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Direct Measurement of the Accretion Disk Formed in Prompt Collapse Mergers with Future Gravitational-Wave Observatories

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Pith's one-line read The paper claims that the mass and angular momentum of the accretion disk left when a neutron-star merger immediately collapses into a black hole can be measured directly from the gravitational-wave ringdown, with roughly 10 percent…

desk verdict New calibration between disk mass and ringdown frequency for prompt-collapse BNS mergers; the 10% accuracy claim is an optimistic Fisher bound that needs calibration-uncertainty propagation, but the paper deserves review. read the letter →

arxiv 2507.14071 v1 pith:IKXA5LIZ submitted 2025-07-18 gr-qc astro-ph.HE

Arnab Dhani , Alessandro Camilletti , Alessio Ludovico De Santis , Andrea Cozzumbo , David Radice , Domenico Logoteta , Albino Perego , Jan Harms
show 1 more author
Marica Branchesi
This is my paper · ORCID
classification gr-qcastro-ph.HE
keywords gravitationalwavesbinaryneutronstarmergerspromptcollapseaccretiondiskquasi-normalmodesringdownr-processnucleosynthesisnext-generationdetectors
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

The paper sets out to show that the accretion disk formed in an unequal-mass binary neutron star merger that immediately collapses into a black hole leaves a measurable imprint on the gravitational-wave ringdown. Using 22 full general-relativistic merger simulations, it finds that the ringdown frequency shifts with disk mass and angular momentum. It then argues that with next-generation observatories such as Einstein Telescope and Cosmic Explorer, a postmerger signal-to-noise ratio of 5 would measure the disk mass to about 10 percent relative error for binaries up to roughly 30 Mpc, and the disk angular momentum to similar accuracy. Such a direct measurement would place a tight constraint on the ejecta that powers kilonovae and on the accretion that powers short gamma-ray bursts, bypassing the nuclear and atomic modeling uncertainties that currently dominate kilonova interpretation.

What carries the argument

The load-bearing object is the complex ringdown frequency $\omega = \omega_r + i\omega_i$ of the remnant black hole, defined as the characteristic complex frequency at which a perturbed black hole rings while settling. The paper fits this frequency with a phenomenological postmerger model whose amplitude is $A(t) = (a_1 + a_2\tanh(a_3 + a_4 t))e^{-\omega_i t}$ and whose phase is $\Phi(t) = \phi_0 + \omega_r t + b_1\log(1 + b_2 e^{-b_3 t})$. The argument then runs through two empirical relations extracted from the simulations: a quadratic fit $m_{\rm disk}/M = a + bX + cX^2$ with $X = (m_1-m_2)\omega_r$, and a linear map from disk mass to disk angular momentum. A Fisher-matrix propagation, using white Gaussian noise and an SNR of 5 over the 3-10 kHz band, turns the frequency error into the claimed mass and angular momentum accuracies.

What would settle it

Run a full Bayesian parameter-estimation injection on one of the 22 numerical relativity waveforms: add realistic colored noise from an Einstein Telescope and Cosmic Explorer network at 30 Mpc, leave the total mass and amplitude free, and check whether the recovered disk mass is unbiased and within about 10 percent. Alternatively, a real prompt-collapse event with postmerger SNR of 5 or higher whose ringdown frequency lies far from the fitted $(m_1-m_2)\omega_r$ versus $m_{\rm disk}/M$ relation would falsify the correlation.

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Extended reading notes

Core claim

The central discovery is that the ringdown of a black hole formed by prompt collapse is not the ringdown of an isolated black hole: the surrounding accretion disk shifts the quasi-normal mode frequencies, and the shift correlates with the disk's mass. The paper demonstrates the correlation with 22 unequal-mass simulations spanning four nuclear equations of state, fitting the combination $(m_1-m_2)\omega_r$ against $m_{\rm disk}/M$ with a quadratic function and the disk angular momentum against disk mass with a linear function. It then converts a projected ringdown frequency measurement error of about 60 Hz, obtained from a Fisher matrix at fixed SNR 5, into a median disk-mass error of about 10 percent. The result is a proposed method to directly measure the mass and angular momentum of the accretion disk powering kilonova and gamma-ray-burst emission.

