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REVIEW 3 major objections 4 minor 3 cited by

The cosmic history of Primordial Black Hole accretion and its uncertainties

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Primordial black holes are unlikely to grow substantially by accreting radiation or gas once radiative feedback is included; the large growth previously predicted requires a specific stack of optimistic assumptions.

desk verdict A careful uncertainty map of PBH accretion; the radiation-growth correction and BHL-vs-PR comparison are genuinely new, but the 'negligible PR growth' headline leans on a poorly justified sound-speed choice. read the letter →

arxiv 2412.11921 v1 pith:KGRFVZ4M submitted 2024-12-16 astro-ph.CO hep-ph

Pratibha Jangra , Daniele Gaggero , Bradley J. Kavanagh , J. M. Diego This is my paper · ORCID
classification astro-ph.COhep-ph
keywords primordialblackholesaccretionBondi-Hoyle-LyttletonmodelPark-Ricottiradiativefeedbackdarkmatterhaloscosmichistorysupermassiveholeseeds
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 primordial black holes (PBHs) grow substantially by accreting radiation and baryons after formation, and answers that large growth is possible only under a narrow set of assumptions. Radiation accretion before matter-radiation equality adds at most 4% to a PBH's mass for an accretion efficiency of $\lambda=0.1$; earlier claims of up to 40% missed the formation-time factor $\gamma$. For baryons, the traditional Bondi-Hoyle-Lyttleton model predicts that PBHs heavier than about $100\,M_\odot$ can grow by several orders of magnitude by $z\lesssim10$, but only when dark-matter halos are present and the accretion efficiency is large. When radiative feedback is included through the Park-Ricotti model, baryonic accretion changes PBH masses by a negligible amount over cosmic time. The outcome matters for gravitational-wave merger rates, dark-matter constraints, and the proposed role of PBHs as seeds of early supermassive black holes.

What carries the argument

The load-bearing machinery is the Bondi radius together with the Park-Ricotti radiative-feedback prescription. In the standard BHL model the accretion rate is $\dot M = 4\pi\lambda \rho v_{\rm eff} r_B^2$ with $r_B = GM/v_{\rm eff}^2$; in the PR model the accreting black hole ionizes a surrounding bubble, the sound speed inside rises to $c_s^{\rm in} = 25 c_s$, and the accretion rate is computed from the density and effective velocity inside that ionized region, $\dot M_{\rm PR} = 4\pi \rho_{\rm in} v^{\rm in}_{\rm eff} (r^{\rm in}_B)^2$. The ionization front and the heated gas suppress inflow, which is why the PR rates lie far below BHL rates. A second piece of machinery is the ROM07 analytic accretion-efficiency formula $\lambda(z)$, which encodes gas viscosity, Compton drag, and Hubble expansion, and the two velocity profiles (ROM07 and SPIK20) used to quantify the spread in predictions.

What would settle it

A radiation-hydrodynamic simulation of a $10^2$-$10^3\,M_\odot$ black hole with a dark-matter mini-halo at $z\sim10$-$20$, resolving the ionization front and measuring the baryonic accretion rate, would settle the matter: if the rate approaches the Bondi-Hoyle-Lyttleton prediction rather than the Park-Ricotti suppression, the paper's central conclusion fails.

Watch

Extended reading notes

Core claim

The paper establishes that the answer to 'do PBHs grow by accretion?' depends on which accretion model is used, and that the more complete model suppresses growth. For radiation accretion, the fractional mass increase is at most 4% for $\lambda=0.1$ and is independent of the initial PBH mass once the formation redshift is computed self-consistently with the collapse fraction $\gamma$, correcting earlier estimates of up to 40%. For baryons, the BHL model with the ROM07 efficiency and dark-matter mini-halos yields several orders of magnitude of growth for PBHs with initial masses above roughly $100\,M_\odot$ by $z\lesssim10$, but this requires the accretion efficiency to saturate near unity after recombination. In the Park-Ricotti model, whose radiative feedback was calibrated on simulations of intermediate-mass black holes, the accretion rate is suppressed so strongly that the fractional mass change is negligible for the entire mass range and is insensitive to the cutoff redshift.

Load-bearing premise

The argument assumes that the radiative-feedback prescription calibrated for intermediate-mass black holes in low-redshift simulations, with the ionized bubble's sound speed set to 25 times the ambient speed of sound and accretion efficiency unity inside the bubble, also holds for primordial black holes accreting the cosmological baryon fluid at all redshifts, including the nonlinear regime of structure formation.

