Probing Primordial Black Holes with upcoming Radio Telescopes: a case study for LOFAR2.0, FAST Core Array and BINGO

Amilcar R. Queiroz; Guillem Dom\`enech; Joao R. L. Santos

REVIEW 2 major objections 5 minor 2 cited by

Probing Primordial Black Holes with upcoming Radio Telescopes: a case study for LOFAR2.0, FAST Core Array and BINGO

T0 review · 2 major / 5 minor · reviewed 2026-07-12 · grok-4.5

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Pith's one-line read Null detections of lensed FRBs by LOFAR2.0, FAST Core Array and BINGO will bound the PBH dark-matter fraction below 0.16–0.39.

desk verdict Clean instrument-specific forecast that correctly plugs LOFAR2.0/FAST/BINGO numbers into the standard Muñoz/Leung/Kalita FRB-lensing pipeline; useful for survey planning, not competitive with existing bounds. read the letter →

arxiv 2604.16154 v3 pith:ABNGI64M submitted 2026-04-17 astro-ph.CO gr-qchep-th

Joao R. L. Santos , Guillem Domènech , Amilcar R. Queiroz This is my paper · ORCID

classification astro-ph.COgr-qchep-th

keywords fastradioburstsprimordialblackholesgravitationallensingdarkmatteropticaldepthLOFAR2.0CoreArrayBINGO

topics 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 forecasts the power of three near-term radio telescopes—LOFAR2.0, the FAST Core Array and BINGO—to test whether primordial black holes constitute a non-negligible fraction of dark matter. Using each instrument’s planned signal-to-noise ratio, time resolution and expected FRB yield, together with a fit to the present catalog of 131 localized bursts, the authors compute the optical depth for gravitational lensing by point-mass black holes. Under a null result they obtain $f_{\mathrm{PBH}} < 0.16$ for masses above one solar mass with LOFAR2.0, and $f_{\mathrm{PBH}} < 0.39$ for masses above $10\,M_\odot$ (FAST) and $0.1\,M_\odot$ (BINGO). Although existing microlensing and CMB limits are tighter, FRB lensing supplies an independent, complementary probe whose reach will grow automatically as more bursts are recorded. A sympathetic reader cares because these facilities are already funded and will deliver the required data within a few years.

What carries the argument

The integrated optical depth $\bar{\tau}(M_L)$ for FRB lensing by a monochromatic population of point-mass PBHs; it is obtained by folding the survey FRB redshift distribution with the lensing cross-section set by each telescope’s SNR and time-resolution window, so that $1/(N_{\mathrm{FRB}} \bar{\tau})$ supplies the maximum allowed $f_{\mathrm{PBH}}$.

What would settle it

Detection by any of the three telescopes of even one securely lensed FRB pair whose measured time delay and magnification ratio match a point-mass lens inside the forecasted mass window would immediately falsify the corresponding one-event upper limit and convert it into a positive measurement of $f_{\mathrm{PBH}}$.

Watch

Extended reading notes

Core claim

Under a monochromatic mass function and the one-event criterion, LOFAR2.0 is forecast to constrain the PBH dark-matter fraction to $f_{\mathrm{PBH}} < 0.16$ for $M_{\mathrm{PBH}} > 1\,M_\odot$, while FAST Core Array and BINGO each reach $f_{\mathrm{PBH}} < 0.39$ for $M_{\mathrm{PBH}} > 10\,M_\odot$ and $M_{\mathrm{PBH}} > 0.1\,M_\odot$ respectively, assuming null detection of lensed FRBs at design sensitivity and event rate.

Load-bearing premise

The forecasts treat the published design event rates (4500 for LOFAR2.0, 900 for the others) and time-resolution figures as fixed numbers that will be fully realized; any shortfall scales the optical depth and therefore weakens the quoted $f_{\mathrm{PBH}}$ limits.

Editorial extensions

If this is right

A null result from LOFAR2.0 alone will exclude PBHs as more than 16 % of dark matter above solar mass, independently of stellar-microlensing or CMB bounds.
BINGO’s microsecond resolution extends the same 0.39 limit down to 0.1 solar masses, covering a mass window complementary to FAST.
Reaching N_FRB ≈ 2 × 10^4 with the same method would push f_PBH < 0.01, matching current stellar-microlensing sensitivity.
At high mass the bounds become plateaus fixed only by SNR and event number, so further gains require either higher SNR or larger catalogs rather than better timing.

Reading between the lines

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

If intergalactic-medium decoherence proves milder than the conservative estimates omitted here, the high-mass plateaus could become competitive with binary-merger limits once a few thousand FRBs are in hand.
A joint optical-depth analysis of the three telescopes’ overlapping redshift ranges could tighten the combined bound by a factor of roughly two without new hardware.
The same machinery can be inverted once the first confirmed lensed FRB appears, converting upper limits into a direct mass measurement of the lens.

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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

This is a straightforward forecast paper. The authors take the established thin-lens optical-depth calculation (Muñoz et al. 2016, Leung et al. 2022, Kalita et al. 2023), feed in the published SNR, time-resolution windows and expected FRB yields for LOFAR2.0, FAST Core Array and BINGO, and read off the resulting f_PBH plateaus. The headline numbers—f_PBH < 0.16 above 1 M_⊙ for LOFAR2.0 and < 0.39 for the other two—are new only in the sense that nobody had run these three instruments through the pipeline before.

What they do well is keep the calculation transparent. The optical-depth integral (Eq. 2.14), the plateau derivation (Eqs. 3.2–3.4), the AIC-selected Gamma fit to the 131-event redshift catalog, and the conversion to one-event and 95 % Poisson limits are all standard and free of algebraic error. Telescope parameters come from public design documents; the FRB sample is tabulated in the appendix. Limitations (monochromatic mass function, neglected IGM decoherence, optimistic event yields) are stated openly in Sec. III B and the final paragraph of Sec. IV. No circularity: f_PBH is simply the reciprocal of N_FRB × τ.

The soft spots are exactly the ones the authors flag. The quoted limits scale linearly with the assumed N_FRB (4500 / 900) and with the assumption that the design time resolution and SNR will be fully realized; any shortfall or decoherence immediately weakens them. The one-event criterion is the most optimistic bound; the 95 % Poisson version is already three times weaker. None of this is hidden, and none of it breaks the internal logic.

The paper is for people who need concrete numbers for these three instruments when planning FRB or PBH programs. It will not change the dark-matter landscape—existing microlensing and CMB bounds are tighter—but it is a clean, reproducible application of an established method. I would send it to referees; the math and data are solid enough to deserve a proper look, and the caveats are already on the table.

Referee Report

2 major / 5 minor

Summary. The manuscript forecasts constraints on the PBH dark-matter fraction from the non-detection of gravitationally lensed FRBs with three forthcoming radio facilities (LOFAR2.0, FAST Core Array, BINGO/ABDUS). Using the standard thin-lens optical-depth integral (Eqs. 2.10–2.15), a monochromatic mass function, an AIC-selected Gamma fit to a 131-event redshift catalog (Eq. 2.17), and published telescope specifications (Table I), the authors obtain one-event-criterion bounds f_PBH < 0.16 (LOFAR2.0, M > 1 M_⊙) and f_PBH < 0.39 (FAST/BINGO, M ≳ 0.1–10 M_⊙). They also present 95 % Poisson limits under more optimistic SNR and N_FRB assumptions and place the forecasts in the context of existing microlensing, GW and CMB constraints (Fig. 6).

