Primordial Black Holes as Coma Cluster Dark Matter and the Unresolved {\gamma}-Ray Background

Bhashin Thakore; Jeremy Mould

REVIEW 4 major objections 5 minor 44 references

Primordial Black Holes as Coma Cluster Dark Matter and the Unresolved {\gamma}-Ray Background

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Hawking radiation from tiny primordial black holes at 0.1% of Coma's dark matter can explain the cluster's GeV glow.

desk verdict The Coma fit rests on a factor-of-100 energy error—the claimed 5 GeV cutoff requires PBHs two orders of magnitude lighter than quoted—but the Draco X overdensity and the honest UGRB feasibility analysis give the paper salvageable pieces. read the letter →

arxiv 2507.01421 v1 pith:GE7B64L2 submitted 2025-07-02 astro-ph.HE astro-ph.COastro-ph.GA

Jeremy Mould , Bhashin Thakore This is my paper · ORCID

classification astro-ph.HEastro-ph.COastro-ph.GA

keywords primordialblackholesHawkingradiationComaclusterunresolvedgamma-raybackgroundweakgravitationallensingdarkmatterFermi-LATDracoX

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 argues that the GeV (giga-electronvolt) gamma-ray glow of the Coma cluster can be explained by Hawking radiation—the quantum evaporation of black holes—from primordial black holes (PBHs, black holes formed in the early universe) with masses between $10^{-19}$ and $10^{-17}$ solar masses, provided those PBHs make up about 0.1% of the cluster's dark matter. It treats that fraction as an upper limit, because the same GeV emission could instead come from a giant radio halo. The paper then tests whether evaporating PBHs can be seen statistically in cross-correlations between the unresolved gamma-ray background (the diffuse glow not tied to individual sources) and weak gravitational lensing (the subtle distortion of distant galaxy shapes by intervening mass), and concludes that the measured correlation is consistent with known astrophysical sources such as blazars (active galaxies whose jets point toward Earth), not with PBH evaporation. It also identifies a massive cluster-of-clusters, Draco X, that emits no detectable GeV radiation despite being a scaled-up analogue of Coma. If the central claim is right, galaxy clusters become a concrete site for testing this particular PBH dark-matter scenario, while unresolved-background cross-correlations remain too insensitive to see it.

What carries the argument

The machinery that carries the Coma argument is the Hawking evaporation rate $\dot{m}=-\alpha\hbar c^4/(G^2m^2)$, equivalently a fractional mass-loss rate of about $3\times10^{-23}\,\mathrm{s}^{-1}$, which makes lighter black holes evaporate faster and radiate at higher energies; when convolved with the assumed scale-invariant initial mass function $n(m)\propto m^{-1}$, it sets both the downward slope of the GeV spectrum and the $\sim5$ GeV cutoff. For the large-scale-structure test, the load-bearing object is the redshift-dependent PBH window function $W_{\mathrm{PBH}}$, a line-of-sight integral over the evaporation rate with $(1+z)^{-4}$ dimming and attenuation, whose poor overlap with the weak-lensing shear window functions is the reason the cross-correlation approach cannot see PBH evaporation.

What would settle it

A gamma-ray measurement of Coma that resolves the predicted spectral turnover just above 5 GeV would settle this: if the spectrum continues smoothly beyond 5 GeV instead of cutting off, the assumed one-over-mass distribution and the 0.1% abundance fit are ruled out.

Watch

Extended reading notes

Core claim

The paper's central claim is that a specific, modest abundance of evaporating PBHs can account for Coma's GeV emission. Using the Hawking mass-loss rate and an assumed initial mass function $n(m)\propto m^{-1}$, a dark-matter fraction $f=10^{-3}$ in the mass window $10^{-19}{-}10^{-17}\,M_\odot$ yields a spectrum that fits the cluster's measured GeV flux, with a turnover just above 5 GeV produced by the exhaustion of the lowest-mass black holes, whose evaporation rate scales as $m^{-2}$. Because a competing explanation (secondary emission from a giant radio halo) can also match the data, the paper frames $f=10^{-3}$ as an upper limit. Extrapolating the same evaporation model to cosmological scales with $f=1$ gives an unresolved gamma-ray background intensity roughly five orders of magnitude below the observed one, so the detected UGRB--lensing cross-correlation (signal-to-noise 8.9) is attributed to clustered astrophysical sources rather than PBHs, and the method is judged unable to constrain PBH evaporation. Separately, the paper reports the identification of Draco X, an overdensity of X-ray clusters at $z=0.12$ with mass around $7\times10^{16}\,M_\odot$, which shows no corresponding excess of extended gamma-ray sources.

