to photodissociate $\mathrm{H}^-$ (energies $\gtrsim0.8\,$eV) and suppress $\mathrm{H}_2$ cooling, while avoiding premature evaporation and strong X-ray feedback. When such PBHs are modeled as a monochromatic population at fixed distance, spread uniformly through a halo, or distributed isothermally out to the virial radius, the resulting Lyman-Werner specific intensity at the halo center is many orders of magnitude below the temperature-dependent critical value $J_{\rm crit}$ from Sugimura et al. (2014), even if PBHs make up all of the dark matter. Even the most optimistic isothermal case would require the PBHs to approach within roughly $3\,$km of the halo center to reach $J_{\rm crit}\sim5$, which is unphysical. The paper therefore concludes that the mechanism fails, while explicitly preserving the possibility that strong central clustering, of the kind found necessary for evaporating PBHs by Lu et al. (2024), could rescue it.

Load-bearing premise

The paper assumes that the spatial distribution of PBHs in primordial halos is adequately represented by point-source, uniform, or isothermal profiles with nothing closer than about 1 parsec to the center and density normalized to the virial density, so extreme central clustering is not part of the model.

Editorial extensions

If this is right

  • PBHs in the mass range $4\times10^{-13}$ to $7.5\times10^{-12}\,M_\odot$ are excluded as standalone Lyman-Werner sources for direct collapse black hole formation, despite this mass range being otherwise largely unconstrained as a dark matter fraction.
  • Even under the most optimistic assumptions allowed by the model — $f_{\rm PBH}=1$, an isothermal profile, and the lowest critical intensity $J_{\rm crit}\sim5$ — the Lyman-Werner intensity remains orders of magnitude below threshold, with the required minimum radius of about $3\,$km being physically impossible.
  • The Lyman-Werner background contributed by such PBHs, roughly $J_{21}\sim10^{-26}$ to $10^{-20}$, is negligible compared with the stellar background of order $J_{21}\sim3.6$, so PBH Hawking radiation does not add to the cosmological Lyman-Werner background in a way that matters for $\mathrm{H}_2$ suppression.
  • If any PBH-based direct collapse mechanism is to work for non-evaporating PBHs, it must rely on extreme central clustering inside the halo, qualitatively confirming the density-contrast requirement previously found for evaporating PBHs.
  • Extended (non-monochromatic) PBH mass functions cannot rescue the scenario, because the product $B_{\rm LW}R_S^2$ that controls the intensity is maximized within the monochromatic mass window studied.

Reading between the lines

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

  • A consequence the authors leave implicit is that the same mass window, currently almost unconstrained by observations, becomes the natural target for searches if PBHs turn out to cluster as strongly as evaporating models require; the negative result would then apply only to unclustered PBH populations.
  • One testable extension is to include accretion luminosity onto these PBHs in dense halos; because accretion is neglected here, any additional Lyman-Werner photons from that channel would be a separate mechanism, but one that could alter the formation outcome.
  • A future measurement of the extragalactic background light in the 0.8–13.6 eV band with sensitivity near $J_{21}\sim10^{-20}$ could directly test the background calculation; a detection of a blackbody-shaped component from PBH Hawking radiation would reopen the mechanism.
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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

0 major / 5 minor

Summary. The paper tests whether Hawking radiation from non-evaporating primordial black holes (PBHs) with masses in the range approximately 4e-13 to 7.5e-12 M_sun can supply the Lyman-Werner (LW) radiation intensity required for direct collapse black hole (DCBH) formation at redshifts z ~ 10-30. The authors derive mass cuts from evaporation, X-ray-to-LW flux ratios, and a critical-temperature requirement, then compute the LW specific intensity for point-source, uniform-density, isothermal, and cosmological-background PBH distributions. They compare the resulting J21 values with the temperature-dependent Jcrit prescription of Sugimura et al. (2014) and find a shortfall of many orders of magnitude for the modeled distributions, while explicitly leaving open the possibility that extreme central clustering could change the conclusion.

