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Not-quite-primordial black holes seeded by cosmic string loops

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Moving cosmic string loops can seed the early black holes JWST sees, without any boost to primordial fluctuations.

desk verdict Genuinely useful mass-function formalism, but the JWST abundance claim rides on an unmeasured angular-momentum efficiency factor. read the letter →

arxiv 2507.17833 v1 pith:CBAOT45N submitted 2025-07-23 astro-ph.CO gr-qchep-ph

Bryce Cyr This is my paper
classification astro-ph.COgr-qchep-ph
keywords cosmicstringsdirectcollapseblackholeshalomassfunctionlittlereddotsJWSThigh-redshiftstructureformationloopvelocitydistributionheavyseeds
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 tries to show that cosmic string loops, relics of phase transitions in many particle physics models, can form the heavy seeds of high-redshift black holes. It argues that loops are usually moving fast relative to dark matter, so they accrete cylindrical wakes rather than spherical halos, and these filaments fragment into beads that collapse directly into black holes of about $10^5$ solar masses. Using a halo mass function that works for any loop velocity distribution, it finds that for string tension $G\mu$ near $10^{-9}$ and a plausible fraction of halos with low angular momentum, the predicted black hole abundance matches the observed density of JWST little red dots. If right, this gives a cosmic string origin for a population JWST currently struggles to explain within standard galaxy formation.

What carries the argument

The load-bearing mechanism is the extension of the Zel'dovich accretion formalism to moving string loops. A loop moving relative to dark matter accretes a cylindrical wake whose total mass $M_{\mathrm{fil}} = (3/2) M_{\mathrm{nl}}^{\mathrm{III}}$ is independent of velocity; when the wake's radial extent exceeds the Jeans length it fragments into $n_{\mathrm{bead}} = L_{\mathrm{fil}}/L_{\mathrm{bead}}$ beads, each growing as $M_{\mathrm{bead}} = M_{\mathrm{fil}}/n_{\mathrm{bead}}$. The paper folds the loop number density spectrum together with a velocity distribution $f(v) = B v^2 (1-v^2)^{10}$ into a mass function with two terms: filaments weighted by $F(v) = \int_0^{v_{\mathrm{fil}}} f(v')\,dv'$ and beads weighted by $K(v) = \int_{v_{\mathrm{frag}}}^1 f(v')/v'\,dv'$. The direct collapse conditions ($T_{\mathrm{vir}} \gtrsim 10^4\,\mathrm{K}$ and $M \gtrsim 10^5\,M_\odot$) become constraints on loop velocity and formation redshift, while the angular momentum suppression factor $\epsilon_L$ is left as a free parameter.

What would settle it

Run N-body or hydrodynamic simulations of moving cosmic string loops with the velocity distribution $f(v) = B v^2 (1-v^2)^{10}$ and measure the spin parameter distribution of the resulting beads at $z \sim 500$; if the fraction of beads with angular momentum below the direct collapse threshold is less than about one percent, the central abundance claim fails. Alternatively, a precise measurement of the low-mass cutoff in the high-redshift halo mass function would directly test the predicted $G\mu$ dependence.

Watch

Extended reading notes

Core claim

The central claim is that cosmic string loops, formed with velocities peaking near $v \sim 0.3$, produce a beaded halo population capable of hosting direct collapse black holes at $z \sim 500$, and that integrating the mass function over the loop velocity distribution yields $N_{\mathrm{DCBH}} = \epsilon_L \times (0.18,\, 2\times 10^{-3},\, 1.7\times 10^{-5})\,\mathrm{Mpc}^{-3}$ for $G\mu = (10^{-7},\,10^{-8},\,10^{-9})$ respectively. With $G\mu \sim 10^{-9}$ and $\epsilon_L \sim 0.6$, this matches the little red dot abundance $N_{\mathrm{LRD}} \sim 10^{-5}\,\mathrm{Mpc}^{-3}$ inferred from JWST; the paper states that the abundance of high-redshift black holes and galaxies detected by JWST could have a cosmic string origin. It also derives a nearly universal critical mass $M_* \sim 10^6\, M_\odot$ (redshift dependent) that separates hot filaments from hot beads. This happens without enhancing the primordial power spectrum, thereby avoiding CMB spectral distortion bounds.

