Primordial Black Hole mass growth from neutrinos during the radiation era

Ma\"el Gonin

Primordial black holes can grow substantially by absorbing free-streaming neutrinos during the radiation era, rewriting their mass spectrum.

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2026-07-13 04:08 UTC pith:6E67F2T5

load-bearing objection Neutrino free-streaming can let intermediate-mass PBHs grow by O(1) and distort a thermal-history spectrum, but the quantitative claim sits right at the runaway edge of a free collapse fraction. the 4 major comments →

arxiv 2607.09285 v2 pith:6E67F2T5 submitted 2026-07-10 astro-ph.CO hep-th

Primordial Black Hole mass growth from neutrinos during the radiation era

Ma\"el Gonin This is my paper

classification astro-ph.CO hep-th

keywords primordial black holesneutrino absorptionradiation eramass spectrumdark matter fractionthermal historycollapse fraction

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

For decades the standard view has been that primordial black holes (PBHs) form in the hot early Universe and then essentially freeze their masses until much later. This paper argues that picture is incomplete: once neutrinos free-stream, intermediate-mass and supermassive PBHs can absorb them efficiently and gain a sizable fraction of their mass while the Universe is still radiation-dominated. The growth is strongest for black holes born near the QCD-to-MeV window, shifts the well-known electron-positron peak to higher masses, can generate an extra intermediate-mass peak, and simultaneously raises the PBH dark-matter fraction. Because the mechanism relies only on known weak interactions and the thermal history, it revises how observers should map today’s PBH mass distribution back to early-Universe formation physics and dark-matter constraints.

Core claim

Using a semi-classical geometric cross-section for high-frequency radiation absorption, the author shows that PBHs in the range roughly 10^3–10^7 solar masses experience order-unity or larger mass growth R = M_abs/M_init when the collapse fraction γ is near 0.55. The growth is controlled by an ODE whose source term is proportional to the neutrino energy fraction and is gated by a free-streaming weight; the resulting mass mapping shifts spectral features and increases f_PBH.

What carries the argument

The mass-growth ODE dR/dx = 12π γ_eff (δ_hf/α) x^{-3} R^2 W, where W = exp(−κ r_s/λ_ν) (or a step function) turns on once the neutrino mean free path exceeds the Schwarzschild radius, and γ_eff incorporates the critical overdensity. Integrating this map converts the initial thermal-history spectrum into the absorbed spectrum.

Load-bearing premise

The calculation assumes that an ad-hoc exponential (or step) weight accurately captures how efficiently free-streaming neutrinos are absorbed once their mean free path exceeds the horizon radius; if that transition is far less efficient, the predicted growth vanishes.

What would settle it

A full Boltzmann or radiation-hydrodynamic calculation of neutrino capture by a Schwarzschild hole in a realistic early-Universe plasma that shows R remaining near unity for γ ≲ 0.55 across 10^3–10^7 M_⊙ would falsify the central claim.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

Neutrino free-streaming can let intermediate-mass PBHs grow by O(1) and distort a thermal-history spectrum, but the quantitative claim sits right at the runaway edge of a free collapse fraction.

read the letter

The punchline is simple: once neutrinos free-stream, the geometric high-frequency cross-section lets PBHs with M ≳ 10^{3} M⊙ absorb enough energy to shift the e^{+}e^{-} peak, raise f_PBH, and (for high enough γ) produce an extra intermediate-mass bump. That is a concrete revision of the Carr–Hawking non-growth lore, applied to a thermal-history spectrum rather than monochromatic seeds.

What is actually new is the spectral application. The ODE itself is taken from the concurrent geometric-absorption paper [24]; a similar idea appears the same week in [31]. Gonin couples it to the free-streaming window for neutrinos only, introduces a smooth weight W, defines an effective γ_eff that tracks δ_c(T), and shows the resulting distortions on a Press–Schechter thermal-history spectrum. The numerics are transparent (Figs. 2–4, Tables I–II) and the appendices derive the runaway bound cleanly. That is useful work.

The soft spot is real and load-bearing. Significant growth (R ≳ few) appears only when γ sits at 0.55, which is exactly the analytic γ_div on the absorption sweet spot. Drop γ to the more conventional 0.2–0.4 range and the effect becomes modest; at 0.56 you are already climbing the pole of R = 1/(1–G). The transition weight W is pure phenomenology and only modulates amplitude. The spectrum itself is a toy model with free A and f_init = 0.1. None of this is hidden—the paper states the bounds—but it means the “significant” claim is an edge-case result of a free parameter, not a robust prediction.

Who it is for: anyone who works on PBH mass functions, thermal-history peaks, or intermediate-mass seeds for little red dots. The calculation is checkable and the idea is worth having on the table. I would send it to referees; they will force a proper scan over γ and a clearer statement of how much growth survives for realistic collapse fractions. I would cite the spectral figures if I am writing on extended PBH spectra, but I would not treat the quantitative growth as settled.

