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arxiv: 2605.18595 · v1 · pith:FCL4KUGZnew · submitted 2026-05-18 · 🌀 gr-qc

Impact of sky localization uncertainty on ringdown inference

Kallol Dey , Enrico Barausse , Marco Crisostomi , Roberto Trotta This is my paper

Pith reviewed 2026-05-20 08:48 UTC · model grok-4.3

classification 🌀 gr-qc
keywords gravitational wavesringdownquasinormal modessky localizationblack hole spectroscopyKerr testsGW250114GW190521
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The pith

Fixing sky location to a point estimate in ringdown analyses artificially narrows uncertainties on quasinormal-mode amplitudes.

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

Standard gravitational-wave ringdown studies often lock sky position, polarization, and inclination to single values taken from a prior full-signal analysis. This choice can break natural degeneracies between extrinsic parameters and the amplitudes of quasinormal modes, producing tighter posteriors than the data actually support. The authors test two alternatives: drawing uninformative priors on the extrinsic parameters and sampling them jointly with remnant mass, spin, and mode amplitudes, or importing informed priors from the complete inspiral-merger-ringdown posterior. Both methods yield broader amplitude constraints and remove the risk of bias from the fixed-sky choice. Amplitude ratios between modes remain stable across all three approaches, identifying them as a more trustworthy observable for black-hole spectroscopy.

Core claim

Fixing sky localization to a point estimate from the full signal breaks degeneracies and underestimates the uncertainty on quasinormal-mode amplitudes; joint sampling with uninformative priors or use of informed priors drawn from the full-signal posterior produces wider marginal posteriors on amplitudes while keeping amplitude ratios consistent.

What carries the argument

Joint sampling of sky position, polarization, and inclination together with remnant black-hole parameters and quasinormal-mode amplitudes and phases inside the ringdown likelihood.

Load-bearing premise

That either uninformative priors or priors taken from the full-signal posterior capture the relevant degeneracies without adding new biases to the ringdown-only likelihood.

What would settle it

Re-analyze a set of simulated ringdown signals with known sky locations using both fixed-sky and jointly sampled extrinsic parameters and check whether the recovered amplitude uncertainties match the expected increase.

Figures

Figures reproduced from arXiv: 2605.18595 by Enrico Barausse, Kallol Dey, Marco Crisostomi, Roberto Trotta.

Figure 1
Figure 1. Figure 1: FIG. 1. Posteriors (68% and 95% regions for 2D marginals) for GW250114 using a (2 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Posteriors for [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Posteriors for [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Posterior distributions (68% and 95% regions for 2D marginals) for a GW250114-like simulated noiseless signal using [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Posterior distributions (68% and 95% regions for 2D marginals) for a GW190521-like simulated noiseless signal using [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Posteriors (68% shaded region) of the mode-amplitude ratios for the noiseless ringdown injections: (a) GW250114-like [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
read the original abstract

As gravitational-wave ringdown signals grow louder, quasinormal-mode inference depends increasingly on the treatment of extrinsic parameters. Standard analyses fix sky localization - and sometimes also polarization and inclination - to point estimates from a prior inspiral-merger-ringdown analysis, artificially breaking degeneracies and underestimating the true uncertainty of mode-amplitude values. We test two alternatives: uninformative priors on the extrinsic parameters, sampled jointly with the remnant mass, spin, mode amplitudes, and phases; and informed priors on sky position from the full signal posterior. The former yields wider marginal constraints on amplitude posteriors, and both avoid potential bias introduced by fixing the sky localization. In contrast, mode amplitude ratios remain consistent across approaches, making them a robust observable for Kerr spectroscopy. Our publicly available pipeline enables fast ringdown analyses capable of sampling all parameters, requiring tens of minutes on a laptop for a full inference. Applied to GW250114 and GW190521, our methods confirm the robust detection of the $(2,2,1)$ overtone in GW250114, and, for GW190521, find only mild evidence for the $(3,3,0)$ mode.