Load-bearing premise

The calculation assumes that a non-negligible fraction of string-seeded halos have low enough angular momentum to collapse directly into black holes, meaning $\epsilon_L$ is not extremely small; the paper presents no calculation of $\epsilon_L$, and if it falls below about $0.01$ for $G\mu \sim 10^{-9}$, the predicted abundance drops below the little red dot count.

Editorial extensions

If this is right

  • If the claim holds, JWST little red dots and high-redshift quasars need no enhanced primordial power spectrum; cosmic string loops could supply the heavy seeds directly.
  • A sharp lower cutoff in the high-redshift halo mass function would be a smoking gun for string seeding, with the cutoff position encoding $G\mu$.
  • The mass functions are analytic for any loop velocity distribution: replacing $f(v)$ only changes the two integrals $F(v)$ and $K(v)$.
  • The model predicts filamentary correlations between high-redshift galaxies, since beads from a single filament form early black holes in aligned chains.
  • String tensions near $10^{-9}$, which are allowed by CMB bounds, are the ones favored for matching the observed little red dot abundance.

Reading between the lines

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

  • If $\epsilon_L$ turns out to be large, the same machinery would predict an abundant population of intermediate-mass black hole seeds that grow into supermassive black holes, giving gravitational wave observatories a concrete high-redshift target.
  • The velocity dependence suggests that a precise measurement of the beaded halo cutoff could simultaneously constrain $G\mu$ and the loop velocity distribution, turning JWST galaxy counts into a probe of cosmic string physics.
  • A testable extension would compare the predicted $z \sim 500$ atomic-cooling halos with 21-cm observables, since their heating and ionization pattern differs from what enhanced primordial curvature perturbations would produce.
  • The paper's conservative choice $T_{\mathrm{bead}}^{\mathrm{vir}} = T_{\mathrm{fil}}^{\mathrm{vir}}$ may underestimate bead temperatures; if beads are hotter, the viable parameter space for direct collapse would expand.
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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

4 major / 4 minor

Summary. The paper derives comoving halo mass functions for dark-matter overdensities seeded by cosmic string loops, extending earlier stationary-loop accretion theory to an arbitrary loop-velocity distribution. It then selects halos satisfying virial-temperature and mass criteria for direct-collapse black hole (DCBH) formation, integrates the resulting mass function to obtain a DCBH number density, and compares it to the observed abundance of JWST little red dots and high-redshift quasars. The main analytic results are closed-form mass functions for filamentary and beaded halos, Eqs. (38) and (41), which generalize the earlier Shlaer et al. result and reproduce it in the delta-function velocity limit. The paper is transparent about its main approximations, including the normal-growth limit for moving loops, T_bead = T_fil, hard mass cutoffs, and the unconstrained angular-momentum suppression factor epsilon_L.

Significance. If it holds, the framework provides a reusable, analytic description of string-seeded halo abundances and identifies a genuinely interesting route to heavy seeds that bypasses boosted primordial power and CMB spectral-distortion constraints. The paper's strengths are its explicit closed-form mass functions, the reduction to known limits, and its honest enumeration of approximations and missing ingredients. However, the headline consistency with the little-red-dot abundance is conditional on an essentially uncalibrated factor, epsilon_L, which multiplies the final DCBH number density; the paper itself notes that the fragmentation process could produce large angular momenta and hence epsilon_L << 1. The central abundance claim is therefore best viewed as a conditional demonstration rather than a robust prediction until that factor is quantified.

