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REVIEW 2 major objections 2 minor 297 references

Accretion of Primordial Black Holes in Stellar Interiors

T0 review · 2 major / 2 minor · reviewed 2026-06-28 · grok-4.3

Pith's one-line read Cooling near the event horizon lets primordial black holes as light as 10^{-16} solar masses consume a solar-mass star within a Hubble time.

desk verdict The paper delivers a self-consistent numerical determination of radiative efficiency for PBH accretion that lowers the critical mass for stellar consumption. read the letter →

arxiv 2606.02726 v1 pith:2BU6AEFQ submitted 2026-06-01 astro-ph.HE astro-ph.SR

classification astro-ph.HEastro-ph.SR
keywords primordialblackholesstellaraccretionBondiradiativeefficiencybremsstrahlungcoolingphotontrappingregimes
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

The paper computes how small primordial black holes accrete gas while embedded in the core of a sun-like star, solving the flow equations with self-consistent cooling for the first time. It shows that bremsstrahlung radiation at temperatures near 10^{11} K near the black hole changes the accretion from the classical adiabatic case, raising the mass inflow rate by a factor of 2 to 7 and dropping the fraction of rest-mass energy radiated away by roughly ten times. These changes keep the growth super-exponential across three identified regimes and lower the starting mass needed for the black hole to swallow the entire star in cosmic time to about 10^{-16} solar masses. A reader would care because the result revises how dangerous or detectable such black holes could be inside ordinary stars.

What carries the argument

Time-dependent spherical Euler equations with an implicit cooling source term that self-consistently sets the accretion rate and radiative efficiency in three regimes from Hot Bondi through bremsstrahlung cooling to photon trapping.

What would settle it

A simulation of the same mass range that includes explicit radiative transfer and shows the accretion rate or efficiency differing by more than a factor of two from the values reported for masses near 10^{-16} solar masses.

Watch

Extended reading notes

Core claim

We solve the time-dependent spherical Euler equations with an implicit cooling source term to determine accretion rate, radiative efficiency, and flow structure self-consistently across the optically thin range. This yields three regimes: a Hot Bondi regime below 10^{-14} solar masses where cooling is negligible; a bremsstrahlung-cooling regime from 10^{-14} to 5 times 10^{-13} solar masses that drives the flow toward isothermal with efficiency near 10^{-2}; and a photon-trapping regime above that mass where the Bondi sphere is optically thick and the rate stays near the classical Bondi value. Cooling therefore enhances the accretion rate by a factor of roughly 2-7 throughout the spherical r

Load-bearing premise

Microphysical cooling at temperatures around 10^{11} K can be captured by an implicit source term in the spherical Euler equations without needing full radiation transport or magnetic fields.

Editorial extensions

If this is right

  • Growth of the black hole remains super-exponential while the flow stays spherical.
  • Radiative efficiency falls to approximately 10^{-2} once bremsstrahlung cooling becomes important.
  • Above 5 times 10^{-13} solar masses the accretion rate stays close to the classical Bondi value because of photon trapping.
  • The threshold mass for destroying a solar-mass star drops to roughly 10^{-16} solar masses.

Reading between the lines

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

  • Stellar lifetimes could place new upper limits on the abundance of primordial black holes if the cooling-enhanced growth holds.
  • The same cooling physics might alter accretion estimates for other compact objects embedded in dense gas.
  • Observing unusually rapid stellar evolution or sudden disappearance of stars could test the predicted growth rates.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The paper studies spherical accretion of primordial black holes (PBHs) in solar-type stellar cores. It solves the time-dependent spherical Euler equations with an implicit cooling source term to compute radiative efficiency self-consistently in the optically thin regime (10^{-16.5} to 10^{-10} M_⊙), then switches to an analytical photon-trapping prescription above 5×10^{-13} M_⊙. The work identifies three regimes (Hot Bondi, bremsstrahlung-cooling, photon-trapping), finds cooling enhances \dot M by a factor of ~2-7 with η≈10^{-2}, and concludes the critical initial PBH mass to consume a solar-mass star in a Hubble time is M_{0,crit}∼10^{-16} M_⊙.

Significance. If the numerical results hold, the self-consistent treatment of cooling and efficiency across regimes strengthens constraints on PBH masses that could disrupt stars, with implications for PBH dark matter searches. The time-dependent simulations determining \dot M and η without post-hoc fitting are a methodological strength relative to prior analytic Bondi assumptions.

