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Precession in black-hole binaries becomes detectable when the orbital plane sweeps through "plus nulls" where the non-precessing signal vanishes, and a new toy waveform parameterized by precession amplitude and frequency shows this can happ

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2026-08-04 17:42 UTC pith:7PY6KFBA

load-bearing objection Useful toy model and a genuinely new geometric observation, but the detectability numbers are optimistic because the NP template is not searched over. the 2 major comments →

arxiv 2509.10628 v1 pith:7PY6KFBA submitted 2025-09-12 gr-qc astro-ph.HE

Detecting regular precession using a new gravitational waveform model directly parameterized by both precession amplitude and frequency

Tamanjyot Singh , Evangelos Stoikos , Saif Ali , Nathan Steinle , Michael Kesden , Lindsay King This is my paper
classification gr-qc astro-ph.HE PACS 04.30.-w
keywords gravitational wavesbinary black holesspin precessionwaveform modelmismatchLindblom criteriondetectabilityredshift
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 builds a simplified frequency-domain waveform for binary black holes whose orbital plane precesses regularly, treating the precession amplitude and frequency as direct parameters. It argues that precession is distinguishable from a non-precessing signal whenever the waveform mismatch exceeds 1/(2 rho^2), where rho is the signal-to-noise ratio. Under this Lindblom criterion, precession is easiest to detect when the orbital angular momentum sweeps through orientations the authors call "plus nulls," where a non-precessing binary emits only the polarization that a single L-shaped detector cannot see. For maximally spinning, isotropically oriented binaries with chirp masses 10 to 40 solar masses and mass ratios above 0.5, the model predicts precession would be detectable in a majority of systems out to redshift ~0.3. The paper matters because it offers a clean, parameter-light way to predict when precession should be looked for in existing and future gravitational-wave data.

Core claim

The central claim is that a regularly precessing binary can be distinguished from a non-precessing template whenever the mismatch epsilon satisfies epsilon >= 1/(2 rho^2), with rho the signal-to-noise ratio, and that under this criterion precession is most detectable when the orbital angular momentum L precesses through "+ nulls": binary orientations and sky locations where F_+ = 0 and the non-precessing signal vanishes because the detector is blind to the only polarization emitted. At such configurations the precessing source still produces a signal, so the mismatch with the vanishing non-precessing waveform is large. Applying this to a toy waveform in which the dimensionless precession amp

What carries the argument

The carrying object is a toy frequency-domain waveform built from the quadrupole approximation, in which the orbital angular momentum L precesses around the total angular momentum J with a cone opening angle and precession frequency set by two constant dimensionless parameters, theta-tilde and Omega-tilde. These parameters enter the waveform through the polarization angle, the GW amplitude, and a phase correction, producing characteristic oscillations in amplitude and phase. The detectability of precession is assessed with the Lindblom criterion, which compares the mismatch between the precessing and non-precessing waveforms against the inverse-square of the signal-to-noise ratio. The "+ nul

Load-bearing premise

The whole analysis rests on the assumption that the precession amplitude and frequency follow their lowest post-Newtonian frequency scalings throughout the inspiral, so the dimensionless parameters theta-tilde and Omega-tilde stay constant; the toy waveform is never compared with a full post-Newtonian or numerical-relativity waveform.

What would settle it

Take a binary with specified masses and spins, generate its full post-Newtonian or numerical-relativity waveform, and compare it to the toy model with the same effective theta-tilde and Omega-tilde; if the mismatch between the two is comparable to or larger than 1/(2 rho^2) at typical network signal-to-noise ratios, the paper's detectable-fraction estimates would need revision.

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

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If this is right

  • Precession detection becomes a quantitative model-selection problem: a binary is claimed precessing when the mismatch with a non-precessing template exceeds 1/(2 rho^2).
  • Observational searches should focus on binaries whose orientation and sky location put them near + nulls, where precession imprint is largest.
  • Populations with maximal, isotropically oriented spins are the most promising targets, with detectable precession out to z ~ 0.3 for chirp masses 10-40 solar masses.
  • Reduced spin magnitudes, spin alignment, or strongly unequal masses shrink the redshift reach, often below z ~ 0.1.
  • A detector network or future third-generation detectors would raise the detectable fractions beyond the single-detector estimates presented here.

Where Pith is reading between the lines

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

  • The + null concept extends naturally to detector networks: because different detectors have different beam-pattern nulls, a network would spread the most-detectable orientations across a larger fraction of parameter space, an effect the paper notes but does not quantify.
  • The toy model could be stress-tested against existing catalog events: if known precessing candidates lie near predicted + nulls, that would support the criterion; if not, the constant-theta-tilde approximation may be the culprit.
  • A Bayesian evidence comparison between the precessing and non-precessing families would likely replace the Lindblom threshold in practice; the paper suggests such degeneracies are small, so the detectability fractions could be robust, but this remains untested.
  • Relaxing the constant theta-tilde and Omega-tilde assumption—for example, letting them evolve with frequency as higher-order post-Newtonian corrections suggest—would directly test whether the reported redshift reach survives in real waveforms.

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 / 5 minor

Summary. The paper proposes a frequency-domain toy waveform model for regularly precessing binary black holes, directly parameterized by a dimensionless precession amplitude theta-tilde and precession frequency Omega-tilde, plus a precessional phase gamma_p. The model is built from the quadrupole waveform with L precessing about J under the assumption that theta-tilde and Omega-tilde are constant throughout the inspiral. The authors compute mismatches between these RP waveforms and non-precessing templates with otherwise identical parameters, apply the Lindblom criterion epsilon >= 1/(2 rho^2), and identify '+ nulls' (configurations where F_+ = 0 and L·N = 0 for the NP system) as regions of enhanced precession detectability. They report detectability fractions as functions of redshift for fixed precession parameters and for populations drawn from spin distributions, claiming that precession is detectable in a majority of isotropic maximal-spin systems out to z ~ 0.3 for chirp masses 10-40 solar masses and q >= 0.5.

Significance. If the quantitative claims are robust, this work would provide a useful new parameterization of precessing waveforms and a concrete population-level forecast for detecting precession in LVK data. The paper is clearly written, the derivations are transparent, and the authors release code and a web app, which are strengths. The identification of + nulls as particularly favorable orientations is a new and interesting observation. However, the central detectability claim currently rests on two unvalidated ingredients: the toy waveform is not compared against full post-Newtonian or numerical-relativity precessing waveforms, and the mismatch is not minimized over the non-precessing template family. Both issues directly affect the numerical fractions in Tables II and III, so the significance of the paper, as it stands, is primarily methodological rather than a robust astrophysical prediction.

major comments (2)
  1. [Sec. IV, Eqs. (24)-(26) and (29); Tables II and III] The Lindblom criterion is applied to the mismatch between the RP waveform and an NP template with 'otherwise identical parameters', i.e., the same total-angular-momentum direction and sky location, with L aligned with J. This is not the best-matching NP template. In a real search, the NP template bank would be maximized over orientation and sky location as well as over time and coalescence phase. At the + nulls highlighted as the main new result, the fixed NP template has exactly zero strain (F_+ = 0 and L·N = 0), so epsilon = 1 and IP > 0 for any rho > 1/sqrt(2). A different NP template with a slightly different L direction could produce a much larger overlap with the RP signal, reducing epsilon below the Lindblom threshold. Since the paper never minimizes over NP parameters, the detectability fractions in Tables II and III, and the prominence of + nulls in Figs. 8-10, are not yet quant
  2. [Sec. III, Eq. (18); Appendix B] The load-bearing assumption that theta-tilde and Omega-tilde are constant throughout the inspiral is checked in Appendix B by examining the precession-averaged parameters as functions of separation. However, the paper never validates the resulting full waveform against an existing precessing waveform model (e.g., IMRPhenomXPHM or SEOBNRv4PHM) or against numerical relativity. The mismatches computed in Secs. IV and V are therefore internal to the toy model. If the true evolution of the precession cone, or the higher-order phase corrections, differ from Eq. (18), the computed epsilon and hence the reported detectability fractions will change. At minimum, the paper should state more clearly that all quantitative detectability estimates are conditional on the toy-model assumption, and ideally include a comparison at the waveform level with a standard precessing model for a few benchmark syst
minor comments (5)
  1. [Abstract and Sec. IV] The phrase 'otherwise identical parameters' is used repeatedly, but the precise definition of the NP template is not stated until one infers it from the construction: same masses, same J direction, same sky location, and L aligned with J. This should be made explicit at first use.
  2. [Fig. 2] The axis labels in the bottom panels ('cos L' and 'L') appear clipped or misaligned in the submitted version; please enlarge fonts and clean up the panel labels.
  3. [Table III] The table is very wide and the column headers are dense. Consider splitting the precession-parameter percentiles and the detectability fractions into separate tables, or rotating the table, to improve readability.
  4. [Appendix A, Eq. (A25)] The Taylor expansion leading to Eq. (A25) is concise but would benefit from a sentence stating the order at which terms are retained and why the expansion remains valid when L is exactly aligned with N.
  5. [Sec. VI] The statement that 'preliminary studies suggest that such degeneracies are small' is not backed by a reference or a figure. Given the central role of degeneracies with NP parameters, this claim should either be substantiated or removed.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained forward modeling.

full rationale

The paper's derivation chain is not circular. The regularly precessing (RP) waveform is an explicit toy model built from the quadrupole approximation (Eqs. 1-12), a precession taxonomy from prior work [40], and an explicit assumption about the frequency scaling of the precession parameters (Eq. 18). This assumption is transparently stated and independently checked in Appendix B using the precession package, which is code-reproduced and not merely a citation. No parameters are fitted to any target result: the precession amplitude theta-tilde and frequency Omega-tilde are either varied directly or drawn from spin distributions via the precession package, and the mismatch and Lindblom criterion (Eqs. 24-29) are applied as defined. The resulting detectability fractions in Tables II and III are forward-model calculations, not predictions forced by fitted inputs. The enhanced detectability at '+ nulls' is a mathematical consequence of the definition of the non-precessing (NP) template (zero detector response when F_+ = 0 and L·N = 0) and the mismatch definition; while the exact + null point gives epsilon = 1 by construction, this is not the load-bearing element of the majority detectability claim, which averages over orientations. The main caveat is the choice to compare against an NP template with 'otherwise identical parameters' rather than a maximized NP template bank; this is a robustness concern acknowledged only qualitatively in Sec. VI, but it is a limitation of the analysis, not a circular step. The self-citations to [40] and the precession package provide independently derived inputs and do not by themselves force the conclusions.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 0 invented entities

The central results depend on the precession parameter definitions, the lowest-PN scaling assumption, the quadrupole-only inspiral waveform, and the Lindblom detectability criterion. No genuinely new physical entities are introduced; '+ nulls' is a geometric condition on existing beam-pattern and polarization expressions.

free parameters (3)
  • theta-tilde
    Dimensionless precession amplitude defined in Eq. 18a. It is an intrinsic model parameter, varied across populations, not fitted to data.
  • Omega-tilde
    Dimensionless precession frequency defined in Eq. 18b. It is an intrinsic model parameter, varied across populations, not fitted to data.
  • gamma_p
    Initial azimuthal precession phase entering Eq. 19. Treated as a nuisance parameter with flat prior; minimized over for epsilon_P and marginalized in the population tables.
axioms (4)
  • standard math The inspiral gravitational wave is described by the lowest-order quadrupole-moment approximation of Eq. 5.
    The waveform uses the Newtonian, quadrupole-moment strain with 2PN spin-independent phase; higher harmonics and merger-ringdown are absent. This is a standard but simplified domain assumption.
  • domain assumption Simple precession applies, with J nearly constant and L precessing uniformly about J as parameterized by precession-averaged quantities.
    Section IIB invokes the two-degree-of-freedom reduction and precession averaging of Kesden, Gerosa, Gangardt, and others. This excludes transitional precession and nutational resonances.
  • ad hoc to paper The precession amplitude and frequency retain their lowest post-Newtonian frequency scalings through merger, so theta-tilde and Omega-tilde are constant.
    Eq. 18 assumes this scaling. Appendix B checks the constancy using the precession package, finding small deviations except for extreme mass ratios, but the toy waveform is not validated against full waveform models or numerical relativity.
  • domain assumption The Lindblom criterion, epsilon >= 1/(2 rho^2), determines when precession is detectable.
    Eq. 28 is taken as the distinguishability threshold; Appendix C derives the appropriate SNR choice. This is a standard but idealized model-selection criterion.

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Cite this review

Pith. "Pith review of Detecting regular precession using a new gravitational waveform model directly parameterized by both precession amplitude and frequency." pith.science (2026). https://pith.science/paper/7PY6KFBA

@misc{pith2026250910628,
  author       = {Pith},
  title        = {Pith review of: Detecting regular precession using a new gravitational waveform model directly parameterized by both precession amplitude and frequency},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7PY6KFBA}},
  note         = {Machine review of arXiv:2509.10628}
}
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read the original abstract

Nearly 210 binary black hole (BBH) mergers have been observed by the LIGO-Virgo-KAGRA network during its four observing runs. Generic BBHs are spinning, and their spins are misaligned with the orbital angular momentum $\vec{L}$. These misaligned spins cause $\vec{L}$ to precess in a cone with dimensionless precession amplitude $\tilde{\theta}$ and frequency $\tilde{\Omega}$ about the nearly constant direction of the total angular momentum. This precession modulates the observed GWs. We propose a model of regularly precessing (RP) waveforms that incorporates $\tilde{\theta}$ and $\tilde{\Omega}$ directly as parameters. We investigate how these waveforms vary as functions of these precessional parameters, as well as binary orientation and sky location. We use the Lindblom criterion to estimate that precession can be detected in a RP source with signal-to-noise ratio $\rho$ when the mismatch $\epsilon$ with a non-precessing (NP) source with otherwise identical parameters exceeds $1/2\rho^2$. Precession is most detectable when $\vec{L}$ precesses through configurations we call +~nulls during the inspiral. At +~nulls, a NP source only emits +-polarization to which the GW detector is insensitive. The large mismatch between a RP source and this vanishing NP signal enhances the detectability of precession. We also explore the detectability of precession as a function of redshift $z$ for different BBH populations. We find that for BBHs with isotropically oriented maximal spins, precession is detectable in a majority of systems out to $z \approx 0.3$ for chirp masses $10 \lesssim M_c/M_\odot \lesssim 40$ and mass ratios $q \gtrsim 0.5$. Reduced spin magnitudes or greater alignment between the spins and $\vec{L}$ make it difficult to observe beyond $z \approx 0.1$. (abridged)

Figures

Figures reproduced from arXiv: 2509.10628 by Evangelos Stoikos, Lindsay King, Michael Kesden, Nathan Steinle, