Constraining the evaporation rate of primordial black holes using archival data from VERITAS

Sajan Kumar (for the VERITAS Collaboration)

REVIEW 3 major objections 6 minor 12 references

Constraining the evaporation rate of primordial black holes using archival data from VERITAS

T0 review · 3 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Adding 1,300 hours of newer VERITAS data should halve the upper limit on how often primordial black holes evaporate in our local neighborhood.

desk verdict A clean, honest status report from VERITAS with one projected number and no final measurement; it belongs in conference proceedings, but not in a journal until the analysis is finished. read the letter →

arxiv 1909.01171 v1 pith:5XYI5I4H submitted 2019-09-03 astro-ph.HE

Sajan Kumar (for the VERITAS Collaboration) This is my paper · ORCID

classification astro-ph.HE

keywords primordialblackholesHawkingradiationgamma-rayburstsVERITASevaporationratedensityupperlimitvery-high-energygammaraysatmosphericCherenkovtelescopes

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 reports work in progress: adding roughly 1,300 hours of VERITAS observations taken after the 2012 camera upgrade to the earlier 750-hour dataset is expected to tighten the upper limit on how often primordial black holes evaporate in the local universe, from $2.22\times10^4$ to about $10^4\,\mathrm{pc}^{-3}\,\mathrm{yr}^{-1}$. This matters because every non-detection of the short gamma-ray burst that Hawking evaporation is predicted to produce narrows the allowed abundance of primordial black holes, and with it the early-universe conditions that could have formed them. The improvement is expected to come from both the larger exposure and the lower energy threshold of the newer data, which makes the array sensitive to more of the burst photons. The analysis uses a likelihood-based burst search, a scrambled-event background estimate, and a time-integrated burst spectrum adopted from the Milagro analysis; the quoted new limit is a projection, not a final measured result.

What carries the argument

The load-bearing object is the time-integrated Hawking burst spectrum of Eq. (5.1), $$\frac{dN_\gamma}{dE_\gamma}\approx 9\$times10^{{35}}$\left\{(1\,\mathrm{GeV}/T_\tau)^{3/2}(1\,\mathrm{GeV}/E_\gamma)^{3/2}\ \mathrm{for}\ E_\gamma<kT_\tau;\ (1\,\mathrm{GeV}/E_\gamma)^3\ \mathrm{for}\ E_\gamma\ge kT_\tau\right\},$$ with $kT_\tau=7.8(\tau/1\,\mathrm{s})^{-1/3}\,\mathrm{TeV}$, taken from the Milagro analysis. Convolved with the VERITAS detector response, this spectrum fixes the expected photon count $N_\gamma$ from a burst at distance $r$, and through the Poisson probability $P(b,N_\gamma)$ it defines the effective volume $V_{\mathrm{eff}}$ within which a burst of $b$ photons would be seen. The expected number of bursts is then $n_{\mathrm{exp}}=\dot{\rho}_{\mathrm{PBH}}\times T_{\mathrm{obs}}\times V_{\mathrm{eff}}$, so an observed null result bounds the evaporation rate density $\dot{\rho}_{\mathrm{PBH}}$ directly. The other mechanism is the likelihood-ratio burst search: events are grouped in time windows of 1 to 45 seconds, their directions are compared with a modified hyperbolic secant point-spread function whose width parameter $\sigma$ is re-fitted for the post-2012 camera in four energy and three elevation bins, and the background is estimated by scrambling arrival times ten times.

What would settle it

Complete the burst search on the full 2,100-hour dataset and compare the resulting 99% confidence upper limit with $2.22\times10^4\,\mathrm{pc}^{-3}\,\mathrm{yr}^{-1}$; if it is not close to half that value, about $10^4\,\mathrm{pc}^{-3}\,\mathrm{yr}^{-1}$, the paper's central projection fails. Independently, recompute the effective volume with a differently derived time-integrated Hawking spectrum, for example from a full particle-physics evaporation code, and check whether the limit shifts by more than the quoted factor of two.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central claim is that applying the established VERITAS burst-search procedure to 2,100 hours of archival data — 747 hours from 2009–2012 plus roughly 1,300 hours from 2012–2017, the latter with a lower energy threshold below 100 GeV — should yield a 99% confidence upper limit on the local rate density of evaporating primordial black holes of about $10^4\,\mathrm{pc}^{-3}\,\mathrm{yr}^{-1}$, a factor of two below the previous VERITAS limit of $2.22\times10^4\,\mathrm{pc}^{-3}\,\mathrm{yr}^{-1}$. No burst signal has been found in the data examined so far; the paper presents the angular-resolution calibration for the new camera configuration and the likelihood cuts that will separate real bursts from chance coincidences, then uses the time-integrated Hawking spectrum of Eq. (5.1) to convert the null result into a rate-density bound. The factor-of-two improvement is the paper's central projection and is explicitly labeled as work in progress.

Load-bearing premise

The projected limit assumes the time-integrated Hawking burst spectrum of Eq. (5.1), taken from the Milagro analysis, correctly predicts how many gamma-ray photons a dying primordial black hole emits; if that spectrum is wrong, the effective volume changes and the computed upper limit moves by an amount the paper does not quantify.

Editorial extensions

If this is right

If the final analysis confirms the projection, the 99% confidence upper limit on the local PBH evaporation rate density becomes about $10^4\,\mathrm{pc}^{-3}\,\mathrm{yr}^{-1}$, halving the previous VERITAS bound.
At that level the VERITAS limit would sit below the $1.4\times10^4\,\mathrm{pc}^{-3}\,\mathrm{yr}^{-1}$ H.E.S.S. limit quoted in the introduction, making the 2,100-hour combined dataset the most sensitive of the searches listed there.
The lower energy threshold of the post-2012 data contributes to the improvement independently of exposure, because it lets the search count lower-energy photons from the burst spectrum.
A null result in the final search would leave the predicted Hawking-radiation burst undetected and further compress the allowed abundance of $10^{15}$ gram primordial black holes.

Reading between the lines

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

If the true rate density were close to the projected limit, the 2,100-hour dataset would be expected to contain only a small number of burst candidates; a search that finds zero bursts would push the limit below $10^4\,\mathrm{pc}^{-3}\,\mathrm{yr}^{-1}$, while a few candidates would move the field from limit-setting toward detection.
The factor-of-two projection is hostage to the adopted Milagro spectrum; replacing Eq. (5.1) with a spectrum from a full standard-model evaporation calculation could shift the effective volume, and hence the limit, by more than the quoted statistical factor, so the final limit should be read as model-dependent.
Because the post-2012 threshold reaches below 100 GeV, the combined search is sensitive to a slightly earlier part of the final burst than the 2009–2012 analysis; correlating the limit with the assumed remaining-lifetime window $\tau$ could separate the effect of added exposure from the effect of the new energy reach.
The same effective-volume method transfers to next-generation instruments with larger collecting area, where the same burst-search logic would scale to proportionally tighter limits without any change to the analysis machinery.

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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

Read the ICRC paper. Short version: it's a status report, and it says so itself. The only quantitative claim is in Sec. 5: combining 747 h of old data with ~1,300 h of post-upgrade data should tighten the PBH evaporation rate-density upper limit from 2.22e4 to about 1e4 pc^-3 yr^-1. That's a nice prospect, not a result. No burst counts, no effective volume, no limit calculation, no systematics. So I agree with the reader's UNVERDICTED tag: there is nothing for a referee to check as a measurement.

What is actually new: the paper re-fits the VERITAS PSF from Crab data after the 2012 camera upgrade, in elevation/energy bins, and gives the sigma values in Table 1. That is a small but real piece of calibration work, and it is needed if the old search method is to be applied to the new data. The paper also describes the dataset and the likelihood/burst-search chain clearly and cites the earlier methodology properly. The honesty is a point in its favor: the abstract says 'work in progress', and Sec. 5 says the new limit is 'expected', not measured.

Soft spots, in proportion: the projected factor-of-two is plausible from the exposure growth (750 to ~2,100 h) plus the lower threshold, but the text doesn't connect Eqs. (5.1)-(5.4) to that number. There is no effective-volume ratio shown and no calculation of how the 90% likelihood retention cut and the lower threshold change signal efficiency. The Milagro time-integrated spectrum in Eq. (5.1) is load-bearing and is not cross-checked against VERITAS data. That's normal for this field, but it means the factor-of-two is best read as an expectation, not a derived result.

Bottom line: this is a legitimate conference status report and I'd take it as one. For a journal submission, I'd desk reject until the analysis is complete. No one should cite the 1e4 number as a measurement. If the final paper delivers the actual limit and effective volumes, it will be worth a proper referee.

Referee Report

3 major / 6 minor

Summary. This manuscript reports an ongoing VERITAS search for gamma-ray bursts from evaporating primordial black holes, using archival data taken between 2009 and 2017. The data are divided into Dataset I (~750 h, pre-upgrade) and Dataset II (~1300 h, post-upgrade), and the paper describes the preparation of Dataset II: calibration of the point-spread function, a likelihood-based discrimination between real bursts and background coincidences, and a background-estimation method based on time scrambling. The only quantitative result appears in Section 5, where the authors state, as a work in progress, that the new upper limit on the local PBH evaporation rate density is expected to be about a factor of two more constraining than the previous limit of 2.22e4 pc^-3 yr^-1, i.e. about 1e4 pc^-3 yr^-1.

Significance. If the projected factor-of-two improvement were demonstrated, it would update the strongest VERITAS constraint on the local PBH evaporation rate density and would illustrate the benefit of the post-upgrade lower energy threshold. The methodological framework—Poisson effective volume, likelihood cuts, and time-scrambled background estimation—is standard and credible, and the paper is clear that this is an expected rather than final result. However, the paper's central quantitative claim is not backed by any numerical analysis in the manuscript: no N_gamma values, no effective volume, no background rates, no 99% confidence-level calculation, and no systematic uncertainties are presented. The manuscript therefore cannot be verified or falsified as written, and its significance as a research paper is currently limited to a status report.

major comments (3)

[Sec. 5] The central quantitative claim—'The new limit, which is still a work in progress, is expected to be a factor of two more constraining from the previous limit, at a value of about 10^4 pc^-3 yr^-1'—is not derivable from Eqs. (5.1)-(5.4) as presented. The text provides no numerical values for N_gamma, no effective volume V_eff, no estimate of the background burst rate, and no calculation of the 99% confidence-level limit. Consequently, the factor-of-two improvement cannot be checked from the manuscript. Please show the actual projected-limit calculation, or state explicitly the scaling assumption (e.g., from 747 h of Dataset I to the total exposure) and the resulting uncertainty.
[Sec. 5, Eq. (5.1)] The projected limit rests on the time-integrated PBH spectrum borrowed from Milagro [7], with kT_tau = 7.8 (tau/1s)^(-1/3) TeV. This spectrum determines the expected photon number N_gamma and hence the effective volume in Eq. (5.3); the manuscript neither validates this spectrum against VERITAS data nor quantifies the systematic uncertainty in its normalization or slope. The impact of plausible variations in this model on the projected limit should be estimated, or at least discussed.
[Sec. 3.1, Table 1] It is not stated whether the sigma values in Table 1 are for Dataset II only, for the combined dataset, or for both. The text says that the angular resolution must be re-evaluated for Dataset II, while Dataset I uses the values from [9], but the table caption merely says the fit is done 'using Crab data.' This ambiguity matters because the likelihood function in Eq. (3.2) and the effective volume in Eq. (5.3) depend directly on these sigma values.

minor comments (6)

[Abstract, Sec. 3, Sec. 5] The exposure for Dataset I is quoted as '750 hours' in the abstract and Section 3, but Section 5 uses '747 hours'; these numbers should be harmonized.
[Sec. 3] Section 3 states the total exposure is 'about 2100 hours', but the quoted components are approximately 750 + 1300 = 2050 hours; please correct or clarify which total is intended.
[Sec. 3.2, Fig. 2] The text and figure caption contain the typo 'centriod' for 'centroid' in two places.
[Table 1] The last row of Table 1 is labeled 'Eenergy' in one column; it should read '(1.0-50 TeV)' to match the other bins.
[Sec. 5, Eq. (5.1)] The piecewise definition in Eq. (5.1) is typeset in a way that may confuse readers; the conditions 'for E_gamma < kT_tau' and 'for E_gamma >= kT_tau' should appear explicitly on each branch, and the unmatched curly brace should be fixed.
[References] Reference [6] contains a stray 'and.' after the author name 'G Teši´c'; this should be corrected.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity identified: the projected PBH limit is an explicitly preliminary expectation based on external model spectra and archival VERITAS data, with no fitted parameter recycled as a prediction.

full rationale

The paper does not make a first-principles derivation that surreptitiously uses its own conclusion. The central expectation in Section 5, that the new limit will be about 10^4 pc^-3 yr^-1, is an extrapolation from the previous VERITAS limit [9] using roughly 2100 hours of data with a lower energy threshold. No equation in the text numerically derives the factor of two, and the author explicitly states the work is still in progress. While this makes the quantitative claim underived and uncheckable as presented, that is a support/verifiability issue, not circularity. The model spectrum in Eq. (5.1) is taken explicitly from the Milagro analysis [7], and the burst-search methodology is taken from [9]; these are external inputs rather than conclusions derived from the new data. The angular-resolution fits in Table 1 are calibration measurements from Crab data and are not fitted to the PBH target quantity. The final upper limit is not obtained by fitting the PBH evaporation rate to the VERITAS data in this paper, so there is no fitted input being renamed as a prediction. No self-citation chain forces the stated conclusion; the previous VERITAS work provides the previous limit but the claimed improvement is presented as an expectation, not as a mathematical consequence of that citation. Therefore no circular step can be quoted and exhibited, and the appropriate score is 0.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The central projection inherits several inputs from prior work: Hawking radiation as the emission mechanism, the Milagro time-integrated spectrum (Eq. 5.1), and the Poisson treatment of burst multiplicities. Instrument PSF widths in Table 1 are fitted to Crab data; these are calibration inputs, not free parameters tuned to the PBH result. No new physical entities are introduced.

free parameters (2)

VERITAS PSF width parameter sigma per energy and elevation bin = 0.027 to 0.068 deg (Table 1)
Obtained by fitting Eq. (3.1) to Crab theta-squared distributions; enters the burst search region and the likelihood in Eq. (3.2). Instrument calibration, not fitted to the PBH signal.
Likelihood retention cut (90% of simulated signal) = not stated in paper
A cut value is chosen for each burst size to retain 90% of simulated signal bursts (Section 3.2); the paper does not list the values, so the exact choice is not reproducible.

assumptions (3)

domain assumption Primordial black holes of initial mass around 1e15 g are still evaporating at the present epoch.
The search target is motivated by Hawking radiation and PBH formation literature (Refs. [2,3,5]); no direct observational evidence is provided.
domain assumption The time-integrated burst spectrum in Eq. (5.1), taken from the Milagro analysis [7], is valid for the VERITAS burst search.
This spectrum determines N_gamma and the effective volume V_eff; the paper does not re-derive or test it.
standard math Poisson statistics describe the probability of detecting b photons from a PBH emitting N_gamma photons.
Standard statistical model used in Eq. 5.3; a reasonable assumption for independent gamma-ray counts.

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Cite this review

Pith. "Pith review of Constraining the evaporation rate of primordial black holes using archival data from VERITAS." pith.science (2026). https://pith.science/paper/5XYI5I4H

@misc{pith2026190901171,
  author       = {Pith},
  title        = {Pith review of: Constraining the evaporation rate of primordial black holes using archival data from VERITAS},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5XYI5I4H}},
  note         = {Machine review of arXiv:1909.01171}
}