Editorial extensions

If this is right

  • Under the PR model, baryonic accretion changes PBH masses by a negligible amount for the whole mass range considered, so claims that accretion-driven growth weakens PBH abundance constraints would not hold if feedback operates as in the simulations.
  • Under the BHL model with dark-matter halos and high late-time accretion efficiency, PBHs above roughly 100 solar masses can grow by several orders of magnitude by $z\sim10$, which would affect their mass function, merger rates, and possible role as seeds for early supermassive black holes.
  • Radiation accretion alone saturates at about a 4% mass increase for $\lambda=0.1$, independent of initial mass, so pre-recombination growth cannot substantially alter the PBH mass function unless the accretion efficiency is near unity, where it reaches about 60%.
  • The accretion rate and final mass depend so strongly on the assumed sound speed and PBH velocity profiles that order-of-magnitude growth should be treated as model-dependent rather than a generic PBH property.

Reading between the lines

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

  • If the PR feedback description is right, PBHs need to form with nearly their final masses if they are to explain early supermassive black holes; accretion cannot do the heavy lifting after formation.
  • The five-orders-of-magnitude sensitivity of the accreted mass to the assumed ionized-region sound speed suggests that observations of PBH accretion luminosity, for instance through the cosmic microwave background or the 21-cm signal, could be used in reverse to measure the effective feedback strength rather than treat it as a free parameter.
  • The ROM07 accretion-efficiency formula is applied down to $z\sim10$ even though the authors note it breaks down in the structured low-redshift universe, so the 'several orders of magnitude' BHL growth estimate should be read as an upper bound until a local, inhomogeneous treatment of accretion is available.
  • The large disagreement between the ROM07 and SPIK20 velocity profiles highlights that the relative velocity between baryons and dark matter, rather than the accretion model itself, may dominate the uncertainty in PBH growth predictions.
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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

3 major / 4 minor

Summary. The paper revisits accretion onto primordial black holes (PBHs), separating radiation accretion in the early Universe from baryonic accretion at later times. For radiation accretion, it derives an analytic mass-growth integral and finds a maximum mass increase of about 4% for λ=0.1, considerably smaller than earlier claims of up to 40%, because the formation-time factor γ and an improved z(t) are included. For baryons, the authors compare the traditional Bondi-Hoyle-Lyttleton (BHL) model with the Park-Ricotti (PR) model, including radiative feedback, and study both isolated PBHs and PBHs surrounded by dark-matter halos, in linear and non-linear regimes, with SPIK20 and ROM07 velocity profiles. The central claims are that BHL accretion with DM halos can grow PBHs with Mi ≳ 100 M⊙ by several orders of magnitude by z ≲ 10, while PR feedback makes baryonic growth negligible; the paper emphasizes that both results are highly sensitive to the sound speed and velocity assumptions.

Significance. The paper is a useful, transparent mapping of the uncertainties in PBH accretion, an important ingredient for early supermassive-black-hole seed scenarios, CMB constraints, and gravitational-wave merger-rate predictions. Its strengths include an analytic treatment of radiation accretion that clearly identifies the role of the formation time, a systematic side-by-side comparison of BHL and PR models, and an explicit exploration of velocity-profile and parameter sensitivities (λ, x_e, c_in_s, DM halo profile). If the results hold, the paper would usefully temper recent claims of guaranteed large PBH growth and would sharpen the conditions under which growth is possible. The main caveat is that the headline PR result is conditional on a specific extrapolation of a feedback closure calibrated on local IMBH simulations, which the authors themselves show to be highly sensitive.

major comments (3)
  1. [Sec. 4, Eq. (4.7)] The linear-regime PR accretion rate in Eq. (4.7) scales as (c_in_s)^{-5}, and Sec. 4.1 reports that varying c_in_s in the range 10-50 km/s changes the accreted mass by about five orders of magnitude; yet Fig. 12 fixes c_in_s = 25 c_s. At z ~ 1000, where Eq. (3.7) gives c_s ≈ 6 km/s, this corresponds to c_in_s ≈ 150 km/s, far above the ~10-20 km/s photoionized sound speed relevant to the Park-Ricotti calibration, and at z ~ 100 it is still ≈ 48 km/s. Because this choice directly drives the 'negligible PR growth' conclusion, the paper should show ∆M/Mi for alternative physically motivated prescriptions (for example, constant c_in_s ≈ 10, 15, or 20 km/s, or a value tied to photoionization equilibrium) and state how the conclusion changes when c_in_s is lower. Without this, the claim that PR mass evolution is negligible is not established outside the specific 25 c_s assumption.
  2. [Sec. 3, Eq. (3.4)] The ROM07 accretion-efficiency formula in Eq. (3.4) is applied down to z ≲ 15, and into the non-linear regime z ≤ 10, although the text itself notes at the end of Sec. 3 that this description breaks down once structure forms. The large BHL growth shown in Fig. 12 (left panel) is driven by saturation of λ near unity after recombination together with the DM-halo enhancement; the authors state in Sec. 5 that fixing λ = 0.1 instead gives less than 60% growth. The abstract's claim that PBHs heavier than about 100 M⊙ 'can grow in mass by several orders of magnitude' should therefore be qualified as contingent on an extrapolated, high-efficiency regime, or the paper should provide a quantitative test (for example, comparing with local simulation-calibrated efficiencies) showing that the saturation is not an artifact of applying Eq. (3.4) outside its validity range.
  3. [Sec. 4.1, Eq. (4.8)] The PR model is inherited from simulations of intermediate-mass black holes accreting from a local, relatively dense medium (Refs. [63-65]) and is applied here to PBHs accreting from the cosmological fluid at redshifts up to z ~ 10^4, where the density, ionization state, Hubble flow, and radiative-transfer conditions differ substantially from the calibration environment. The additional assumption that the DM halo does not affect the ionized-region density and velocity profiles is stated but not tested; at low redshift the effective Bondi radius for massive halos can approach the size of the ionized region, weakening the 'sufficiently smaller' criterion. A dedicated sensitivity test that relaxes the PR closure (for instance, the unit efficiency inside the ionized region, or the ρin and vin relations in Eqs. (4.3)-(4.6)) is needed to support the conclusion that PR growth is negligible across the full redshift range.
minor comments (4)
  1. [Figs. 6 and 11 captions] Both captions say 'The left panel shows ... while the left panel depicts ...'; the second occurrence should be 'right panel'. This typo should be corrected.
  2. [Fig. 10] The exponent labels '10□8', '10□6', etc. appear to be rendering artifacts in the provided manuscript; the published version should ensure the exponents are legible.
  3. [Appendix B, footnote 3] The paper reports an unexplained discrepancy between its accretion rates and those of ROM07 and Ref. [61], attributing it possibly to the velocity averaging choice. Since the velocity-profile comparison is central to the uncertainty analysis, a sentence identifying the likely origin (or a check against the original code) would substantially increase confidence in the comparison.
  4. [General] The manuscript does not include a data or code availability statement. Given that the main output is a set of sensitivity scans and integrated mass-growth curves, making the integration code available would aid reproducibility and let readers test the c_in_s sensitivity directly.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the paper's predictions are conditional calculations from external models and are explicitly stress-tested, with the only self-citation (the c_in^s = 25 c_s choice) transparently flagged as a free parameter.

full rationale

The paper's derivation chain is self-contained with respect to its own conclusions. The radiation-accretion result (Sec. 2) follows from the Bondi formula plus the formation-time relation Mi = gamma MH, and the claimed correction to earlier 40% growth estimates is a genuine recalculation with explicit γ and z(t) inputs, not a renaming of the outputs. The BHL baryonic results (Sec. 3) use the externally established ROM07 efficiency formula, SPIK20/ROM07 velocity profiles, and secondary-infall DM halo profiles; the large-growth claim is explicitly conditional on DM halos and λ ~ 1, and the paper shows that fixing λ=0.1 caps growth at 60%. The PR results (Sec. 4) use the externally simulation-based Park-Ricotti feedback model. The one potentially load-bearing self-citation is the choice c_in^s = 25 c_s taken from Ref. [67] (Scarcella et al., which includes author D. Gaggero). However, the paper quotes this choice transparently: 'The value of c_in^s depends on the details of radiative feedback inside the bubble and is typically treated as a free parameter. Analogous to Ref. [67], we fix c_in^s = 25 c_s' and immediately quantifies the sensitivity: 'varying c_in^s in the range 10–50 km/s ... leads to a variation in the accreted mass of around 5 orders of magnitude.' This is a stated modeling assumption with explicit sensitivity analysis, not a fitted parameter renamed as a prediction and not a conclusion forced by definition. No equation in the paper reduces to its own input by construction, and no external benchmark is silently replaced by a self-citation. The strongest caveat is that the PR-suppression conclusion is sensitive to the c_in^s choice, but the paper acknowledges this limitation and frames its conclusions as conditional; this is a robustness concern, not circularity.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central claims rest on standard accretion models (BHL, PR) with several parameters adopted from previous literature or chosen by hand: λ, γ, c_in_s/c_s, x_e, the velocity profiles, and the halo slope. No new particles or forces are introduced. The PR model extrapolation to the cosmological context is the most fragile input, and the ROM07 λ formula is applied near its validity boundary.