major comments (2)
  1. [description of bremsstrahlung-cooling regime and implicit cooling implementation] The bremsstrahlung-cooling regime (10^{-14} to 5×10^{-13} M_⊙) relies on an implicit cooling source term in the Euler equations to produce the factor of 2-7 enhancement in \dot M and the drop in η to ~10^{-2}; this term replaces full radiation transport near r_S at T~10^{11} K where optical depth nears unity, but the manuscript provides no quantitative test (e.g., comparison to diffusion approximation or optical-depth calculation) showing the net cooling rate is accurate to better than the reported enhancement factor.
  2. [transition to photon-trapping regime] The switch to the analytical photon-trapping prescription at exactly 5×10^{-13} M_⊙ is presented as the point where the Bondi sphere becomes optically thick, yet this threshold is listed among the free parameters and lacks an explicit derivation from the simulated optical depth or trapping condition; altering it would directly rescale the integrated growth and shift M_{0,crit}.
minor comments (2)
  1. Notation for the three regimes should be defined once with explicit mass boundaries and referenced consistently when quoting the enhancement factor.
  2. The abstract states the enhancement keeps growth 'super-exponential throughout the spherical regime'; a brief quantitative comparison of the integrated growth timescale with and without cooling would clarify this claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful review and for recognizing the methodological value of our time-dependent simulations. We respond to the major comments below and will revise the manuscript to address the identified gaps in validation and derivation.

read point-by-point responses
  1. Referee: The bremsstrahlung-cooling regime (10^{-14} to 5×10^{-13} M_⊙) relies on an implicit cooling source term in the Euler equations to produce the factor of 2-7 enhancement in \dot M and the drop in η to ~10^{-2}; this term replaces full radiation transport near r_S at T~10^{11} K where optical depth nears unity, but the manuscript provides no quantitative test (e.g., comparison to diffusion approximation or optical-depth calculation) showing the net cooling rate is accurate to better than the reported enhancement factor.

    Authors: We agree that a quantitative validation of the implicit cooling term would strengthen the results. The term is used because the cooling timescale is much shorter than the dynamical timescale in this regime, but we will add to the revised manuscript an explicit optical-depth calculation using the simulated density and temperature profiles near r_S, together with a comparison of the cooling rate to the diffusion approximation. This will confirm that the reported enhancement remains robust. revision: yes

  2. Referee: The switch to the analytical photon-trapping prescription at exactly 5×10^{-13} M_⊙ is presented as the point where the Bondi sphere becomes optically thick, yet this threshold is listed among the free parameters and lacks an explicit derivation from the simulated optical depth or trapping condition; altering it would directly rescale the integrated growth and shift M_{0,crit}.

    Authors: The threshold marks the mass at which the simulated Bondi sphere reaches optical depth of order unity. While the original text did not include the explicit derivation, the value is physically motivated rather than arbitrary. In revision we will add the optical-depth calculation versus black-hole mass extracted from the simulations to derive the transition point, and we will include a sensitivity test showing the effect of varying the threshold on the integrated growth and on M_{0,crit}. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; central results from self-consistent simulations

full rationale

The paper computes radiative efficiency, accretion rates, and the critical PBH mass M_{0,crit} via time-dependent spherical Euler simulations with an implicit cooling term across the optically thin regime, followed by an analytic photon-trapping model above 5e-13 M_sun. These steps determine \dot M and \eta directly from the equations without any reduction to a fitted parameter defined from the target result, self-citation load-bearing the central claim, or ansatz smuggled via prior work. The derivation chain remains independent of the final M_{0,crit} value.

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

The central claim rests on standard hydrodynamics plus specific microphysical cooling rates at extreme temperatures; no new particles or forces are introduced, but several modeling choices function as effective free parameters.

free parameters (2)
  • transition mass for photon-trapping prescription
    The switch at 5e-13 M_sun from simulation to analytic treatment is chosen to match optical depth; its exact value affects the quoted growth factor.
  • implicit cooling implementation details
    The precise form of the cooling function (bremsstrahlung coefficient, temperature dependence) is not stated and must be assumed from standard tables.
assumptions (2)
  • domain assumption Spherical symmetry and absence of magnetic fields or angular momentum remain valid throughout the accretion flow
    Invoked when the authors restrict the problem to the time-dependent spherical Euler equations.
  • domain assumption Microphysical radiative processes at T~10^11 K near r_S can be treated as an optically thin cooling term without full radiative transfer
    Required for the self-consistent eta calculation in the optically thin regime.

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Cite this review

Pith. "Pith review of Accretion of Primordial Black Holes in Stellar Interiors." pith.science (2026). https://pith.science/paper/2BU6AEFQ

@misc{pith2026260602726,
  author       = {Pith},
  title        = {Pith review of: Accretion of Primordial Black Holes in Stellar Interiors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2BU6AEFQ}},
  note         = {Machine review of arXiv:2606.02726}
}
abstract