major comments (4)
  1. [Sec. III C, after Eq. (42)] The final abundance is N_DCBH = epsilon_L times (0.18, 2e-3, 1.7e-5) Mpc^-3 for Gmu = (1e-7, 1e-8, 1e-9). The factor epsilon_L is left completely unconstrained: no estimate is made for string-seeded halos, and the text itself notes that the fragmentation procedure could yield large angular momenta, suggesting that epsilon_L << 1. Matching the little-red-dot density N_LRD ~ 1e-5 Mpc^-3 at Gmu = 1e-9 requires epsilon_L ~ 0.6, so if the true efficiency is below about 0.01 the central claim fails by two orders of magnitude. Because this factor is the only bridge between the halo mass function and the black-hole abundance, the claimed consistency with JWST observations is conditional rather than established. The authors should provide at least an order-of-magnitude estimate of epsilon_L for their bead and filament geometries, or clearly reframe Eq. (42) as an upper limit.
  2. [Sec. III C, after Eq. (42)] The phrase 'Neglecting the filament component' is inconsistent with the mass function defined in Eq. (30) and plotted in Fig. 7, where dN/dM_fil satisfies the same virial-temperature and mass criteria that are used to select DCBH candidates. If the filamentary halos are excluded from the integral at the last step, the quoted values of N_DCBH are not the integral of the DCBH-candidate mass function presented above; if they are included, the numbers change. Please state explicitly which halo morphologies are considered able to undergo direct collapse, justify the omission of filaments, or recompute N_DCBH including the filament term.
  3. [Sec. III C and Appendix C] The abundance N_DCBH is obtained by integrating mass functions that are truncated by Heaviside functions at M_min and M_max, yet Appendix C explains that these boundaries mark regions where a more refined analysis is required and should not be treated as hard cutoffs. Since the bead mass function has the steep power law M_bead^{-8/3} and the filament mass function behaves as M_fil^{-5/2}, the integrated number density can be sensitive to the lower boundary, especially for the smallest Gmu. Please demonstrate that the quoted N_DCBH values are insensitive to the cutoff choices, for example by varying M_min and M_max within the stated uncertainty range, or replace the hard cutoffs with smooth transitions.
  4. [Sec. II B, Eq. (25) and Sec. III A] The DCBH conditions are evaluated with T_bead equal to T_fil and with the normal-growth limit assumed at all times after matter-radiation equality. The paper explicitly flags both as approximations, and the first is conservative for the temperature threshold, but the impact on N_DCBH is not quantified. In particular, if the accelerated-growth regime is important for loops with v_form ~ 0.3, the bead masses and hence the mass range contributing to Eq. (42) could differ substantially. A quantitative estimate of the resulting uncertainty in N_DCBH would strengthen the central result.
minor comments (4)
  1. [Sec. II B 3, Eq. (22)] The velocity distribution f(v) = B v^2 (1 - v^2)^10 is posited rather than taken from a simulation, and the quoted numerical abundances depend on this choice through F(v) and K(v); a short sensitivity test, for example varying p between 2 and 20, would help the reader assess the robustness of the JWST comparison.
  2. [Fig. 4 caption] The dotted vertical lines labeled '10% loops' and '1% loops' are not explained in the caption or the text; please state that they indicate the velocity below which the stated fraction of loops is produced according to Eq. (22).
  3. [Sec. III C, Eq. (34)] The replacement of dN/dL using L = L(M_fil) is not derived in the text; a one-line inversion of the Jacobian in Appendix B would make the prefactor in Eq. (38) directly verifiable.
  4. [Appendix B, Eq. (B1)] The relation L ~ alpha t_eq [(1+z_eq)/(1+z_form)]^2 is used several times before it is stated; moving it earlier in the main text would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the mass function is derived from Zel'dovich dynamics and simulation inputs, with the final abundance explicitly conditional on the free efficiency factor.

full rationale

I find no circular step requiring a score above 0. The loop number-density input (Eqs. 3-4) is taken from independent Nambu-Goto simulations [75], and the velocity weight f(v) (Eq. 22) is posited to mimic the simulated peak near vform ~ 0.3; neither is constructed from the JWST little-red-dot abundance. The halo mass functions (Eqs. 38 and 41) follow from the stated Zel'dovich evolution equation (Eq. 8), the smeared loop profile (Eq. 5), and the filament/bead masses (Eqs. 16-21), with Jacobians given in Appendix B. No step sets dN/dM equal to the target N_LRD. The final DCBH abundance (Eq. 42) is the mass-function integral multiplied by an explicitly unconstrained efficiency epsilon_L, and the paper explicitly says the consistency with N_LRD depends on its value rather than claiming a measurement of it. The check that the delta-function velocity limit reproduces Shlaer et al.'s mass function is a consistency check against prior external work, not an input. Prior papers by the author are used for the stationary-loop density profile and early accretion rates, but these are specific analytic results, not an unverified self-citation chain invoked to forbid alternatives. The central claim is conditional on epsilon_L and on the assumed loop parameters, which is a scientific sensitivity issue, not circularity.

Assumptions & free parameters 2 free parameters · 7 assumptions · 0 invented entities

The ledger shows the central claim rests on several simulation-calibrated inputs (loop spectrum, alpha, Gamma_g), a phenomenological velocity distribution, the Zel'dovich treatment of accretion, and astrophysical assumptions on direct collapse including an unquantified angular-momentum efficiency. The strongest input is the independent loop network simulations; the weakest are the ad hoc velocity distribution and the unknown epsilon_L.

free parameters (2)
  • Loop velocity distribution f(vform) = B v^2 (1-v^2)^p = p = 10, B about 85, yielding <vform> about 0.3
    Posited in Sec. II B 3 (Eq. 22) to match the simulation-inferred central loop velocity. The exact shape is unmeasured and directly controls F(v) and K(v), hence the filament-bead mass function split and the final DCBH abundance.
  • Direct collapse efficiency epsilon_L = unconstrained, not fitted
    Introduced in Eq. (42) as an unknown angular-momentum suppression factor. The claimed consistency with little red dots requires epsilon_L at order 0.1 to 1 for Gmu near 10^-9, and the paper provides no calculation of it for string-seeded halos.
assumptions (7)
  • domain assumption Loop number density spectrum dN/dL from Nambu-Goto simulations (Blanco-Pillado et al. 2014)
    Eqs. (3)-(4) are adopted as inputs; the normalization alpha_r = 0.18, alpha_m = 0.57 and index alpha = 0.1 come from simulations, not derived here.
  • domain assumption Smeared density profile for an oscillating loop (Hao et al. 2024)
    Eq. (5) assumes oscillations are rapid compared to turnaround times, valid for loops forming with zform at least 2 zeq (Sec. II A).
  • standard math Zel'dovich approximation and evolution equation for the perturbation psi
    Eq. (8) is taken from Vilenkin and Shellard and Hao et al.; neglects radiation-era growth with initial conditions psi(zeq) = psi'(zeq) = 0.
  • ad hoc to paper Normal-growth limit for moving loops at all times after matter-radiation equality
    Sec. II B states the filament grows as Eq. (16) at all times, neglecting the accelerated growth regime of Shlaer et al.; this is justified by two heuristic arguments rather than a derivation.
  • ad hoc to paper Velocity distribution shape f(v) = B v^2 (1-v^2)^10
    Eq. (22) with p = 10 is a phenomenological choice to reproduce <v> about 0.3; simulations have not provided the full distribution.
  • domain assumption Direct collapse criteria (T_vir at least 10^4 K, M at least 10^5 solar masses, CMB suppresses H2 at z above 200)
    Sec. III adopts these from the DCBH literature and Qin et al.; the paper assumes baryons can virialize into string-seeded halos from z about 500 and collapse monolithically.
  • domain assumption Each DCBH-forming halo yields one roughly 10^5 solar mass black hole
    Sec. III C assumes hyper-Eddington accretion stops at M_ps about 10^5 solar masses, so the source population is monochromatic; this is taken from protostar simulations.

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Cite this review

Pith. "Pith review of Not-quite-primordial black holes seeded by cosmic string loops." pith.science (2026). https://pith.science/paper/CBAOT45N

@misc{pith2026250717833,
  author       = {Pith},
  title        = {Pith review of: Not-quite-primordial black holes seeded by cosmic string loops},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CBAOT45N}},
  note         = {Machine review of arXiv:2507.17833}
}
abstract

Cosmic strings appear in many well-motivated extensions to the standard model of particle physics. If they exist, an abundant population of compact objects known as cosmic string loops permeate the Universe at all times, providing a secondary source of density perturbations that are large amplitude and non-gaussian in nature. In general, these loops are not stationary in the rest frame of the dark matter, thus their relative velocities will typically seed both spherical and filamentary overdensities in the matter era. Building upon previous work, we provide an improved framework to compute the complete halo mass function for these string seeded overdensities, valid for any loop velocity distribution. Using this mass function, we also compute the subset of halos capable of undergoing a direct collapse, forming a population of black holes with initial mass $10^{4-5} \, M_{\odot}$ at high redshifts. Interestingly, for reasonable values of the string parameters, one can reproduce the abundance of ``Little Red Dots" as inferred by JWST.

Figures

Figures reproduced from arXiv: 2507.17833 by the authors.

Figure 1
Figure 1. A heuristic description of the three different phases of accretion experienced by the string-seeded overdensity, in the [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Contours showing the redshift at which the point [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. From top to bottom, we show the total accreted mass in dark matter halos around string loops with increasingly [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Different accretion scenarios for a given [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: The relationship between loop formation redshift and velocity. The prominent contours in the top left, top right, and [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: Velocity distribution function integrals given in Eqs. 36 (left panel) and 40 (right panel). Brackets represent the [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]
Figure 7
Figure 7. Figure 7: From top to bottom, we show the mass functions for [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]

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Forward citations

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Reference graph

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