Load-bearing premise

The calculation assumes the black holes are distributed in mass as one-over-mass, a power law taken from an earlier paper, and everything about the predicted spectrum and the 0.1% abundance limit follows from that choice; if the true mass distribution is different, the fit changes, and the paper gives no independent evidence for this power law.

Editorial extensions

If this is right

If the Coma fit holds, the cluster's GeV glow can be powered by Hawking radiation from PBHs with masses $10^{-19}$ to $10^{-17}\,M_\odot$ at a dark-matter fraction $f=10^{-3}$, and that fraction is an upper limit if the giant-radio-halo model is correct.
The predicted spectrum declines with decreasing energy according to the assumed $m^{-1}$ mass function and cuts off just above 5 GeV, giving future gamma-ray measurements a sharp feature to confirm or reject.
Attributing a measurable part of the unresolved gamma-ray background to PBH evaporation would require PBH abundances far above what is plausible, so current UGRB--lensing cross-correlations cannot constrain evaporating PBHs in this mass range.
Because the PBH gamma-ray window and the shear window overlap only weakly in redshift, deeper lensing surveys under these assumptions will not substantially improve sensitivity to PBH evaporation.
A Coma-like Draco X should emit more than twice Coma's GeV flux, yet no extended gamma-ray source excess is seen there, implying that the GeV emission mechanism is not universal across massive clusters.

Reading between the lines

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

The $f=10^{-3}$ limit is conditional on the assumed $n(m)\propto m^{-1}$ mass function; a different mass distribution would change the spectral slope and the inferred abundance, so the limit is only as secure as that external input.
Because the predicted UGRB contribution sits about five orders of magnitude below the measured background, more sensitive cross-correlation analyses are unlikely to reveal PBH evaporation in this mass range; the Coma spectral cutoff and independent abundance probes would be sharper tests.
Draco X's null GeV detection could mean that Coma's glow is produced by the radio halo rather than Hawking radiation, or that Draco X's dark-matter distribution differs from Coma's; matched X-ray and gamma-ray observations of the two systems would separate those options.
A targeted search for the predicted 5 GeV turnover in Coma, with good energy resolution, would provide a nearly parameter-free test of the $m^{-1}$ mass function and the $10^{-3}$ abundance.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

The central claim in this paper doesn't survive a basic Hawking-evaporation check. The authors say PBHs in the mass range 10^-19 to 10^-17 Msun produce GeV emission in Coma, with a cutoff just above 5 GeV. For that mass range, the Hawking temperature is 0.5–50 MeV, primary photons peak between roughly 0.1 and 0.3 GeV, and the flux at 5 GeV is exponentially small. The claimed cutoff from 'exhaustion of lower mass PBHs' is also wrong: a 10^-19 Msun PBH has an evaporation lifetime around 2×10^10 yr, longer than the age of the Universe. So the Coma fit, as written, cannot be produced by the stated PBH population. This is a load-bearing error.

What is actually new: the specific Coma fit with f=10^-3, the identification of the Draco X overdensity, and a UGRB cross-correlation feasibility statement that applies an existing pipeline. The authors are honest that f is fitted, not predicted, and they treat it as an upper limit because of the alternative radio-halo explanation. Draco X looks like a real empirical structure from the MCXC-II catalog, and the window-function analysis in Sec. 4 is a reasonable application of Thakore et al.

Soft spots, proportionally: the energy-scale error invalidates the headline result and also enters the UGRB calculation, where 10^-18 Msun is claimed to peak at ~5 GeV; the correct peak is about 30 MeV. The qualitative conclusion (f=1 PBHs contribute negligibly to the UGRB in this energy range) probably survives, but the numbers need redoing. The Draco X mass of 7.2×10^16 Msun is given without derivation, and the quoted 90% interval does not bracket the central value—likely a typo. The IMF slope n ∝ m^-1 is assumed from Mould (2025) with no independent justification, and the fit cannot distinguish between IMF choices. There is also no comparison with existing PBH evaporation constraints, which is a serious gap even for a short paper.

Who gains: readers working on PBH constraints might find Draco X worth following, and the corrected UGRB cross-correlation argument could be a useful footnote. The Coma claim, as stated, is not credible.