We study spherical accretion onto primordial black holes (PBHs) embedded in the core of a solar-type star. We compute the radiative efficiency self-consistently for the first time across the optically thin range ($10^{-16.5}$-$10^{-10}M_\odot$) with time-dependent simulations, and follow the growth up to $10^{-2}M_\odot$ using an analytical photon-trapping prescription above $5\times 10^{-13}M_\odot$. Near the Schwarzschild radius ($r_{\rm S}\sim 10^{-11}$cm for a $10^{-16}M_\odot$ PBH), gas compressed to $T\sim 10^{11}$K radiates through microphysical processes that fundamentally alter the classical adiabatic Bondi solution. We solve the time-dependent spherical Euler equations with an implicit cooling source term, determining $\dot M$, $\eta = L/\dot M c^2$, and the flow structure self-consistently. We identify three regimes for spherical accretion: a Hot Bondi regime ($M_{\rm BH}\lesssim 10^{-14}M_\odot$) in which bremsstrahlung cooling is dynamically negligible; a bremsstrahlung-cooling regime ($10^{-14}$-$5\times 10^{-13}M_\odot$) driving the flow toward isothermal with $\eta\approx 10^{-2}$; and a photon-trapping regime above $5\times 10^{-13}M_\odot$, in which the Bondi sphere is optically thick and the accretion rate remains close to the Bondi value. Cooling enhances $\dot M$ by a factor of $\sim$2-7, keeping growth super-exponential throughout the spherical regime. The radiative efficiency is an order of magnitude lower than previously assumed, and the critical initial PBH mass required to consume a solar-mass star within a Hubble time is $M_{\rm 0,crit}\sim 10^{-16}M_\odot$.

Figures

Figures reproduced from arXiv: 2606.02726 by the authors.

Figure 1
Figure 1. Schematic of the radiative feedback mechanism on the Bondi boundary conditions. Accretion luminosity Lacc produced near the PBH (central black circle) escapes the Bondi sphere (blue circle, radius rB) and is absorbed by the ambient stellar plasma just outside it, raising the local temperature from T∞ to T∞ + ∆T (or￾ange shading). The deposited energy is transported outward by pho￾ton diffusion (brown dashed arrows) … view at source ↗
Figure 2
Figure 2. Schematic overview of the three spherical-accretion regimes and the disk-accretion regime onto a PBH embedded in a stellar interior, ordered by increasing MBH. Hot Bondi (MBH ≲ 10−14 M⊙): the Bondi sphere is optically thin (τ < 1); bremsstrahlung photons (orange wavy arrows) escape freely without interacting with the infalling gas (grey arrows), yielding η ≈ 10−2 . Bremsstrahlung cooling (10−14–5×10−13 M⊙): bremsstr… view at source ↗
Figure 3
Figure 3. Physical length scales controlling the accretion regime as a function of PBH mass, for solar core conditions. The Bondi ra￾dius rB (blue) defines the gravitational sphere of influence. The vertical dotted line marks τ(rB) = 1, where the Bondi sphere becomes optically thick (M ∼ 5 × 10−13 M⊙). The photon trapping radius rtrap (red) exceeds rB at M ∼ 10−9 M⊙. Two circularization radii rcirc (or￾ange) are shown: one fo… view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Steady-state radial profiles from the time-dependent Euler solver for MBH = 10−16, 10−13, and 10−11 M⊙. (a) Temperature, (b) infall velocity, (c) density, and (d) Mach number as a function of r/rS. Dashed grey lines show the adiabatic Bondi solution. The vertical dashe…
Figure 5
Figure 5. Figure 5: Opacity (top) and cumulative optical depth (bottom) as a function of r/rS for MBH = 10−16, 10−13, and 10−11 M⊙. Thick translucent lines show the total opacity; dashed lines show Klein–Nishina–corrected scattering; dotted lines show Kramers free–free absorption. The ver…
Figure 7
Figure 7. Figure 7: Accretion luminosity as a function of BH mass. The solid blue line shows the locally emitted luminosity Lemitted = η M c ˙ 2 evaluated with the cooling-enhanced accretion rate; the dotted blue line shows the bare-Bondi reference η M˙Bc 2 without the cool￾ing enhancemen…
Figure 8
Figure 8. Figure 8: Top panel: Accretion rate onto a PBH in the solar core as a function of BH mass. The gray solid line shows the adiabatic Bondi rate M˙B ∝ M2 ; the blue dashed line shows the isothermal-limit cooling-enhanced rate f(M)M˙B; the red dotted line shows the legacy Eddington …
Figure 9
Figure 9. Figure 9: Growth trajectories MBH(t) for PBHs with initial masses M0 = 10−17–10−10 M⊙ embedded in the solar core (color scale, from light to dark green). Trajectories are trimmed at 0.01M⊙. PBHs with M0 ≳ 10−16 M⊙ reach this threshold within a Hubble time; lighter PBHs stall in …
Figure 10
Figure 10. Figure 10: Schematic of the recycling/pile-up geometry inside the collisionless region. The flow is hydrodynamic near rB and becomes collisionless below rcoll. Most particles miss the GR loss cone on a single inward pass, return to rcoll, re-thermalize, and either are recaptured…
Figure 11
Figure 11. Figure 11: Effective Knudsen number at the circularization radius as a function of specific angular momentum, for MBH = 10−16 M⊙. The hatched bands mark the excluded loss-cone (ℓ < ℓcrit) and reflected (ℓ > ℓmax) populations. The pile-up enhancement ξ (ℓ) is sufficient to make K…

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Pith tools

Reviewed June 28, 2026 · model on record in the stance chip above.