Significance. The work supplies concrete, instrument-specific forecasts that can guide observing strategies for LOFAR2.0, FAST Core Array and BINGO. The optical-depth calculation is standard and free of algebraic error; the Gamma fit is documented and AIC-selected; telescope parameters are taken from public design papers. The authors correctly emphasize that FRB lensing is complementary rather than competitive with existing bounds, and they openly flag the monochromatic-mass and neglected-decoherence assumptions. The result is therefore a useful, falsifiable planning tool for the community.

major comments (2)

Sec. III B and Eq. (3.1): the headline bounds rely on the one-event criterion f_PBH max = 1/(N_FRB τ̄). The more conservative 95 % Poisson limit (Eq. 3.5) weakens every bound by a factor 3.05, rendering the FAST/BINGO forecasts essentially uninformative under the baseline N_FRB = 900. The abstract and conclusions should quote both the optimistic and the 95 % figures (or clearly label the former as “one-event”) so that the central claim is not overstated.
Sec. IV (final paragraph) and the discussion surrounding Fig. 4: IGM decoherence and plasma-screen effects are acknowledged only as future work, yet they are known to degrade the large-mass plateau that drives the quoted limits (Leung et al. 2022). A short quantitative estimate—or at least a clear statement that the plateaus are upper limits on constraining power—should be added before the forecasts are presented as design targets.

minor comments (5)

Abstract vs. Sec. III B: the abstract quotes f_PBH < 0.16 while the body text states < 0.14 for LOFAR; reconcile the two numbers.
Table I: the “Max number of FRBs” column mixes design goals with joint-collaboration projections; a footnote clarifying the origin of each entry would help.
Fig. 1 caption: “∆t variations are scaled in ms” is ambiguous; state the contour values explicitly.
Eq. (2.17): report the AIC values (or ∆AIC) that selected the Gamma distribution over Lognormal and Weibull.
Throughout: occasional typos (“FBRs”, “LOF AR”, “F AST”) and inconsistent hyphenation of LOFAR2.0 should be cleaned.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: pure instrument forecast from external specs and independent FRB catalog

full rationale

The paper is a standard forecast of PBH constraints from FRB lensing with three upcoming telescopes. Optical depth (Eq. 2.14) is computed from the monochromatic mass function, the Einstein-radius cross-section, and tabulated telescope parameters (SNR, time resolution, expected N_FRB from Table I and public design documents). The Gamma distribution (Eq. 2.17) is a nuisance fit to an external 131-event redshift catalog used only to normalize the source distribution; its parameters do not enter the claimed exclusion curves as free variables that are later re-used. f_PBH is then obtained by the one-event criterion (Eq. 3.1) or the 95 % Poisson rescaling (Eq. 3.5) as the reciprocal of N_FRB imes aū. No fitted quantity is renamed a prediction, no uniqueness theorem is imported from the authors’ prior work, and the plateau derivation (Eqs. 3.2–3.4) follows algebraically once y_max ≫ y_min. The authors openly list the soft premises (event yields, neglected IGM decoherence) in Sec. III B and the final paragraph of Sec. IV. The derivation chain is therefore self-contained against external benchmarks and exhibits no circular reduction.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central forecasts rest on (i) standard gravitational-lensing and FRB-dispersion formulae taken as given, (ii) a handful of instrument and cosmological numbers fixed by external references or by a fit to the 131-FRB sample, and (iii) the modeling choices of monochromatic mass function and optically-thin one-event statistics. No new physical entities are postulated.

free parameters (4)

Gamma-distribution parameters (N0, a1, a2) = N0=208.7210, a1=0.2465, a2=4.6269
Fitted by maximum-likelihood + AIC to the histogram of 131 localized FRB redshifts (Eq. 2.17); the normalized N(z) enters every optical-depth integral.
Expected FRB yields N_FRB = 4500 / 900 / 900
Taken from design papers (4500 for LOFAR2.0, 900 for FAST/BINGO); f_PBH scales as 1/N_FRB, so the numbers are load-bearing free inputs.
SNR thresholds and time-resolution windows = SNR=7/10/10; Δt ~ µs–ms
Instrument design values that set y_max and Δt_min; different choices move the exclusion curves by factors of order unity (Table I).
f_IGM = 0.83 = 0.83
Baryon fraction in the IGM used in the Macquart relation for redshift estimation; fixed by external literature.