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 paper claims that standard ringdown analyses, which fix sky localization (and sometimes polarization/inclination) to point estimates from a prior full-signal analysis, artificially break degeneracies and underestimate uncertainties in quasinormal-mode amplitudes. It tests two alternatives—joint sampling with uninformative priors on extrinsic parameters, and informed priors drawn from the full-signal posterior—on GW250114 and GW190521. Both alternatives yield wider marginal amplitude posteriors and avoid potential bias from fixed sky position, while amplitude ratios remain consistent across methods and support robust Kerr spectroscopy. A publicly available pipeline enables fast full-parameter ringdown inference.

Significance. If the central results hold, the work is significant for highlighting a systematic underestimation of uncertainties in ringdown parameter estimation as signals strengthen, and for demonstrating that mode-amplitude ratios are robust observables. The public pipeline for sampling all parameters in tens of minutes on a laptop is a practical strength that supports reproducibility. Application to real events (confirming the (2,2,1) overtone in GW250114 and mild evidence for (3,3,0) in GW190521) provides concrete, falsifiable demonstrations.

major comments (2)
  1. [Methods and Results sections (informed-prior implementation)] The central claim that informed priors from the full-signal posterior avoid bias while correctly capturing extrinsic degeneracies for the ringdown-only likelihood is load-bearing but rests on an untested assumption. Because the full-signal posterior encodes sky-position correlations driven by inspiral and merger antenna patterns (different from the damped-sinusoid ringdown likelihood), feeding it as a prior risks importing inconsistent correlations that could either bias or artificially inflate the marginal amplitude posteriors. This needs explicit validation, e.g., via injection studies comparing the informed-prior posterior against a true ringdown-only ground truth.
  2. [Results for GW250114 and GW190521] The manuscript reports that amplitude ratios remain consistent across the three approaches, but without quantitative comparison of the ratio posteriors (e.g., overlap integrals or credible-interval widths) it is unclear whether the consistency is merely qualitative or statistically robust enough to support the claim that ratios are a reliable observable for Kerr spectroscopy.
minor comments (2)
  1. [Methods] Clarify the exact data-selection window and tapering used for the ringdown-only likelihood; this detail is essential for reproducibility of the reported posteriors.
  2. [Results] The abstract states 'wider posteriors when sky position varies' but the main text should explicitly tabulate the 90% credible-interval widths for the dominant-mode amplitudes under each prior choice for direct comparison.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and the recommendation for major revision. We address each major comment point by point below, agreeing where revisions are warranted to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Methods and Results sections (informed-prior implementation)] The central claim that informed priors from the full-signal posterior avoid bias while correctly capturing extrinsic degeneracies for the ringdown-only likelihood is load-bearing but rests on an untested assumption. Because the full-signal posterior encodes sky-position correlations driven by inspiral and merger antenna patterns (different from the damped-sinusoid ringdown likelihood), feeding it as a prior risks importing inconsistent correlations that could either bias or artificially inflate the marginal amplitude posteriors. This needs explicit validation, e.g., via injection studies comparing the informed-prior posterior against a true ringdown-only ground truth.

    Authors: We agree that this is an important point and that the assumption requires validation. The informed prior is used to marginalize over the uncertainty in sky localization informed by the full signal, which is reasonable given that the ringdown provides weak constraints on extrinsic parameters. Nevertheless, to directly address the concern about potential inconsistent correlations, we will perform and include injection studies in the revised manuscript. These studies will involve generating simulated ringdown signals with known sky positions and amplitudes, analyzing them with the informed-prior method, and comparing the recovered posteriors to the known ground truth to assess any bias or inflation in uncertainties. revision: yes

  2. Referee: [Results for GW250114 and GW190521] The manuscript reports that amplitude ratios remain consistent across the three approaches, but without quantitative comparison of the ratio posteriors (e.g., overlap integrals or credible-interval widths) it is unclear whether the consistency is merely qualitative or statistically robust enough to support the claim that ratios are a reliable observable for Kerr spectroscopy.