Referee Report

4 major / 4 minor

Summary. The manuscript argues that primordial black holes (PBHs) in the mass range 10^{-3}–10^9 M_⊙ can absorb free-streaming neutrinos once λ_ν_mfp ≳ r_s, contrary to the long-standing Carr–Hawking hydrodynamical picture. Using the high-frequency geometric cross-section of Ref. [24], a phenomenological transition weight W = exp(−κ r_s/λ_ν), and an effective collapse fraction γ_eff = γ(1+δ_c), the authors integrate an ODE for the mass-growth factor R (Eq. 8) from T_start to equality. For γ ≈ 0.55 they obtain R ≳ few for M ≳ 10^3 M_⊙, which shifts the e^{+}e^{-} peak, can generate an extra intermediate-mass peak, and raises f_PBH relative to an arbitrary initial normalization f_init_PBH = 0.1 (Figs. 2–4, Tables I–II). The result is presented as a revision of the standard view that PBHs do not grow appreciably during the radiation era.

Significance. If the growth mechanism is robust, the paper would reopen the question of PBH mass evolution in the radiation era and alter the mapping between thermal-history features and the present-day mass spectrum. That would affect abundance constraints, the interpretation of intermediate-mass and supermassive seeds (including possible JWST “little red dots”), and the fraction of dark matter in PBHs. The explicit ODE, the analytic runaway bound γ_div(T) (Eq. 10), and the tabulated sensitivity to γ and κ constitute concrete, falsifiable predictions that can be checked against more detailed kinetic or hydrodynamical calculations. The work is therefore of potential interest provided the free-parameter dependence is clarified.

major comments (4)

Appendix B and Eq. (10) derive the analytic runaway condition γ_div ≳ 0.55 on the absorption sweet spot; above this value G(x,γ) ≥ 1 and R diverges (Eq. B5). All quantitative claims of “significant” growth (R ≳ few, spectral shifts, extra peak, Δf_PBH) are shown only for γ = 0.55 (Figs. 2–4, Tables I–II). Conventional estimates of the collapse fraction lie in the range ∼0.2–0.4; the manuscript treats γ as a free phenomenological parameter (Sec. II) without an independent dynamical calculation that places it near the pole. Lowering γ to 0.4 already reduces the effect to a few-percent change in f_PBH (Table II). The central claim is therefore an edge-case result of this tuning and must be re-examined for a broader, better-motivated range of γ.
Section III and Eq. (7) introduce the absorption efficiency via the purely phenomenological weight W = exp(−κ r_s/λ_ν_mfp) with free κ ∈ {0.5,1,2} (or a pure step function). No derivation from kinetic theory or radiative transfer is supplied, nor is the validity of the high-frequency geometric cross-section (Eq. B1) demonstrated once free-streaming begins. Because the entire mass-growth hierarchy and the additional peak rest on this transition, a more microscopic justification (or at least a systematic exploration of alternative transition models) is required before the spectral distortions can be regarded as robust.
The updated spectrum is defined by d f_abs / d ln M = R(M) × d f_init / d ln M (Eq. 11), with f_init_PBH fixed by hand to 0.1 and A left free. While the shape of R(M) is independent of the overall normalization, the reported values of f_abs_PBH (Tables I–II) and the visual prominence of the extra peak are partly by construction. The manuscript should either (i) present results for a range of f_init or (ii) emphasize that only the relative distortion of the spectrum, not the absolute abundance, is a prediction of the absorption mechanism.
The definition γ_eff = γ(1 + δ_c(w(T))) (Eq. 9 and Appendix B.2) is introduced to “map the overdensity threshold into the mass-growth ODE.” The factor (1 + δ_c) is not derived from the geometric cross-section or from the horizon-mass relation; it is an ad-hoc rescaling whose temperature dependence further amplifies growth near the QCD and e^{+}e^{-} transitions. Its necessity and uniqueness should be justified or removed, and the ODE re-integrated with the conventional γ alone.

minor comments (4)

Abstract and Introduction contain multiple typographical errors (“predictede +e−”, “kinetic of the early plasma”, “the fraction of DM in PBHf PBH also change”). A careful proof-reading pass is needed.
Figure 1 caption and axis labels are incomplete; the physical meaning of T_start(rs) should be stated explicitly in the caption.
The simultaneous appearance of Refs. [24] and [31] is acknowledged but the precise differences in mechanism (geometric vs. Stefan–Boltzmann) are only briefly contrasted; a short comparative paragraph would help the reader.
Natural units are declared, yet G and M_P appear inconsistently in Eqs. (4)–(5); a uniform convention would improve readability.