assumptions (5)

domain assumption Point-mass Schwarzschild lens produces two images with the standard magnification ratio and time-delay formula (Eqs. 2.4–2.9).
Standard GR result assumed throughout Sec. II B; no higher-order or extended-lens corrections.
ad hoc to paper PBH mass function is monochromatic (delta-function at M_L).
Explicitly adopted “for simplicity” (Sec. II C and final paragraph of Sec. IV); broad mass functions would only re-weight the mass range, not the amplitude of f_PBH.
domain assumption Optically thin regime: P_lens ≈ τ̄, and the one-event criterion f_PBH max = 1/(N_FRB τ̄).
Standard approximation used by Muñoz et al. and subsequent FRB-lensing papers; later relaxed to 95 % Poisson (Eq. 3.5).
ad hoc to paper Intergalactic-medium decoherence and plasma-screen effects can be neglected (best-case scenario).
Stated in the final paragraph of Sec. IV; the authors note that these effects mainly degrade the high-mass plateau.
domain assumption Cosmological parameters fixed to Planck 2018 best-fit values.
Used for all distance and Hubble-function integrals (Sec. I).

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Pith. "Pith review of Probing Primordial Black Holes with upcoming Radio Telescopes: a case study for LOFAR2.0, FAST Core Array and BINGO." pith.science (2026). https://pith.science/paper/ABNGI64M

@misc{pith2026260416154,
  author       = {Pith},
  title        = {Pith review of: Probing Primordial Black Holes with upcoming Radio Telescopes: a case study for LOFAR2.0, FAST Core Array and BINGO},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ABNGI64M}},
  note         = {Machine review of arXiv:2604.16154}
}

abstract

Fast Radio Bursts (FRBs) are among the most intriguing phenomena observed in radio astronomy. So far, about 130 FRB signals have been confirmed and characterized by different surveys, and the CHIME telescope has recently reported a new catalog of 4539 bursts. Therefore, these numbers are expected to increase in the coming years. The detection, or lack thereof, of lensed FRB events can be used to probe Primordial Black Holes (PBHs) as a fraction of dark matter. We investigate the potential of three upcoming radio telescopes, LOFAR2.0, FAST Core Array, and BINGO, to test the PBH scenario. We forecast that LOFAR2.0 will constrain $f_{\mathrm{PBH}} < 0.16$ for PBH masses $M_{\rm PBH}>1\,{M_{\odot}}$, while FAST Core Array and BINGO will restrict $f_{\mathrm{PBH}} < 0.39$ for $M_{\rm PBH}>10\,{M_{\odot}}$ and $M_{\rm PBH}>10^{-1}\,{M_{\odot}}$, respectively. Despite the existence of stricter constraints, FRB lensing offers an independent and complementary probe of PBHs in the Universe, which will improve in the future.

Figures

Figures reproduced from arXiv: 2604.16154 by the authors.

**Figure 2.** FIG. 2: Histogram of the recent data of 131 confirmed FRB events. The fit (2.16) is shown with [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** FIG. 3: Total optical depth for LOFAR, FAST, and BINGO. In these graphics, we consider the [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: FIG. 4: Forecast for the fraction of primordial black holes allowed as point lenses. [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]

**Figure 5.** Figure 5: FIG. 5: Constraints on the fraction of primordial black holes from different surveys combined [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

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Forward citations

Cited by 2 Pith papers

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

Constraints on Primordial Black Hole Dressed by Dark Matter Halo from Microlensing Effect of Fast Radio Bursts
astro-ph.CO 2026-07 conditional novelty 5.0 of 10

A new conversion formula turns monochromatic bare-PBH microlensing bounds into extended-mass dressed-PBH bounds, and a 10^5-FRB forecast places f_PBH near 10^-4.
Constraints on the baryon density from fast radio bursts using a non-parametric reconstruction of the Hubble parameter
astro-ph.CO 2026-05 conditional novelty 5.0 of 10

FRB dispersion measures combined with non-parametric H(z) reconstruction yield Ω_b h² = 0.02236 ± 0.00090, agreeing with BBN and Planck CMB to within 0.05%.

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