Load-bearing premise

The 10 percent accuracy rests on assuming the ringdown frequency is the only unknown parameter, that the binary's total mass is already known exactly, and that the noise is white and Gaussian; if any of those assumptions fails, the accuracy can degrade.

Editorial extensions

If this is right

  • A postmerger detection at SNR 5 would pin the disk mass to about 10 percent for a nearby event, giving a direct anchor for kilonova ejecta models.
  • Subtracting the measured disk mass and angular momentum from the remnant's total mass and spin would yield the black hole mass and spin, constraining the accretion power available to launch gamma-ray bursts.
  • The estimated rate of 0.001 to 0.25 usable events per year means that a single good event could calibrate disk-outflow fractions, which simulations currently place anywhere between 10 and 50 percent.
  • Because the full detector transfer function lowers the projected SNR by roughly a factor of four relative to the long-wavelength approximation, future detector design should prioritize the 3-10 kHz band for such measurements to be practical.

Reading between the lines

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

  • If the quadratic relation between $(m_1-m_2)\omega_r$ and $m_{\rm disk}/M$ holds across more equations of state, the ringdown measurement would double as a new equation-of-state probe, since the bare black hole frequency is already fixed by inspiral-measured masses.
  • A natural next test is a full Bayesian injection study with realistic colored noise, unknown total mass, and amplitude/phase freed, to see whether the 10 percent accuracy survives outside the Fisher-matrix assumptions.
  • A 10 percent measurement of disk angular momentum, combined with kilonova light curves, could help separate ejecta mass from the nuclear physics uncertainties that currently limit r-process yield estimates.
  • The correlation could be checked independently by running new simulations with different neutrino-transport treatments or resolutions and verifying that the same $(m_1-m_2)\omega_r$ versus $m_{\rm disk}/M$ curve is recovered.
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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

3 major / 5 minor

Summary. The paper proposes that the ringdown gravitational-wave signal from a promptly collapsing binary neutron star (BNS) merger carries an imprint of the surrounding accretion disk, and that the disk mass (and angular momentum) can be inferred from a measurement of the ringdown frequency. Using 22 numerical-relativity simulations spanning four equations of state and a range of mass ratios, the authors fit a quadratic relation between m_disk/M and X=(m1-m2)omega_r, and a linear relation between J_disk and m_disk. They then estimate the postmerger signal-to-noise ratio for next-generation detectors (Cosmic Explorer and Einstein Telescope) including finite-arm transfer functions, and use a single-parameter Fisher forecast (omega_r unknown, total mass M known exactly, white Gaussian noise, SNR=5) to propagate a frequency uncertainty of ~60 Hz into a claimed ~10% fractional accuracy on the disk mass for binaries at distances up to 30 Mpc. The paper is explicitly framed as a proof-of-principle, with the authors acknowledging the limited simulation set and the simplified postmerger model.

Significance. If the empirical relation is robust, this work opens a new observational window: a direct gravitational-wave measurement of the mass and angular momentum of the remnant disk, which is currently inferred only indirectly from kilonova and gamma-ray burst modeling. The study is carefully connected to the multi-kHz sensitivity of next-generation observatories, and the inclusion of the full detector transfer function (Appendix D) is a methodological strength. The authors are transparent about the idealizations in the Fisher forecast and about the limited NR sample. However, the headline 10% accuracy and the causal claim that the disk influences the ringdown are load-bearing and require additional support, as detailed below.