    Authors: We concur that adding quantitative metrics will better substantiate the robustness of the amplitude ratios. In the revised manuscript, we will compute the overlap integrals between the posterior distributions of the amplitude ratios from the different sampling approaches. We will also tabulate and compare the widths of the credible intervals for these ratios. These additions will provide a statistical basis for claiming that the ratios are consistent and thus reliable for Kerr spectroscopy. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical posterior sampling on real data

full rationale

The paper performs direct Bayesian sampling of ringdown posteriors on actual detector data (GW250114, GW190521) under three treatments of extrinsic parameters: fixed point estimates, uninformative joint priors, and informed priors drawn from the full-signal posterior. All reported outcomes—wider amplitude uncertainties, consistent mode ratios, and mode detections—are numerical results of the sampling procedure itself. No algebraic derivation, parameter fit, or self-referential definition is claimed or used; the comparisons are external to any equation within the paper and are benchmarked against real strain data. The analysis is therefore self-contained and does not reduce any claimed result to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The analysis rests on standard Bayesian inference machinery and the assumption that the ringdown can be modeled as a sum of quasinormal modes with extrinsic parameters marginalized.

axioms (2)
  • domain assumption The ringdown waveform is accurately described by a linear superposition of Kerr quasinormal modes with amplitudes and phases as free parameters.
    Invoked when defining the likelihood for mode-amplitude inference.
  • standard math Standard Bayesian sampling (e.g., nested sampling or MCMC) correctly explores the joint posterior over intrinsic and extrinsic parameters.
    Underlying the comparison of fixed versus joint sampling approaches.

pith-pipeline@v0.9.0 · 5736 in / 1303 out tokens · 45447 ms · 2026-05-20T08:48:32.597850+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

30 extracted references · 30 canonical work pages · 7 internal anchors

  1. [1]

    Black Hole Spectroscopy: Testing General Relativity through Gravitational Wave Observations

    O. Dreyer, B. J. Kelly, B. Krishnan, L. S. Finn, D. Garrison, and R. Lopez-Aleman, “Black hole spectroscopy: Testing general relativity through gravitational wave observations,” Class. Quant. Grav. 21(2004) 787–804,arXiv:gr-qc/0309007

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  2. [2]

    On gravitational-wave spectroscopy of massive black holes with the space interferometer LISA

    E. Berti, V. Cardoso, and C. M. Will, “On gravitational-wave spectroscopy of massive black holes with the space interferometer LISA,” Phys. Rev. D73 (2006) 064030,arXiv:gr-qc/0512160

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  3. [3]

    Quasinormal modes of black holes and black branes

    E. Berti, V. Cardoso, and A. O. Starinets, “Quasinormal modes of black holes and black branes,” Class. Quant. Grav.26(2009) 163001, arXiv:0905.2975 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  4. [4]

    Spectroscopy of Kerr black holes with Earth- and space-based interferometers

    E. Berti, A. Sesana, E. Barausse, V. Cardoso, and K. Belczynski, “Spectroscopy of Kerr black holes with Earth- and space-based interferometers,” Phys. Rev. Lett.117no. 10, (2016) 101102,arXiv:1605.09286 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  5. [5]

    Bhagwat, C

    S. Bhagwat, C. Pacilio, E. Barausse, and P. Pani, “Landscape of massive black-hole spectroscopy with LISA and the Einstein Telescope,” Phys. Rev. D105 no. 12, (2022) 124063,arXiv:2201.00023 [gr-qc]

    work page arXiv 2022

  6. [6]

    Black hole spectroscopy: from theory to experiment

    J. Abedi et al., “Black hole spectroscopy: from theory to experiment,”arXiv:2505.23895 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv

  7. [7]

    Black hole ringdown: the importance of overtones,

    M. Giesler, M. Isi, M. A. Scheel, and S. Teukolsky, “Black Hole Ringdown: The Importance of Overtones,” Phys. Rev. X9no. 4, (2019) 041060,arXiv:1903.08284 [gr-qc]. 7 0.0 0.4 0.8 χ 0.0 1.5 3.0 A220 0.0 2.5 5.0 φ220 0 2 4 A221 0.0 2.5 5.0 φ221 −0.8 0.0 0.8 cos ι 0.0 2.5 5.0 α −0.8 0.0 0.8 sin δ 55 65 75 85 M 0.0 1.5 3.0 ψ 0.0 0.4 0.8 χ 0.0 1.5 3.0 A220 0.0 ...

    work page arXiv 2019

  8. [8]

    Testing the no-hair theorem with GW150914

    M. Isi, M. Giesler, W. M. Farr, M. A. Scheel, and S. A. Teukolsky, “Testing the no-hair theorem with GW150914,” Phys. Rev. Lett.123no. 11, (2019) 111102,arXiv:1905.00869 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  9. [9]