Significance. If correct, this is a useful negative result: it closes a proposed mechanism for producing massive black hole seeds under standard assumptions, and it does so with a transparent and easily modifiable analytical framework. The comparison against an independent temperature-dependent Jcrit is appropriate, and the use of the most optimistic f_PBH = 1 normalization makes the failure conservative. The margin of failure is so large that the simplifying choices in the spectral treatment are unlikely to invert the conclusion for the distributions considered. The paper also makes its code publicly available, although the data-availability statement lacks a working link. The main qualification is that the abstract's caveat about significant central clustering is not quantified, and the title and Section 6 are worded more categorically than the analysis supports.

minor comments (5)
  1. [Sec. 4.4.3] The argument that reaching Jcrit would require rmin ~ 3 km and that this is unphysical because a 10^5 M_sun seed black hole has a larger Schwarzschild radius is not valid for a cluster of 4e-13 to 7.5e-12 M_sun PBHs; the relevant scale is set by the PBH distribution, not by the final seed. This does not affect the robust shortfall found for the adopted uniform and isothermal profiles, but the sentence should be reworded, or an explicit cusp calculation should be added.
  2. [Sec. 4.4.3] The text refers to "a halo of mass M_h ~ 10^-13 M_sun" in the paragraph discussing the rmin ~ 3 km requirement; this value is many orders of magnitude below any plausible atomic-cooling halo mass and appears to be a typo.
  3. [Sec. 6 and title] The abstract appropriately states that the mechanism cannot work "unless, perhaps" PBHs are significantly clustered, but the title and the Section 6 conclusion state the result categorically. Since Section 5.3 explicitly leaves the extreme-clustering case open, the wording should be aligned with the qualified claim.
  4. [Sec. 8] The data-availability statement says "We make our code public in DCBHs_HR_PBHs" but provides no repository URL or identifier; please include one so that the code is actually accessible.
  5. [Sec. 5.2] The constant greybody factor fGamma = 0.24 is described as a power-integrated ratio from Page (1976), but it is then applied uniformly to Bnu at every frequency. The text should explicitly state that this is an approximation and that the frequency dependence of the greybody factor is not modeled.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the negative result follows from an independent comparison of a first-principles Hawking spectrum against external Jcrit benchmarks, with no fitted parameters or self-citation chain doing the work.

full rationale

The derivation chain is self-contained and does not reduce to its own inputs. The Hawking spectrum (Eqs. 1-3) uses standard physics with constants from Page (1976). The flux estimate (Eqs. 9-10) is a geometric calculation. The PBH mass window in Section 4 is set by evaporation, X-ray, and critical-temperature constraints, each tied to external literature (e.g., Sugimura et al. 2014 for Tcrit and Jcrit; Ricotti 2016 and Park et al. 2021 for X-ray ratios). The intensity integrals (Eqs. 14-15) are evaluated under explicitly stated optimistic assumptions (fPBH=1, no self-shielding), and the result is compared against an external, temperature-dependent Jcrit range of 5.12-1400 from Sugimura et al. (2014). No parameter is fitted to make the scenario fail, and no prediction is constructed from the conclusion. The paper explicitly flags in Section 5.3 that extreme PBH clustering, as in Lu et al. (2024), is not modeled and could in principle alter the conclusion; this is a stated scope limitation, not circularity. Citations to the authors' own prior work are corroborating rather than load-bearing: the halo mass function comparison cites both Lovell et al. (2023) and O'Brennan et al. (2024), and the central intensity comparison rests on external Jcrit values. Therefore the paper earns a circularity score of 0.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central claim rests on standard Hawking radiation inputs, an external Jcrit benchmark, and the assumed spatial distribution of PBHs. The fiducial choices rmin = 1 pc and virial normalization are comparison-motivated, not fitted. No invented entities are introduced.