Recommendation: send it to referees, but ask for a quantitative re-derivation of the evaporation spectrum and mass range. If the authors shift the mass range to ~10^-21–10^-19 Msun (where the cutoff would actually fall near 5 GeV) or reframe it as MeV emission, the fit could become testable. As written, it should not be accepted.

Referee Report

4 major / 5 minor

Summary. The paper has three parts. First, it proposes that Hawking radiation from primordial black holes with masses 1e-19 to 1e-17 solar masses, at a fraction f=1e-3 of the Coma cluster dark matter, can explain the cluster's GeV emission measured by Baghmanyan et al. (2022); this fraction is presented as an upper limit because alternative emission from a giant radio halo may also explain the data. Second, it uses 12 years of Fermi-LAT data and DES Y3 weak-lensing measurements, together with a PBH window function, to argue that even with f=1 and a single PBH mass of 1e-18 solar masses, the predicted intensity is about five orders of magnitude below the unresolved gamma-ray background, so the cross-correlation approach cannot constrain PBH evaporation. Third, it identifies a cluster of X-ray clusters, Draco X, at z=0.12, estimates its mass and luminosity, and discusses the absence of corresponding GeV emission.

Significance. If the central calculation were sound, the Coma PBH interpretation would be an interesting application of Hawking radiation to cluster-scale dark matter, and the UGRB cross-correlation analysis would provide a useful null result. The manuscript is transparent that f is fitted and that the UGRB estimate uses f=1 as a conservative upper bound, and it makes use of real Fermi-LAT and DES data. However, the mass-energy mapping in the Coma fit is off by about two orders of magnitude, and the quoted UGRB peak energy is off by about three orders of magnitude. These errors invalidate the quantitative conclusions of Sections 3 and 4, so the paper's current significance is limited.

major comments (4)

[Sec. 3, Fig. 2] The central claim that PBHs with masses 1e-19 to 1e-17 solar masses can explain the Coma GeV emission is inconsistent with Hawking evaporation physics. For a Schwarzschild PBH, T = 1.06e13 (1 g/M) GeV, so the stated mass range corresponds to T between about 53 MeV and 0.53 MeV; the primary photon spectrum peaks below about 100 MeV and is exponentially suppressed at 5 GeV. The Figure 2 caption's cutoff 'just above 5 GeV' therefore cannot arise from the stated PBH population. The caption's explanation that the cutoff is due to exhaustion of lower-mass PBHs is also not viable: a 1e-19 solar mass PBH has an evaporation timescale of about 2e10 yr, longer than the age of the Universe. A PBH light enough to emit a 5 GeV peak (M about 1e-21 solar masses) would have evaporated in about 2e4 yr and would not be present at z=0. The mass range and the resulting fit need to be corrected before the Coma interpretation can be evaluated.
[Sec. 4, Eq. (2)] The statement after Eq. (2) that for f=1 and m=1e-18 solar masses the average PBH intensity 'peaks at ~5 GeV' is incorrect by about three orders of magnitude: the Hawking temperature for 1e-18 solar masses is about 5.3 MeV, so the primary photon spectrum peaks in the MeV range, not at 5 GeV. Because Eq. (1) uses this spectrum to compute the PBH window function, the quoted intensity of about 1e-13 cm^-2 s^-1 sr^-1 and the conclusion that PBHs contribute negligibly to the UGRB must be recalculated with the correct energy assignment.
[Sec. 5] The Draco X mass estimate is internally inconsistent and lacks derivation. The text gives an integrated mass of about 7.2e16 solar masses with a 90% confidence interval ranging from 0.66e16 to 2.0e16 solar masses, but this interval does not contain the quoted central value, and no method is given for either number. This needs to be corrected or substantiated before Draco X can be used as a cosmological probe.
[Sec. 3] The agreement with the Baghmanyan et al. (2022) spectrum is not a quantitative fit: f=1e-3 is chosen to match the observed flux, and no error bars or statistical measure are presented for the predicted spectral shape. Since the assumed initial mass function n(m) proportional to m^-1 determines both the slope and the cutoff location, the reported agreement cannot by itself constrain the PBH fraction or distinguish this IMF from other choices.

minor comments (5)

[Eq. (1)] The quantities dt/dz and e^-tau in Eq. (1) are not clearly defined; tau is said to be integrated along the line of sight for the DES source galaxies, but gamma-ray attenuation should also account for extragalactic background light absorption, which is not discussed.
[Fig. 1] The y-axis label 'GeV/M /s' and the relation between the 'proportion of PBH fuel consumed' and the plotted curves are confusing; the color-bar labels 'Timestep' should be explained in the caption.
[Table 1] The footnote spells the author name as 'Fusco-Fermiano', while the reference list has 'Fusco-Fermiano R.'; please check the correct spelling and make it consistent.
[Abstract] The abstract states 'If 0.1% of the dark matter in the Coma cluster is PBH in this mass range, a fit to the cluster's GeV emission is obtained' as if it were a result; the conditional nature of the assumption should be explicit throughout the text.
[Sec. 5] The phrase 'a lower limit on its X-ray luminosity, relative to Coma, is estimated to be 58 times greater' is grammatically ambiguous; please clarify whether the lower limit is 58 times the Coma luminosity.

Circularity Check

1 steps flagged · score 6.0 of 10

Central Coma 'fit' is a normalization fit: f=1e-3 is chosen to match the GeV data, so the amplitude claim reduces to the fitting condition.

fitted input called prediction [Section 3, 'Source of the Emission']
"To fit the available GeV data, we set the fraction of DM that lies between 10−19 and 10−17 M⊙ to f = 10−3."

The predicted GeV flux from PBHs is directly proportional to f, with the same spatial template and distance for all energies. Setting f = 10^-3 so that the model matches the Baghmanyan et al. (2022) flux makes the statement 'If 0.1% of the Coma cluster’s dark matter is PBH ... a fit to the cluster’s GeV emission is obtained' true by construction for the normalization. The paper does not derive f from an independent constraint; the 'fit' is the fitting equation itself. The spectral shape and the separate UGRB calculation with f=1 are not circular, so this is a partial, amplitude-level circularity.

full rationale

The Coma section is a transparency-explicit fit: f=1e-3 is selected 'to fit the available GeV data', so the claim that a 0.1% PBH fraction reproduces the Coma GeV amplitude is an identity in normalization, not an independent prediction. The spectral shape is not fitted; it follows from the assumed Hawking spectrum and the n~m^-1 IMF taken from Mould (2025). We did not treat the IMF as a separate circularity because the paper does not derive it from the Coma data, and its status as an independent prior cannot be judged from this manuscript; at most it is an ansatz-dependent assumption. The UGRB cross-correlation section uses f=1 as a forward, non-circular upper-limit calculation, and its null conclusion is independent of the Coma fit. The paper itself acknowledges that 'such an interpretation is speculative', which supports treating the Coma section as an illustrative fit rather than a derived prediction. A separate physical inconsistency exists as written: 1e-19 to 1e-17 solar-mass PBHs have Hawking temperatures of roughly 0.5 to 50 MeV, not the 5 GeV cutoff claimed, and the low-mass end is not exhausted at z=0; that is a correctness concern rather than circularity. Overall score 6 reflects the central amplitude claim reducing to its fitted input, while the spectral shape remains independent.

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

The Coma scenario is underdetermined: the normalization f is fitted to the same GeV data it is supposed to explain, and the spectral shape depends on an assumed IMF. No new particles or forces are introduced; Draco X is an empirical overdensity, not a theoretical entity.

free parameters (4)

PBH dark matter fraction f in Coma = 10^-3
Set to 1e-3 to fit the GeV data (Sec. 3). The amplitude of the predicted Hawking radiation spectrum is therefore matched to the observation.
PBH mass range lower bound = 10^-19 M_sun
Chosen so that Hawking temperatures can reach the GeV band; no independent constraint from Coma data.
PBH mass range upper bound = 10^-17 M_sun
Chosen by hand; heavier PBHs emit mostly below the GeV band and would not contribute to the fit.
Single PBH mass for UGRB window function = 10^-18 M_sun at f=1
Section 4 adopts f=1 and m=1e-18 M_sun to estimate a maximum PBH contribution to the UGRB. A true maximum over the allowed mass distribution is not computed.

assumptions (4)

domain assumption Hawking mass-loss rate from Mosbech and Picker (2022)
The evaporation rate dm/dt is taken from this reference and used for both the Coma fit and the UGRB intensity. It is not derived in the paper.
ad hoc to paper PBH initial mass function n(m) proportional to m^-1
Adopted from Mould (2025). It sets the slope of the GeV spectrum and is not independently constrained by the data used in this paper.
domain assumption DM and hot baryons have the same spatial distribution in Coma
Stated in Section 3 as an approximation. The flux contours assume this co-spatiality, which is approximate given baryonic outflows.
domain assumption Coma is optically thin to electron scattering and pair production for GeV photons
Section 2 argues the optical depth is low, allowing GeV photons to escape. The UGRB calculation also uses an e^-tau factor without specifying tau.