    Cotesta, G

    R. Cotesta, G. Carullo, E. Berti, and V. Cardoso, “Analysis of Ringdown Overtones in GW150914,” Phys. Rev. Lett.129no. 11, (2022) 111102, arXiv:2201.00822 [gr-qc]

    work page arXiv 2022

  10. [10]

    Revisiting the ringdown of GW150914,

    M. Isi and W. M. Farr, “Revisiting the ringdown of GW150914,”arXiv:2202.02941 [gr-qc]

    work page arXiv

  11. [11]

    Searching for a ringdown overtone in GW150914,

    E. Finch and C. J. Moore, “Searching for a ringdown overtone in GW150914,” Phys. Rev. D106no. 4, (2022) 043005,arXiv:2205.07809 [gr-qc]

    work page arXiv 2022

  12. [12]

    Neural posterior estimation with guaranteed exact coverage: The ringdown of GW150914,

    M. Crisostomi, K. Dey, E. Barausse, and R. Trotta, “Neural posterior estimation with guaranteed exact coverage: The ringdown of GW150914,” Phys. Rev. D 8 0.0 0.4 0.8 χ 0 2 4 A220 0.0 2.5 5.0 φ220 0.0 0.5 1.0 A330 0.0 2.5 5.0 φ330 −0.8 0.0 0.8 cos ι 0.0 2.5 5.0 α −0.8 0.0 0.8 sin δ 240 280 320 M 0.0 1.5 3.0 ψ 0.0 0.4 0.8 χ 0 2 4 A220 0.0 2.5 5.0 φ220 0.0 0...

    work page arXiv 2023

  13. [13]

    Gating-and-inpainting perspective on GW150914 ringdown overtone: Understanding the data analysis systematics,

    Y.-F. Wang, C. D. Capano, J. Abedi, S. Kastha, B. Krishnan, A. B. Nielsen, A. H. Nitz, and J. Westerweck, “Gating-and-inpainting perspective on GW150914 ringdown overtone: Understanding the data analysis systematics,” Phys. Rev. D112no. 8, (2025) 083023,arXiv:2310.19645 [gr-qc]

    work page arXiv 2025

  14. [14]

    Low evidence for ringdown overtone in GW150914 when marginalizing over time and sky location uncertainty,

    A. Correia, Y.-F. Wang, J. Westerweck, and C. D. Capano, “Low evidence for ringdown overtone in GW150914 when marginalizing over time and sky location uncertainty,” Phys. Rev. D110no. 4, (2024) L041501,arXiv:2312.14118 [gr-qc]

    work page arXiv 2024

  15. [15]

    Capano et al

    C. D. Capano, M. Cabero, J. Westerweck, J. Abedi, S. Kastha, A. H. Nitz, Y.-F. Wang, A. B. Nielsen, and B. Krishnan, “Multimode Quasinormal Spectrum from a Perturbed Black Hole,” Phys. Rev. Lett.131no. 22, 9 0.5 1.0 1.5 2.0 A221/A220 Full-sky Fixed-sky (a) 0.2 0.4 0.6 0.8 A330/A220 Full-sky Fixed-sky (b) FIG. 7. Posteriors (68% shaded region) of the mode-...

    work page arXiv 2023

  16. [16]

    Searching for ringdown higher modes with a numerical relativity-informed post-merger model,

    V. Gennari, G. Carullo, and W. Del Pozzo, “Searching for ringdown higher modes with a numerical relativity-informed post-merger model,” Eur. Phys. J. C 84no. 3, (2024) 233,arXiv:2312.12515 [gr-qc]. [17]LIGO Scientific, VIRGO, KAGRACollaboration, R. Abbott et al., “Tests of General Relativity with GWTC-3,” Phys. Rev. D112no. 8, (2025) 084080, arXiv:2112.06...

    work page arXiv 2024

  17. [17]

    A nonlinear voice from GW250114 ringdown,

    Y.-F. Wang, S. Ma, N. Khera, and H. Yang, “A nonlinear voice from GW250114 ringdown,” arXiv:2601.05734 [gr-qc]

    work page arXiv

  18. [18]

