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 →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
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.
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
- 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.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
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)
- [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.
- [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)
- Notation for the three regimes should be defined once with explicit mass boundaries and referenced consistently when quoting the enhancement factor.
- 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
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
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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
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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
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
free parameters (2)
- transition mass for photon-trapping prescription
- implicit cooling implementation details
assumptions (2)
- domain assumption Spherical symmetry and absence of magnetic fields or angular momentum remain valid throughout the accretion flow
- 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
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 from the paper (7 more)
Reference graph
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