Circularity Check

0 steps flagged

No load-bearing circularity: mass-growth ODE and spectral update are independent of the free normalization; mild self-citation of prior thermal-history spectra is not definitional.

full rationale

The central derivation (ODE (8) for R(x) from the high-frequency geometric cross-section of Ref. [24], weighted by the ad-hoc W or a step, then d f_abs / d ln M = R * d f_init / d ln M) does not reduce to its inputs by construction. R is solved from plasma kinetics and BH absorption physics that are independent of the abundance A or f_init; the latter is an arbitrary free normalization (standard for extended PBH spectra) that is simply rescaled after the fact. Tables I–II and Figs. 2–4 merely illustrate the parametric dependence on the free collapse fraction γ and transition parameter κ. The analytic runaway bound γ_div(T) of Appendix B is derived from the same ODE and correctly flags the edge-case sensitivity at γ ≈ 0.55, but that is a physical/parameter-tuning issue, not a logical loop. Self-citations to the author’s earlier thermal-history papers ([16,19,20]) supply only the toy initial spectrum (Press–Schechter + EoS peaks); they are not invoked as uniqueness theorems or as the sole justification of the absorption mechanism itself. No fitted subset is re-labeled a prediction, no ansatz is smuggled via self-citation, and no quantity is defined in terms of the result it is claimed to predict. Score 1 only for the non-load-bearing self-citations and the free-parameter control of amplitude; the derivation chain is otherwise self-contained.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The central claim rests on a semi-classical geometric absorption formula taken from concurrent literature, an ad-hoc transition weight, a free collapse fraction tuned near its runaway bound, and a simplified Press–Schechter spectrum. No new particles or forces are invented; the free parameters and domain assumptions listed below are what allow the claimed mass growth to appear.

free parameters (4)

collapse fraction γ = 0.55 (near bound)
Treated as free; results shown for γ = 0.55 near the analytic runaway bound γ_div ≳ 0.55; controls both growth amplitude and whether an extra peak appears.
transition sharpness κ = 1 (fiducial)
Controls the weight W = exp(−κ r_s/λ); scanned over {0.5,1,2} plus pure step; changes f_abs_PBH by ~10 %.
fluctuation amplitude A = chosen for f_init=0.1
Normalizes the initial Press–Schechter spectrum so that f_init_PBH = 0.1; free on PBH scales.
initial dark-matter fraction f_init_PBH = 0.1
Set by hand to 0.1; final f_abs_PBH is then reported relative to this choice.

axioms (5)

domain assumption High-frequency geometric cross-section σ_hf = 27π M_BH^{2}/(64 M_P^{4}) remains valid for free-streaming neutrinos once λ_mfp > r_s.
Taken from Ref. [24] and used without re-derivation (Sec. III, App. B).
ad hoc to paper Absorption efficiency can be modeled by the phenomenological weight W = exp(−κ r_s/λ_ν) or a step function.
Introduced in Sec. III with no first-principles derivation of the functional form.
domain assumption Only neutrinos are absorbed; photons and e± remain tightly coupled and do not contribute.
Stated in Sec. III; justified by mean-free-path comparison but not quantified for residual absorption.
domain assumption Press–Schechter statistics with Gaussian fluctuations and fixed spectral index n_s = 0.97 adequately describe the initial PBH spectrum.
Standard but known to be approximate; used throughout Sec. II and App. A.
ad hoc to paper γ_eff = γ(1 + δ_c(w(T))) correctly maps the overdensity threshold into the mass-growth ODE.
Defined in Eq. (9); the factor (1+δ_c) is motivated but not derived from critical-collapse simulations.

pith-pipeline@v1.1.0-grok45 · 14478 in / 3462 out tokens · 37526 ms · 2026-07-13T04:08:04.860265+00:00 · methodology

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read the original abstract

We present a new picture of primordial black holes mass evolution through neutrino absorption. Using semi-classical approach and a closer look at the kinetic of the early plasma we revisit the thermal absorption of radiation by a population of primordial black holes ranging from $10^{-3}-10^9 M_\odot$ embedded in a thermal bath. We find significant mass growth of intermediate mass and supermassive PBHs, the effect shift the predicted $e^+e^-$ peak from thermal history. Depending on the value of the collapse fraction an additional peak around the intermediate mass range, might become significant. Moreover, because PBH grow from the thermal bath the fraction of DM in PBH $f_{\rm PBH}$ also change. These results revise the previous view on mass evolution of PBH and have implications for dark matter PBH observations.

Figures

Figures reproduced from arXiv: 2607.09285 by Ma\"el Gonin.

Primordial Black Hole mass growth from neutrinos during the radiation era

Core claim

What carries the argument

Load-bearing premise

What would settle it

discussion (0)