    Observational Black Hole Spectroscopy: A time-domain multimode analysis of GW150914

    G. Carullo, W. Del Pozzo, and J. Veitch, “Observational Black Hole Spectroscopy: A time-domain multimode analysis of GW150914,” Phys. Rev. D99no. 12, (2019) 123029,arXiv:1902.07527 [gr-qc]. [Erratum: Phys.Rev.D 100, 089903 (2019)]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  19. [19]

    Frequency-domain analysis of black-hole ringdowns,

    E. Finch and C. J. Moore, “Frequency-domain analysis of black-hole ringdowns,” Phys. Rev. D104no. 12, (2021) 123034,arXiv:2108.09344 [gr-qc]

    work page arXiv 2021

  20. [20]

    Gravitational Wave Ringdown Analysis Using the F-statistic,

    H.-T. Wang, G. Yim, X. Chen, and L. Shao, “Gravitational Wave Ringdown Analysis Using the F-statistic,” Astrophys. J.974no. 2, (2024) 230, arXiv:2409.00970 [gr-qc]

    work page arXiv 2024

  21. [21]

    Isi and W

    M. Isi and W. M. Farr, “Analyzing black-hole ringdowns,”arXiv:2107.05609 [gr-qc]

    work page arXiv

  22. [22]

    Nested sampling for general Bayesian computation,

    J. Skilling, “Nested sampling for general Bayesian computation,” Bayesian Anal.1no. 4, (2006) 833–859

    work page 2006

  23. [23]

    JAXNS: a high-performance nested sampling package based on JAX,

    J. G. Albert, “JAXNS: a high-performance nested sampling package based on JAX,”arXiv:2012.15286 [astro-ph.IM]. [28]https://git.ligo.org/lscsoft/lalsuite

    work page arXiv 2012

  24. [24]

    Ringdown of GW190521: Hints of multiple quasinormal modes with a precessional interpretation,

    H. Siegel, M. Isi, and W. M. Farr, “Ringdown of GW190521: Hints of multiple quasinormal modes with a precessional interpretation,” Phys. Rev. D108no. 6, (2023) 064008,arXiv:2307.11975 [gr-qc]

    work page arXiv 2023

  25. [25]

    2008, Contemporary Physics, 49, 71, doi: 10.1080/00107510802066753

    R. Trotta, “Bayes in the sky: Bayesian inference and model selection in cosmology,” Contemporary Physics 49no. 2, (Mar., 2008) 71–104. http://dx.doi.org/10.1080/00107510802066753

    work page doi:10.1080/00107510802066753 2008

  26. [26]

    Novel Ringdown Amplitude-Phase Consistency Test,

    X. J. Forteza, S. Bhagwat, S. Kumar, and P. Pani, “Novel Ringdown Amplitude-Phase Consistency Test,” Phys. Rev. Lett.130no. 2, (2023) 021001, arXiv:2205.14910 [gr-qc]

    work page arXiv 2023

  27. [27]

    Nonlinear quasinormal mode detectability with next-generation gravitational wave detectors,

    S. Yi, A. Kuntz, E. Barausse, E. Berti, M. H.-Y. Cheung, K. Kritos, and A. Maselli, “Nonlinear quasinormal mode detectability with next-generation gravitational wave detectors,” Phys. Rev. D109no. 12, (2024) 124029,arXiv:2403.09767 [gr-qc]

    work page arXiv 2024

  28. [28]

    Systematic bias in LISA ringdown analysis due to waveform inaccuracy,

    L. Capuano, M. Vaglio, R. S. Chandramouli, C. L. Pitte, A. Kuntz, and E. Barausse, “Systematic bias in LISA ringdown analysis due to waveform inaccuracy,” Phys. Rev. D112no. 10, (2025) 104031, arXiv:2506.21181 [gr-qc]

    work page arXiv 2025

  29. [29]

    skyring

    “skyring.”https://github.com/kallolD/skyRing, 2026

    work page 2026

  30. [30]

    K. Dey, M. Crisostomi, R. Trotta, and E. Barausse, May, 2026. https://doi.org/10.5281/zenodo.20089762

    work page doi:10.5281/zenodo.20089762 2026