major comments (3)
  1. [Measurement prospects / Fig. 4] The fractional errors in Fig. 4 are obtained by propagating the Fisher error on the ringdown frequency through the median quadratic fit, but the uncertainty of the calibration parameters (a,b,c,sigma) from the Bayesian regression in the 'Postmerger model' section is not included. Because the fit is anchored to only 22 NR simulations, the calibration scatter visible as the gray band in Fig. 1 contributes to the error budget for any inferred disk mass. The authors should report the posterior predictive uncertainty (or a calibration-error term) and quote the combined error; if the combined error exceeds 10%, the headline accuracy should be revised.
  2. [Postmerger model / Fig. 1] The independent variable X=(m1-m2)omega_r conflates binary mass asymmetry with ringdown frequency. Since m_disk/M is known to grow with mass asymmetry in prompt-collapse mergers (Refs. [8,9]), the strong correlation in Fig. 1 may be driven by the (m1-m2) prefactor rather than by a physical influence of the disk on omega_r. To support the central claim that 'the accretion disk influences the ringdown gravitational-wave signal,' the paper should demonstrate that the correlation persists when mass ratio is controlled for, e.g., by partial correlation, by including q as an additional regressor, or by plotting m_disk/M against omega_r in bins of q. Without such a control, the relation is at risk of being a proxy for mass ratio, which would also weaken the motivation for using it as a direct disk-mass probe.
  3. [Measurement prospects] The Fisher forecast assumes that the ringdown frequency is the only unknown parameter, that the noise is white Gaussian over 3-10 kHz, and that the total mass M is exactly known. These assumptions are stated explicitly, and the authors justify the M simplification by the high inspiral SNR, but the 10% accuracy claim is a best-case bound rather than a realistic estimate. I request at least one sensitivity test: a two-parameter Fisher including the overall amplitude (or M), or a noise curve consistent with the transfer functions in Appendix D. If the frequency error increases substantially, the paper should present the result as an idealized upper bound on the achievable accuracy and temper the abstract accordingly.
minor comments (5)
  1. [Abstract / Introduction] The verb 'discover' is too strong for a correlation-based empirical relation; 'find evidence' or 'show' would be more appropriate.
  2. [References] References [96] and [98] appear to be the same work (Buonanno and Chen), as do [97] and [99] (Ackley et al.); please merge the duplicates.
  3. [Fig. 1 caption] The gray curves in Fig. 1 are not described in the caption; specify that they are draws from the posterior distribution of the fit parameters.
  4. [Table I] The 90% ranges in Table I are large; please state explicitly that they arise from varying sky position and orientation and that the distances in Fig. 2 are based on the median SNR.
  5. [Appendix B] Please specify the exact definition of the L2 norm used in the ringdown fit, including how the log-amplitude and phase residuals are combined and whether the fit is performed in the time domain.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the disk-mass measurement is a calibrated mapping from a future GW frequency, not an identity with its input.

full rationale

The claimed derivation chain is: (i) 22 WhiskyTHC NR simulations produce both the disk quantities (m_disk, J_disk extracted by volume integrals in App. C) and the ringdown parameters (omega_r from the ansatz fit in App. A/B); (ii) Fig. 1 fits Y=m_disk/M against X=(m1-m2)omega_r with a quadratic Bayesian regression and J_disk against m_disk with a line; (iii) a Fisher calculation with white Gaussian noise, SNR 5, and only omega unknown gives Delta f about 60 Hz; (iv) this Delta omega is propagated through the Fig. 1 quadratic to quote Delta m_disk/m_disk less than about 10% in Fig. 4. No step defines m_disk in terms of omega_r by construction: the calibration is empirical and the paper itself labels the relation a 'phenomenological relationship'. A future GW measurement of omega_r is external to the calibration data, so applying the fit to a future event is inverse calibration, not tautology. Self-citations [63-65] supply the NR data set and a consistency check for the m_disk-J_disk slope; they do not force the central m_disk-omega relation, which is newly fit here. The real weaknesses are accuracy and robustness: the paper states 'our study relies on a limited set of available NR simulations, which restricts the accuracy of the phenomenological relationship we have introduced', and the forecast 'focus[es] on the case where omega is the only unknown parameter... assuming that M is measured exactly.' These omissions (calibration posterior variance, mass uncertainty, colored noise, degeneracies) are important caveats but are not circularity. Hence score 1.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The paper's central measurement is an empirical calibration: m_disk/M is modeled as a quadratic function of (m1-m2)ω_r and J_disk as a linear function of m_disk, with all coefficients fitted to 22 WhiskyTHC simulations. The error forecast then propagates a single-parameter Fisher error on ω_r through that fit. No first-principles derivation, independent validation set, or public data release is provided.

