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arxiv: 2604.26912 · v1 · submitted 2026-04-29 · 🌌 astro-ph.HE · gr-qc

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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
Authors on Pith no claims yet

Pith reviewed 2026-05-07 11:25 UTC · model grok-4.3

classification 🌌 astro-ph.HE gr-qc
keywords gravitational waveseccentricityhierarchical mergerscollapsar diskssubsolar massnumerical relativityaccretion diskscompact object mergers
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The pith

Hierarchical mergers in collapsar disks build eccentricity that can survive to the final merger at levels around 0.1.

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

The paper examines a formation channel for subsolar-mass compact objects in which fragmentation inside a collapsar accretion disk produces multiple fragments that merge hierarchically. Numerical relativity simulations of these repeated mergers, modeled as black holes in a disk-like geometry, show that the capture process generates orbital eccentricity reaching roughly 0.6. The short lifetime of the overall system prevents full circularization, so a substantial fraction of that eccentricity, up to about 0.1, remains at the moment of the final merger. Because eccentricity imprints on the gravitational waveform, its presence in future detections of subsolar-mass events would distinguish this hierarchical disk origin from other possible channels.

Core claim

Numerical relativity simulations of hierarchical compact object mergers modeled as black holes in a disk-like geometry demonstrate the build-up of potentially large eccentricity for the final merger, of order e ≃ 0.6 initially, and show that, because of the short lifetime of the system, a substantial part of this eccentricity, up to e ≃ 0.1, can survive until 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.

What carries the argument

Numerical relativity simulations of repeated black hole mergers in a simplified disk-like geometry that track the evolution of orbital eccentricity through successive captures.

If this is right

  • Eccentricity of order 0.1 can persist until the final merger because the collapsar system lifetime is short.
  • Detection of eccentricity in a subsolar-mass gravitational-wave event would indicate a hierarchical formation channel.
  • Each step in the hierarchy can also produce its own electromagnetic counterpart.
  • The mechanism supplies a concrete way to interpret sub-threshold gravitational-wave candidates linked to possible superkilonova transients.

Where Pith is reading between the lines

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

  • Current and next-generation gravitational-wave detectors could search for this eccentricity signature in low-mass events.
  • Absence of measurable eccentricity in multiple subsolar-mass candidates would constrain the fraction of mergers that proceed hierarchically.
  • The same disk environment could be explored with different initial fragment masses or disk thicknesses to map how eccentricity retention depends on those parameters.

Load-bearing premise

The simplified disk-like geometry used in the simulations accurately represents the repeated capture and merger dynamics inside a real collapsar accretion disk.

What would settle it

A gravitational-wave detection of a subsolar-mass merger whose waveform shows measurable eccentricity near 0.1.

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 ↗
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 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 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.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates gravitational-wave signatures of hierarchical subsolar-mass mergers arising from fragmentation in collapsar accretion disks. It argues that repeated capture and merger dynamics impart kicks that build orbital eccentricity to e ≃ 0.6 initially, with a substantial fraction (up to e ≃ 0.1) surviving to merger owing to the short system lifetime. This is demonstrated via numerical relativity simulations that model the compact objects as black holes in a simplified disk-like geometry. The resulting eccentricity is proposed as a strong indicator for the hierarchical channel in future detections of subsolar-mass events, with reference to candidates such as S250818k and the associated transient AT2025ulz.

Significance. If the modeling assumptions hold, the work supplies a concrete, falsifiable prediction that could distinguish hierarchical formation in collapsar disks from other channels for subsolar-mass compact objects. The direct numerical-relativity demonstration of eccentricity build-up and partial survival constitutes a strength, providing quantitative guidance for gravitational-wave searches and linking to recent electromagnetic candidates.

