arxiv: 2601.22220 · v2 · submitted 2026-01-29 · 🌌 astro-ph.HE · gr-qc

Recognition: 1 theorem link

· Lean Theorem

Subsolar mass black holes from stellar collapse induced by primordial black holes

Thomas W. Baumgarte , Stuart L. Shapiro

Authors on Pith no claims yet

Pith reviewed 2026-05-16 09:17 UTC · model grok-4.3

classification 🌌 astro-ph.HE gr-qc

keywords subsolar mass black holesprimordial black holesdwarf starsstellar consumptionindirect formationdwarf galaxiesgravitational wave candidates

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The pith

A tiny primordial black hole captured by a dwarf star can consume the star entirely and leave behind a subsolar-mass black hole of the star's mass.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper argues that a black hole observed at subsolar mass need not itself be primordial. Instead a much smaller primordial black hole can be captured by a dwarf star whose mass is close to the observed value, after which the primordial seed consumes the entire star and leaves a black hole whose mass matches the original star. Rough estimates indicate the process can occur at appreciable rates, especially inside the dense stellar environments of dwarf galaxies. A sympathetic reader would therefore see that a future gravitational-wave detection of a subsolar black hole would not automatically imply the existence of primordial black holes at exactly that same mass. The indirect route supplies an alternative origin that ties the final mass to ordinary stellar masses rather than to the primordial seed mass.

Core claim

A black hole of mass M_obs can form indirectly when a much smaller primordial black hole (M_PBH ≪ M_obs) is captured by a dwarf star of mass M_* ≃ M_obs and subsequently consumes the entire star, leaving a remnant black hole whose mass is set by the star rather than by the original primordial seed. Rough estimates of densities, velocities and interaction rates suggest this indirect PBH scenario can produce significant populations of such black holes, particularly in dwarf galaxies, and may therefore account for rare subsolar-mass events without requiring primordial black holes of mass M_obs.

What carries the argument

Capture of a much smaller primordial black hole by a dwarf star followed by the star's total consumption by the captured seed, resulting in a remnant black hole of stellar mass.

If this is right

Significant populations of subsolar-mass black holes can form in dwarf galaxies without the primordial black hole having the same mass as the final object.
Gravitational-wave detections of subsolar black holes would not require primordial black holes to exist at exactly the observed mass.
The mechanism allows black holes at masses set by ordinary dwarf-star masses rather than by the primordial seed mass.
Rare subsolar-mass events could be explained by this indirect capture-and-consumption route in dense galactic environments.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same capture process could operate in other high-density stellar regions, producing black holes with masses tied to local stellar populations.
Future surveys that map black-hole mass distributions across different galaxy types could distinguish direct primordial formation from this indirect stellar-consumption channel.
Some black holes might carry hybrid histories in which a primordial seed triggers the collapse of an otherwise ordinary star.

Load-bearing premise

The capture probability and consumption timescale for a much smaller primordial black hole inside a dwarf star allow significant populations to form, based on rough estimates of densities, velocities and interaction rates in dwarf galaxies.

What would settle it

A detailed calculation of capture rates in dwarf galaxies that yields an expected number of such black holes far below the rate implied by any confirmed subsolar-mass gravitational-wave candidates would falsify the scenario.

read the original abstract

While no gravitational-wave detection of subsolar mass black holes has been confirmed to date, a number of candidate detections invite us to speculate on the origin of such black holes should a detection be confirmed. It is generally assumed that the observation of a black hole with subsolar mass $M_{\rm obs}$ would provide strong evidence for primordial black holes (PBHs). The mass $M_{\rm PBH}$ of the PBH, however, does not necessarily have to be equal to $M_{\rm obs}$, as it would in what we term a ``direct PBH scenario". Instead, a black hole of mass $M_{\rm obs}$ may form in a capture of a much smaller primordial black hole, $M_{\rm PBH} \ll M_{\rm obs}$, by a dwarf star of mass $M_* \simeq M_{\rm obs}$, followed by the total consumption of the star by the PBH. We provide some rough estimates and demonstrate that such an ``indirect PBH scenario" may also lead to significant populations of black holes with mass $M_{\rm obs}$, especially in dwarf galaxies, and may be able to explain rare subsolar mass events.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Baumgarte and Shapiro outline an indirect PBH capture route to subsolar black holes but rest the case on rough estimates that lack numbers or formulas.

read the letter

The core idea is straightforward: a tiny primordial black hole gets captured by a dwarf star whose mass matches the observed subsolar value, then consumes the star entirely and leaves behind a black hole of that mass. This decouples the final mass from the primordial seed mass and points to dwarf galaxies as a possible site where the process could matter. The paper does a clean job separating this indirect channel from the usual direct PBH assumption and shows why the distinction matters for interpreting gravitational-wave candidates. That framing is useful even if the rest stays qualitative. The estimates themselves are the weak point. The abstract refers to capture cross-sections, stellar densities, relative velocities, and consumption timescales but supplies none of the explicit expressions, fiducial numbers, or sensitivity checks that would let a reader judge whether the product of those factors actually yields non-negligible rates. Without those details it is impossible to tell whether the scenario competes with other channels or is simply swamped by uncertainties in the inputs. The work is aimed at people already thinking about PBH constraints or alternative formation paths for low-mass black holes. A reader in that niche might pick up the conceptual distinction and file it away, but the paper does not yet deliver a result that can be cited with confidence. I would send it to peer review so referees can press on the rate calculations and see whether the estimates can be made quantitative or whether the central claim needs to be dialed back.