free parameters (4)
  • rmin = 1 pc (fiducial)
    Minimum radius for uniform and isothermal PBH distributions, chosen from Liu et al. (2022); varying it changes intensity but not the conclusion.
  • fGamma greybody factor = 0.24
    Constant factor from Page (1976) applied to the blackbody spectrum at all frequencies; actually an integrated photon-power ratio, used as a per-frequency multiplier.
  • fph photon fraction = 0.2
    Fraction of Hawking emission in photons, from Page (1976); affects luminosity linearly.
  • Jcrit benchmark = 5.12 to 1400 in J21 units
    Taken from the Sugimura et al. (2014) fitting formula; this external critical threshold is the reference the PBH intensity is compared against.
assumptions (6)
  • domain assumption Hawking radiation from a Schwarzschild black hole is a blackbody at temperature T_BH = hbar c^3 / (8 pi k_B G M_BH) with a greybody factor.
    Invoked in Eqs. (1)-(3); Hawking radiation is standard theory but not experimentally confirmed.
  • domain assumption Primary photon emission alone suffices for PBH masses above about 6.5e-17 solar masses.
    Section 5.1 justifies this for the mass range of interest.
  • domain assumption The Sugimura et al. (2014) fitting formula gives the correct Jcrit for blackbody radiation temperatures from 8000 to 2e5 K.
    Section 4.4 sets Jcrit = f(k_H-/k_H2); if the true threshold in realistic halos were much lower, the conclusion could weaken, but literature values remain far above the computed intensities.
  • ad hoc to paper PBH spatial distributions are captured by point-source, uniform, or isothermal profiles with r_min about 1 pc and density normalized to virial density.
    Sections 4.4.1-4.4.3; extreme clustering is not modeled, and the paper's caveat leaves this as the escape route.
  • domain assumption PBH accretion is negligible for masses in the range of interest.
    Appendix 9.2 and Rice and Zhang (2017); accretion feedback is a separate mechanism not considered here.
  • standard math Flat Lambda-CDM cosmology with H0 = 70 km/s/Mpc and Omega_m = 0.3.
    Used for halo virial radius and redshift-age conversions; a standard fiducial cosmology.

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Pith. "Pith review of Hawking Radiation from non-evaporating primordial black holes cannot enable the formation of direct collapse black holes." pith.science (2026). https://pith.science/paper/6V76IJRU

@misc{pith2026241109081,
  author       = {Pith},
  title        = {Pith review of: Hawking Radiation from non-evaporating primordial black holes cannot enable the formation of direct collapse black holes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6V76IJRU}},
  note         = {Machine review of arXiv:2411.09081}
}
abstract

The formation of supermassive black holes (SMBHs) in the early Universe is a subject of significant debate. In this study, we examine whether non-evaporating primordial black holes (PBHs) can offer a solution. We establish initial constraints on the range of PBH masses that correspond to Hawking radiation (HR) effective temperatures in the range needed to suppress $H_2$ cooling, which would facilitate the formation of massive black hole seeds in atomic cooling halos. We also investigate the specific intensity of the HR from non-evaporating PBHs and compare it with the critical radiation needed for direct collapse black holes (DCBHs). We show that HR from non-evaporating PBHs cannot serve as an irradiating mechanism to facilitate the formation of the seeds for the SMBHs we observe in the high-redshift Universe unless, perhaps, the PBHs within the relevant mass range comprise a significant fraction of dark matter and are significantly clustered towards the center of the primordial halo.

Figures

Figures reproduced from arXiv: 2411.09081 by the authors.

Figure 1
Figure 1. Note that these mass limits do not pose any restrictions to [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. — (a) Minimum estimated PBH halo mass (as a function of PBH mass and distance) that is required to produce J tot 21,LW ≳ Jcrit(MPBH) for the simplest scenario considered in this work: a population of monochromatic PBHs within the mass range of interest at a distance d from a primordial gas cloud. The minimum mass of the PBH halos that satisfy this condition (Mh ∼ 1027.8M⊙) are many orders of magnitudes larger than t… view at source ↗
Figure 3
Figure 3. — Specific intensity at the center of the halo for different halo masses. PBHs are distributed within the halo based on a uniform or isothermal density (Section 4.4.2 versus Section 4.4.3). The four panels of this figure investigate the effects of different density profiles (top left), of different initial redshifts of collapse (top right), of different PBH masses (bottom left), and of different minimum distances th… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: When the BH masses are below this threshold, massive particles start being produced6 . These particles are not the final end products for an energetic BH since they can decay further (Arbey & Auffinger 2019; Lu et al. 2024). A percentage of these secondary particles wo…
Figure 4
Figure 4. Figure 4: — Similar to [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]
Figure 5
Figure 5. Figure 5: — (a) PBHs evolution with redshift for specific temperatures of interest: Initial PBH masses for given blackbody temperatures in the redshift range of interest. In practice, the HR emitted from these BHs does not affect their mass evolution. (b) Mass range with effecti…
Figure 6
Figure 6. Figure 6: — Change of BLWR2 S with PBH mass. The dashed line shows the average value from the same range of masses for a specific PBH mass function. 9.3. PBH mass functions At the time of formation, PBHs can have a range of masses that may follow one of several proposed model-de…

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.