free parameters (6)
  • accretion efficiency λ (radiation era) = 0.1 (with λ=1 case also shown)
    Chosen by hand for radiation accretion in Sec. 2; the paper notes typical values 0.001-0.1, and results scale with λ (max +60% for λ=1).
  • γ (PBH mass fraction of horizon mass) = 0.2 (0.37 also discussed)
    Controls PBH formation time in Eq. (2.4); directly affects the radiation-accretion estimate and is identified as the source of the 4% vs 40% discrepancy.
  • c_in_s / c_s ratio (PR model) = 25 (varied 10-50)
    Parameter inside the ionized bubble in the Park-Ricotti model (Sec. 4); varying it by a factor 5 changes accreted mass by ~5 orders of magnitude.
  • electron fraction x_e (z<z_rec) = 10^-3
    Assumed constant after recombination following ROM07; the authors find results insensitive to x_e=1 vs 10^-3 at late times.
  • PBH velocity profiles (v_pbh,L, v_pbh,NL) = SPIK20 Eqs. (3.8)-(3.11) or ROM07 Appendix B
    Chosen from the literature; the paper shows these choices change accreted mass by 5-6 orders of magnitude, making them a dominant uncertainty.
  • DM halo density profile index α = 9/4
    Power-law slope for halo density in Eq. (3.12), adopted from secondary-infall models; governs the Bondi-radius enhancement.
assumptions (5)
  • domain assumption Bondi-Hoyle-Lyttleton accretion rate formula (Eq. 2.1) applies to PBHs in the cosmological fluid.
    Assumes uniform medium to infinity, neglects self-gravity of the accreted gas, and treats the PBH as a point mass. Standard in the field, but an idealization.
  • domain assumption Park-Ricotti radiative feedback prescription, validated for IMBHs at low redshift, holds for PBHs at all redshifts.
    Sec. 4 applies the PR model calibrated in Refs [63-65] to PBH accretion from the cosmological fluid; this is the weakest assumption.
  • domain assumption Baryonic accretion and DM halo growth are independent processes.
    Stated in Sec. 3.1; ignores simultaneous accretion of DM and baryons and their mutual influence on the flow.
  • domain assumption The accretion efficiency λ from ROM07 (Eq. 3.4) describes accretion from the cosmic fluid down to z~10.
    The paper notes this description breaks down at z≲10 as structure forms, yet it is used to compute late-time BHL growth.
  • standard math ΛCDM cosmology with the stated parameters (Ω_r, Ω_m, Ω_Λ, h).
    Used from Eq. (2.8) onward; values are consistent with Planck results and not derived in the paper.

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Pith. "Pith review of The cosmic history of Primordial Black Hole accretion and its uncertainties." pith.science (2026). https://pith.science/paper/KGRFVZ4M

@misc{pith2026241211921,
  author       = {Pith},
  title        = {Pith review of: The cosmic history of Primordial Black Hole accretion and its uncertainties},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KGRFVZ4M}},
  note         = {Machine review of arXiv:2412.11921}
}
abstract

Primordial Black Holes (PBHs) have not been experimentally detected so far, but their existence would provide important insights about the early Universe and serve as one of the possible candidates of dark matter (DM). In this work, we explore the accretion of radiation and matter by PBHs, with relevance for the growth of PBH seeds to form early Supermassive Black Holes; the emission from accreting PBHs; and constraints from gravitational wave observations, among others. We study the growth of PBH masses in the early Universe due to the accretion of radiation, highlighting uncertainties which arise from estimates of the PBH formation time. For baryonic accretion, we review the traditional Bondi-Hoyle-Lyttleton (BHL) and its refined version known as the Park-Ricotti (PR) model, which also includes radiative feedback. We find that in the BHL model, PBHs heavier than $\sim 100 \,\mathrm{M_{\odot}}$ can grow in mass by several orders of magnitude by $z \lesssim 10$, though only when surrounded by DM halos and only when the accretion efficiency is large. By contrast, the inclusion of radiation feedback in the PR model can drastically suppress the baryonic accretion rate of PBHs, leading to a negligible change in PBH mass over cosmic time. Furthermore our calculations show that the accretion rate depends sensitively on the modelling of various parameters such as the speed of sound in the baryonic gas and the velocity of PBHs. These findings highlight the uncertainties associated with accretion onto PBHs, and we find that a large increase in the PBH mass due to accretion is by no means guaranteed.

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