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T0 review · grok-4.3

Eccentricity up to 0.1 can survive hierarchical subsolar-mass mergers in collapsar disks.

2026-07-01 08:17 UTC pith:F6765ZM3

load-bearing objection NR runs with black-hole proxies for NS fragments show eccentricity surviving at ~0.1 to the final merger, but the modeling choice is the part that needs checking. the 2 major comments →

arxiv 2604.26912 v2 pith:F6765ZM3 submitted 2026-04-29 astro-ph.HE gr-qc

Eccentricity as a signature of hierarchical subsolar-mass mergers in collapsar disks

Jiaxi Wu , Elias R. Most , Nils L. Vu , Nils Deppe , Lawrence E. Kidder , Kyle C. Nelli , William Throwe This is my paper
classification astro-ph.HE gr-qc
keywords subsolar-mass mergerscollapsar disksgravitational wavesorbital eccentricityhierarchical mergersneutron star-black hole
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.

The paper investigates gravitational-wave signatures from a subsolar-mass merger channel in which neutron-star fragments form inside a collapsar accretion disk and merge repeatedly. Numerical relativity simulations of these mergers, modeled as black holes in a disk-like geometry, show that repeated captures build eccentricity of order 0.6, with a substantial fraction persisting until the final neutron star-black hole merger because the system lifetime remains short. A sympathetic reader would care because measurable eccentricity in future subsolar-mass gravitational-wave candidates would serve as a direct indicator that the events arose through this hierarchical route rather than isolated formation.

Core claim

Numerical relativity simulations of hierarchical subsolar-mass compact-object mergers in a disk-like geometry consistent with collapsar fragmentation demonstrate the build-up of eccentricity of order 0.6, with up to 0.1 surviving to the final neutron star-black hole merger owing to the short system lifetime.

What carries the argument

Numerical relativity simulations of black-hole mergers in disk-like geometry that model repeated capture and merger of neutron-star fragments.

Load-bearing premise

The disk-like geometry together with black-hole modeling of the neutron-star fragments and the assumption of short enough system lifetime accurately represent actual collapsar-disk fragmentation and merger dynamics.

What would settle it

A confirmed subsolar-mass gravitational-wave event with eccentricity below 0.01 that is otherwise consistent with the collapsar-disk channel would falsify the claim that substantial eccentricity survives the hierarchical process.

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

If this is right

  • Detections of eccentricity in potential subsolar-mass gravitational-wave candidates would indicate a hierarchical formation scenario.
  • In the extreme case of repeated mergers building a solar-mass neutron star, the binary parameters can resemble those of the eccentric neutron star-black hole event GW200105.

Where Pith is reading between the lines

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

  • The same eccentricity signature could connect electromagnetic transients such as AT2025ulz to specific gravitational-wave events.
  • Other eccentric neutron star-black hole candidates might be re-examined for possible collapsar-disk origins.

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 / 0 minor

Summary. The manuscript proposes that hierarchical subsolar-mass mergers inside collapsar accretion disks can produce and retain orbital eccentricity at the final NS-BH coalescence. Using numerical relativity simulations that model the fragments as black holes inside a disk-like geometry, the authors report eccentricity excitation to e ≃ 0.6 during repeated captures, with up to e ≃ 0.1 surviving to merger because of the short system lifetime. They argue that future detections of eccentricity in subsolar-mass GW candidates would favor this hierarchical channel and note a possible resemblance to GW200105.

Significance. If the modeling assumptions are validated, the work supplies a concrete, falsifiable GW signature (residual eccentricity) that could distinguish collapsar-disk hierarchical mergers from isolated or cluster channels. The use of NR to follow the dynamical capture and kick-driven eccentricity evolution is a methodological strength.

major comments (2)
  1. [Abstract / Numerical relativity simulations] Abstract and simulations section: the headline result that e ≃ 0.1 survives to the final NS-BH merger rests on replacing neutron-star fragments with black holes inside an idealized disk geometry. This choice omits NS finite size, tidal deformability, crust/magnetosphere interactions, and gas-drag torques that are expected to modify both eccentricity excitation during captures and damping between mergers; without quantitative tests of these effects the survival claim is not yet load-bearing.
  2. [Abstract] Abstract: no resolution, initial-condition, or convergence information is supplied for the reported eccentricity values (e ≃ 0.6 initially, e ≃ 0.1 at merger). These details are required to establish that the quoted numbers are numerically robust rather than artifacts of the chosen grid or softening.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed review of our manuscript. We address each major comment point by point below and will revise the paper accordingly to improve clarity and robustness.

read point-by-point responses

  1. Referee: [Abstract / Numerical relativity simulations] Abstract and simulations section: the headline result that e ≃ 0.1 survives to the final NS-BH merger rests on replacing neutron-star fragments with black holes inside an idealized disk geometry. This choice omits NS finite size, tidal deformability, crust/magnetosphere interactions, and gas-drag torques that are expected to modify both eccentricity excitation during captures and damping between mergers; without quantitative tests of these effects the survival claim is not yet load-bearing.

    Authors: We agree that our use of black-hole proxies for the neutron-star fragments in an idealized disk geometry constitutes an approximation that omits several NS-specific effects, including finite size, tidal deformability, crust/magnetosphere interactions, and gas-drag torques. These omissions could affect both eccentricity excitation and damping, so the quoted survival of e ≃ 0.1 should be interpreted as a first indication under the adopted model rather than a fully validated result. In the revised manuscript we will add an explicit limitations subsection in the simulations section that discusses these neglected physics and their possible impact on the eccentricity values. We will also qualify the relevant statements in the abstract and conclusions to reflect the approximate nature of the modeling. revision: yes

  2. Referee: [Abstract] Abstract: no resolution, initial-condition, or convergence information is supplied for the reported eccentricity values (e ≃ 0.6 initially, e ≃ 0.1 at merger). These details are required to establish that the quoted numbers are numerically robust rather than artifacts of the chosen grid or softening.