Referee Report

2 major / 2 minor

Summary. The paper proposes an indirect formation channel for subsolar-mass black holes (M_obs) in which a much smaller primordial black hole (M_PBH ≪ M_obs) is captured by a dwarf star of mass M_* ≃ M_obs and subsequently consumes the entire star, leaving a black hole of the observed mass. It presents rough order-of-magnitude estimates of capture rates and consumption timescales to argue that this channel could produce observable populations, particularly in dwarf galaxies, and could explain rare subsolar-mass gravitational-wave events without requiring M_PBH = M_obs.

Significance. If the estimates can be placed on a firmer quantitative footing, the work would usefully expand the set of viable PBH scenarios for subsolar-mass black holes and draw attention to the role of dense stellar environments in dwarf galaxies. It offers a concrete alternative to the direct PBH interpretation that is currently the default assumption in the literature.

major comments (2)

[§3] §3 (Estimates): The central claim that the indirect channel yields 'significant populations' rests entirely on unspecified rough estimates of capture probability, stellar number density, relative velocity, and consumption timescale. No explicit formulas, fiducial numerical values, or scaling relations (e.g., dependence on M_PBH/M_obs or velocity dispersion) are provided, so it is impossible to assess whether the resulting rate is competitive with direct PBH formation or consistent with existing constraints.
[§4] §4 (Discussion): The assertion that the scenario 'may be able to explain rare subsolar mass events' is not supported by any comparison of predicted event rates to LIGO/Virgo upper limits or to the expected direct-PBH rate; the text contains no sensitivity checks against variations in dwarf-galaxy density profiles or PBH abundance.

minor comments (2)

[Abstract] The abstract and introduction would benefit from a single sentence clarifying the mass hierarchy M_PBH ≪ M_* ≃ M_obs that defines the indirect channel.
A short table listing the order-of-magnitude values adopted for stellar density, velocity dispersion, and capture cross-section would make the estimates reproducible and easier to scrutinize.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which correctly identify the need for greater quantitative detail in our presentation of the indirect PBH capture channel. We address each major comment below and will revise the manuscript to improve clarity and rigor.

read point-by-point responses

Referee: [§3] §3 (Estimates): The central claim that the indirect channel yields 'significant populations' rests entirely on unspecified rough estimates of capture probability, stellar number density, relative velocity, and consumption timescale. No explicit formulas, fiducial numerical values, or scaling relations (e.g., dependence on M_PBH/M_obs or velocity dispersion) are provided, so it is impossible to assess whether the resulting rate is competitive with direct PBH formation or consistent with existing constraints.

Authors: We agree that the estimates in §3 were presented too qualitatively. In the revised manuscript we will expand this section to include the explicit capture-rate formula (gravitational focusing cross section times stellar number density times relative velocity), fiducial numerical values for dwarf-galaxy stellar densities and velocity dispersions, the consumption timescale scaling with M_PBH, and the dependence on the mass ratio M_PBH/M_obs. These additions will allow readers to evaluate the order-of-magnitude rates directly. revision: yes
Referee: [§4] §4 (Discussion): The assertion that the scenario 'may be able to explain rare subsolar mass events' is not supported by any comparison of predicted event rates to LIGO/Virgo upper limits or to the expected direct-PBH rate; the text contains no sensitivity checks against variations in dwarf-galaxy density profiles or PBH abundance.

Authors: We acknowledge that a direct numerical comparison to LIGO/Virgo limits is absent. Because the present work is a short proposal focused on identifying the channel, a full population-synthesis calculation lies beyond its scope. In revision we will add an order-of-magnitude comparison of the indirect rate to published direct-PBH rates and to existing subsolar-mass upper limits, together with a brief discussion of sensitivity to dwarf-galaxy density profiles and PBH fraction. We will also state explicitly that more detailed modeling is required for quantitative predictions. revision: partial

Circularity Check

0 steps flagged

No circularity; indirect scenario assessed via independent rough estimates

full rationale

The paper proposes an indirect PBH capture-and-consumption channel as an alternative origin for subsolar-mass black holes and supports its viability with separate rough estimates of capture rates, stellar densities, velocities, and consumption timescales in dwarf galaxies. No equations, parameters, or predictions are defined in terms of the target populations or reduced to self-citation chains; the estimates are presented as external astrophysical inputs whose product determines whether the channel can produce observable numbers. The derivation chain is therefore self-contained against external benchmarks and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on rough estimates of capture rates and consumption timescales that introduce free parameters for stellar and primordial black hole densities and velocities not quantified in the abstract. No new physical entities are postulated.

free parameters (1)

capture rate and density parameters
Rough population estimates depend on assumed values for primordial black hole number density, dwarf star densities, and relative velocities in galaxies.

axioms (2)

standard math General relativity governs black hole formation and accretion during stellar consumption
Invoked for the process by which the captured primordial black hole consumes the star and leaves a black hole of stellar mass.
domain assumption Dwarf stars in dense environments can capture and retain much smaller primordial black holes long enough for consumption
Central premise of the indirect scenario, required for the population estimates to hold.

pith-pipeline@v0.9.0 · 5510 in / 1484 out tokens · 71079 ms · 2026-05-16T09:17:46.668421+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

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Reference graph

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