free parameters (3)
  • Quadratic fit coefficients a, b, c for m_disk/M vs (m1-m2)ω_r = Not reported; median curve shown in Fig. 1
    The disk-mass measurement is the inverse of this empirical curve, so the quoted 10 percent accuracy inherits the uncertainty of these fitted coefficients.
  • Linear slope for J_disk vs m_disk = 90% HDI between 8.8 and 9.4
    Converted disk mass into disk angular momentum; the fit scatter is quoted as negligible, but the slope is still calibrated to the same 22 simulations.
  • Phenomenological postmerger ansatz parameters a_i, b_i, φ0, and complex QNM frequency ω = Fit per NR waveform; values not tabulated
    The extracted ringdown frequency used for the disk-mass correlation depends on the ansatz in Eq. (A1), which is fitted to each NR waveform.
assumptions (5)
  • domain assumption The 22 WhiskyTHC NR simulations with 4 EoS are representative of the prompt-collapse BNS population
    The calibration relation and its scatter come only from these simulations; systematics from missing EoS, resolution, and microphysics are not included in the error budget.
  • ad hoc to paper The postmerger waveform is described by A(t)=(a1+a2 tanh(a3+a4 t)) exp(-ω_i t), Φ(t)=φ0+ω_r t+b1 log(1+b2 exp(-b3 t))
    The ansatz is motivated by BBH waveform models and matches the NR waveforms, but it is not derived from first principles, and the frequency extraction depends on this functional form.
  • domain assumption A Fisher matrix with white Gaussian noise and SNR 5 in 3-10 kHz gives unbiased errors for ω_r
    Real detector noise is colored and correlated with other parameters, so the 10 percent disk-mass error is conditional on this idealization.
  • domain assumption Disk mass and angular momentum are well defined by integrating outside the region with lapse < 0.2 at the last time step
    The disk is still evolving at the extraction time; the measured values depend on the simulation length and on the chosen lapse threshold.
  • domain assumption The total binary mass M is known exactly from the inspiral
    The fractional disk-mass error calculation sets delta-M = 0; an imperfect mass estimate would add to the reported uncertainty.

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Cite this review

Pith. "Pith review of Direct Measurement of the Accretion Disk Formed in Prompt Collapse Mergers with Future Gravitational-Wave Observatories." pith.science (2026). https://pith.science/paper/IKXA5LIZ

@misc{pith2026250714071,
  author       = {Pith},
  title        = {Pith review of: Direct Measurement of the Accretion Disk Formed in Prompt Collapse Mergers with Future Gravitational-Wave Observatories},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IKXA5LIZ}},
  note         = {Machine review of arXiv:2507.14071}
}
read the original abstract

The production site of heavy r-process elements, such as Gold and Uranium, is uncertain. Neutron star mergers are the only astrophysical phenomenon in which we have witnessed their formation. However, the amount of heavy elements resulting from the merger remains poorly constrained, mainly due to uncertainties on the mass and angular momentum of the disk formed in the merger remnant. Matter accretion from the disk is also thought to power gamma ray-bursts. We discover from numerical relativity simulations that the accretion disk influences the ringdown gravitational-wave signal produced by binaries that promptly collapse to black-hole at merger. We propose a method to \emph{directly} measure the mass of the accretion disk left during black hole formation in binary mergers using observatories such as the Einstein Telescope or Cosmic Explorer with a relative error of 10\% for binaries at a distance of up to 30~Mpc, corresponding to an event rate of 0.001 to 0.25 events per year.

Figures

Figures reproduced from arXiv: 2507.14071 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The distance at which the postmerger SNR is 5 for [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Distribution of the measurement errors in the oscilla [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Distribution of the fractional errors on an accretion [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. An illustrative waveform of a prompt collapse merger. [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Transfer function for the considered interferometers. [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

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Forward citations

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Reference graph

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