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Cite this review

Pith. "Pith review of Primordial Black Holes as Coma Cluster Dark Matter and the Unresolved {\gamma}-Ray Background." pith.science (2026). https://pith.science/paper/GE7B64L2

@misc{pith2026250701421,
  author       = {Pith},
  title        = {Pith review of: Primordial Black Holes as Coma Cluster Dark Matter and the Unresolved \gamma-Ray Background},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GE7B64L2}},
  note         = {Machine review of arXiv:2507.01421}
}

read the original abstract

If 0.1% of the dark matter in the Coma cluster is constituted by primordial black holes (PBHs) with masses ranging from 10^-19 to 10^-17 solar masses, then the observed GeV {\gamma}-ray emission from the cluster could potentially be attributed to Hawking radiation. The emitted spectrum is inversely proportional to the black hole's mass, meaning lighter PBHs radiate at higher energies, potentially falling within the GeV range. If 0.1% of the Coma cluster's dark matter is PBH in this mass range, a fit to the cluster's GeV emission is obtained. We then investigate the potential for constraining evaporating PBHs through cross-correlations between the Unresolved Gamma-Ray Background and weak gravitational lensing. Utilizing 12 years of Fermi-LAT observations and weak lensing measurements from the Dark Energy Survey Year 3, we assess whether such correlations can reveal a PBH {\gamma}-ray component. While a statistically significant correlation between the UGRB and large-scale structure has been observed, this signal is consistent with emission from clustered astrophysical sources such as blazars. Attributing a measurable fraction of the UGRB to PBH evaporation would require unrealistically large PBH abundances. We also draw attention to a cluster of Coma-like X-ray clusters, designated Draco X, observed at a redshift of z = 0.12. These systems, characterized by their significant X-ray emission from hot, diffuse intracluster gas, represent massive gravitationally bound structures. The existence and properties of such clusters at these redshifts provide crucial cosmological probes, offering insights into the formation and evolution of large-scale structure and the underlying cosmological parameters. Further investigation of Draco X and similar high-redshift clusters would yield additional constraints on large scale structure.

Figures

Figures reproduced from arXiv: 2507.01421 by the authors.

**Figure 1.** The proportion of PBH fuel consumed as a function of black hole mass after 206 Myr (top left), 855 Myr (top right), 3.5 Gyr (bottom left) and 14 Gyr (bottom right). In each subplot, the x-axis is the PBH mass bins and the y-axis is the fraction of total PBH mass remaining after 10 timesteps. The coloured lines indicate the sequence of timesteps with the first in black and the last in blue, as seen in the vertical co… view at source ↗

**Figure 2.** Coma’s high energy spectral energy distribution. Top left: contours of dark matter density. The outer contour is 0.0002 gm/cm3 and the inner area > 10 times that. Top right: the output flux as a function of the clustercentric radius. The dashed curve shows the loss due to pair production at 5 GeV. Bottom right: Uncertainties are taken from the reference in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** The normalised redshift distribution n(z) of the DES Y3 source galaxies, spanning a weak lensing area of 4143 deg2 , with a total of 100 million galaxies. The data for the redshift distribution is taken from the publicly available DES database: https://des.ncsa.illinois.edu/releases/y3a2/Y3key-catalogs. The calculation of the redshift bin centres has been detailed in Myles et al. (2021), as ⟨z1⟩ = 0.339, ⟨z2⟩ = 0.5… view at source ↗

Figures from the paper (3 more)

**Figure 5.** Figure 5: X-ray clusters in the MCXC-II catalog with redshift < 0.2. This cut was made to improve completeness in the southern celestial hemisphere. The long axis is Galactic longitude, the short axis, Galactic latitude. The red dot in the first quadrant is the Great Attractor (…

**Figure 4.** Figure 4: The window function of Primordial Black Hole evaporation in γ-rays (dashed red) compared to that of the DES Y3 lensing window functions (solid lines) up to redshift z = 1.5. The PBH window function is computed in the energy bin 2.290-4.786 GeV and normalized by the av…

**Figure 6.** Figure 6: X-ray clusters in the MCXC-II catalog enlarged from the previous figure. A control sample is shown below it around the south galactic pole. The red arcs are lines of constant RA. Our results underscore both the opportunities and limitations in using high-energy observ…

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

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