major comments (2)
  1. [Numerical methods and setup] The central simulations model the fragments as black holes in a simplified disk-like geometry (described in the numerical methods and setup). Real fragments are neutron stars whose equation of state, tidal deformability, and interactions with a turbulent, magnetized, accreting disk (gas drag, dynamical friction) are omitted; these effects can alter kick velocities and damp eccentricity beyond pure gravitational-wave emission, directly affecting the claim that e ≃ 0.1 survives until merger in the general case.
  2. [Results] The reported eccentricity values (initial order 0.6, surviving up to 0.1) are obtained from the NR runs, yet no resolution studies, convergence tests, or error estimates on the eccentricity measurements are provided. Given that initial orbital parameters and disk geometry are free parameters, it is unclear how robust the survival result is across the explored space.
minor comments (2)
  1. [Abstract] The abstract states that eccentricity 'can survive until merger in the general case'; a brief summary of the range of initial conditions and disk parameters actually simulated would remove ambiguity.
  2. [Figures] Figure captions and axis labels for the eccentricity evolution plots should explicitly note the time coordinate (e.g., time to merger) and any averaging procedure used.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments on our manuscript. We address each major comment point by point below, providing clarifications on our modeling choices and numerical approach while indicating the revisions incorporated to strengthen the work.

read point-by-point responses

  1. Referee: [Numerical methods and setup] The central simulations model the fragments as black holes in a simplified disk-like geometry (described in the numerical methods and setup). Real fragments are neutron stars whose equation of state, tidal deformability, and interactions with a turbulent, magnetized, accreting disk (gas drag, dynamical friction) are omitted; these effects can alter kick velocities and damp eccentricity beyond pure gravitational-wave emission, directly affecting the claim that e ≃ 0.1 survives until merger in the general case.

    Authors: We agree that the modeling of fragments as black holes in a simplified disk-like geometry represents a deliberate approximation, as stated in the manuscript. This choice isolates the gravitational dynamics of hierarchical capture and kicks to demonstrate the potential for eccentricity build-up to ~0.6 and partial survival to ~0.1 due to short merger timescales. Neutron-star-specific effects and disk interactions could indeed introduce additional damping or alter kicks, and we do not claim quantitative universality. In the revised manuscript, we have expanded the discussion to explicitly acknowledge these limitations, revised the phrasing from 'in the general case' to 'within this simplified model', and emphasized the need for future work with full NS physics and magnetized disks to refine predictions. revision: partial

  2. Referee: [Results] The reported eccentricity values (initial order 0.6, surviving up to 0.1) are obtained from the NR runs, yet no resolution studies, convergence tests, or error estimates on the eccentricity measurements are provided. Given that initial orbital parameters and disk geometry are free parameters, it is unclear how robust the survival result is across the explored space.

    Authors: We appreciate this observation on numerical validation. The original submission presented results from our primary high-resolution runs without explicit convergence details. In the revised manuscript, we have added a new subsection detailing resolution studies across multiple grid resolutions, with convergence demonstrated for the extracted eccentricity values and error estimates provided based on inter-resolution differences. We have also included a brief analysis of variations in initial orbital parameters and disk geometry within the representative range explored, confirming that the qualitative survival of eccentricity persists, although exact values show some dependence. A comprehensive parameter survey remains beyond the current scope but is noted as future work. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results from direct NR simulations

full rationale

The paper's central results on eccentricity build-up (e ≃ 0.6) and survival (up to e ≃ 0.1) are obtained as direct outputs from numerical relativity simulations of black holes in a simplified disk-like geometry. Initial conditions are chosen to represent the hierarchical capture scenario, but the eccentricity values are computed quantities, not fitted parameters renamed as predictions or self-defined by construction. No load-bearing self-citations, uniqueness theorems imported from prior author work, or ansatz smuggling via citation are present. The derivation chain consists of numerical experiments whose outputs are independent of the target claim by the paper's own description.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that fragmentation inside a collapsar disk produces multiple fragments that undergo hierarchical mergers, modeled here as black holes in a simplified disk geometry. No new physical entities are postulated. Initial orbital parameters are chosen by hand to represent the capture dynamics.

free parameters (1)
  • initial orbital parameters and disk geometry
    Chosen to represent hierarchical capture and merger dynamics in the proposed collapsar-disk scenario.
axioms (1)
  • domain assumption Fragmentation in a collapsar accretion disk leads to multiple smaller neutron-star fragments that merge hierarchically and impart kicks driving orbital eccentricity.
    This is the proposed physical scenario being tested; it is stated in the abstract as the motivation for the simulations.

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