    Authors: We acknowledge that the current manuscript does not provide resolution, initial-condition, or convergence information for the reported eccentricity values. In the revised version we will add a dedicated paragraph (or subsection) to the simulations section that specifies the grid resolutions employed, the initial orbital parameters and softening lengths, and the results of convergence tests performed to confirm that e ≃ 0.6 and e ≃ 0.1 are numerically robust. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results from NR simulations of modeled mergers

full rationale

The paper derives its claims about eccentricity build-up (e ≃ 0.6 initially, surviving up to e ≃ 0.1) and its implications for GW signatures directly from numerical relativity simulations of hierarchical mergers modeled as black holes in a disk-like geometry. No load-bearing steps reduce by construction to fitted parameters, self-citations, or ansatzes; the outputs are simulation results under stated modeling choices rather than self-definitional or renamed inputs. The derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review; ledger is therefore minimal and provisional.

axioms (1)
  • domain assumption Numerical relativity accurately captures the dynamics of compact-object mergers in a disk geometry
    Invoked when the paper states it performs NR simulations of the mergers.

pith-pipeline@v0.9.1-grok · 5832 in / 1168 out tokens · 32435 ms · 2026-07-01T08:17:53.757863+00:00 · methodology

0 comments
read the original abstract

In this work, we investigate gravitational-wave signatures of a proposed subsolar-mass merger scenario resulting from fragmentation inside a collapsar accretion disk. This scenario has gained recent interest with the electromagnetic transient AT2025ulz, a possible superkilonova counterpart candidate to the sub-threshold gravitational wave event S250818k. One prediction of fragmentation is the formation of multiple smaller neutron-star fragments, some of which might merge hierarchically. Such mergers are expected not only to produce individual electromagnetic counterparts, but also, because of their repeated capture and merger dynamics, to impart kicks to the system and thereby drive orbital eccentricity. By performing numerical relativity simulations of hierarchical subsolar-mass compact-object mergers modeled as black holes in a disk-like geometry consistent with this scenario, we demonstrate the build-up of potentially large eccentricity for the final merger, of order $e \simeq 0.6$ initially, and show that, because of the short lifetime of the system, a substantial part of this eccentricity , up to $e\simeq 0.1$, can survive until the final neutron star -- black hole merger in the general case. As a result, future detections of eccentricities in potential subsolar-mass gravitational-wave candidate events would be a strong indicator for a hierarchical formation scenario. In the extreme case, where we observe repeated mergers to lead to the formation of a solar-mass neutron star, the expected binary parameters can be in a regime similar to those of the eccentric neutron star -- black hole merger event GW200105.

Figures

Figures reproduced from arXiv: 2604.26912 by Elias R. Most, Jiaxi Wu, Kyle C. Nelli, Lawrence E. Kidder, Nils Deppe, Nils L. Vu, William Throwe.

Figure 1
Figure 1. Figure 1: Fragment merger dynamics in a collapsar-disk-like arrangement. Shown are three different configurations, consisting of 1 initial cluster (top row), 2 clusters (middle row), and 3 clusters (bottom row). Each panel shows the orbital tracks accumulated up to the time t/M = ct/rg printed in the upper-left corner, using the same viewing angle in all panels. Here rg = GM/c2 , where M is the total initial mass of… view at source ↗
Figure 2
Figure 2. Figure 2: (Left) compact-object trajectories in the orbital xy-plane for the two-cluster simulation. Each colored track follows a compact object from its initial position, marked by a circle, to its last recorded position. Crosses mark tracks that terminate in mergers, while upward triangles mark the two remnants that survive to the final simulation time. Trajectories are shown in the inertial coordinate frame. (Rig… view at source ↗
Figure 3
Figure 3. Figure 3: Detector-frame plus-polarization strain h+ for the three simulations, reconstructed from the extracted waveform at r = 80 rg and scaled to a fiducial distance of D = 175 Mpc. The horizontal axis shows retarded time and uses a broken layout to separate the early, intermediate, and late merger episodes. Vertical dashed lines mark the refined merger times during the evolution. Initially the merger of smaller … view at source ↗
Figure 4
Figure 4. Figure 4: Frequency-domain detector-frame gravitation￾al-wave spectrum √ f |h˜| at D = 175 Mpc for the two-cluster simulation extracted at r = 80 rg. The black curve shows the full-signal spectrum, and the colored solid curves correspond to the hierarchical fragment merger and final merger with the central black hole, respectively. The magenta and green curves show the LIGO A+ and Cosmic Explorer sensitivity amplitu… view at source ↗
Figure 5
Figure 5. Figure 5: Same as view at source ↗

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    Draft version May 29, 2026 Typeset using LATEXtwocolumnstyle in AASTeX7.0.1 Eccentricity as a signature of hierarchical subsolar-mass mergers in collapsar disks Jiaxi Wu ,1 Elias R. Most ,1, 2 Nils L. Vu ,1, 2 Nils Deppe ,3, 4, 5 Lawrence E. Kidder ,5 Kyle C. Nelli ,1 and William Throwe 5 1TAPIR, Mailcode 350-17, California Institute of Technology, Pasade...

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