abstract

Primordial black holes (PBHs) are thought to have been formed as a result of density fluctuations in the very early Universe. It is suggested that PBHs of mass $\sim 5 \times 10^{14} \mathrm{\ g}$ or less have evaporated through the release of Hawking radiation by the present day. However, PBHs of initial mass $10^{15} \mathrm{\ g}$ should still be evaporating at the present epoch. Over the past few years, very high-energy (VHE; E $>$ 100 GeV) gamma-ray emission from PBHs in the form of a burst has been searched for using ground-based gamma-ray instruments. However, no observational evidence has been reported on the detection of VHE emission from PBHs yet. Previously, an upper limit on the rate density of PBHs was calculated using 750 hours of archival data taken between 2009 and 2012 by the VERITAS gamma-ray observatory. We will augment this study with additional data taken between 2012 and 2017. In addition to more data, the lower energy threshold on the newer data will help to produce an improved upper limit on the rate at which PBHs are evaporating in our local neighborhood. This work is still in progress, therefore we will only report an expected change to the upper limit on the rate density of PBH evaporation.

Figures

Figures reproduced from arXiv: 1909.01171 by the authors.

**Figure 1.** shows the θ 2 distribution of events from the Crab Nebulae, fitted with the function defined in Equation 3.1 plus a constant function (used to model the background level). Since the PSF of the instrument vary with elevation and energy, separate fits were performed in three elevation bins; 50-70◦ , 70-80◦ , 80-90◦ and four energy bins; 0.08-0.32 TeV, 0.32-0.5 TeV, 0.5-1 TeV, 1-50 TeV [PITH_FULL_IMAGE:figures/full_fi… view at source ↗

**Figure 2.** (Right) shows a likelihood distribution for groups of 5 events coming from background bursts (red curve) and simulated signal bursts (blue curve). In order to maximize the amount of signal bursts and minimize the contamination from background bursts, a cut on the likelihood value is determined which retains 90% of the signal bursts. The same procedure is repeated for a burst size of 2, 3, 4, up to 10 events, after … view at source ↗

**Figure 3.** Burst distribution for a burst duration of 20 seconds. Top: The blue squares are from the data, and the red triangles are the background estimation. Bottom: Residual plot showing the difference between data and background. 5. Model Predictions and expectations The number of expected photons, detected by the VERITAS depends upon the emission model of evaporation of PBH and the effective area of the instrument. Follow… view at source ↗

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Reference graph

Works this paper leans on

12 extracted references · 11 canonical work pages

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [7]

A. A. Abdo, A. U. Abeysekara, R. Alfaro, B. T. Allen, C. Alvarez, J. D. Álvarez, R. Arceo, J. C. Arteaga-Velázquez, T. Aune, and H. A. Ayala Solares. Milagro limits and HAWC sensitivity for the rate-density of evaporating Primordial Black Holes. Astroparticle Physics, 64:4–12, Apr 2015

work page 2015

[2] [9]

Archambault and VERITAS Collaboration

S. Archambault and VERITAS Collaboration. Search for Primordial Black Hole Evaporation with VERITAS. International Cosmic Ray Conference, 301:691, Jan 2017

work page 2017

[3] [1]

Bernard J. Carr. Primordial black holes: Do they exist and are they useful? In 59th Yamada Conference on Inﬂating Horizon of Particle Astrophysics and Cosmology Tokyo, Japan, June 20-24, 2005, 2005. 6 Constraining evaporation rate of PBHs with VERITAS Sajan Kumar1, for the VERITAS collaboration

work page 2005

[4] [2]

Y . B. Zel’dovich and I. D. Novikov. The Hypothesis of Cores Retarded during Expansion and the Hot Cosmological Model. Astronomicheskii Zhurnal, 43:758, 1966

work page 1966

[5] [3]

S. Hawking. Gravitationally collapsed objects of very low mass. Monthly Notices of the Royal Astronomical Society, 152:75, 1971

work page 1971

[6] [4]

B. J. Carr, K. Kohri, Y . Sendouda, and J. Yokoyama. New cosmological constraints on primordial black holes. Physical Review D, 81(10):104019, May 2010

work page 2010

[7] [5]

S. W. Hawking. Black hole explosions? Nature, 248(5443):30–31, Mar 1974

work page 1974

[8] [6]

Searching for primordial black holes with the VERITAS gamma-ray experiment

G Teši ´c and. Searching for primordial black holes with the VERITAS gamma-ray experiment. Journal of Physics: Conference Series, 375(5):052024, jul 2012

work page 2012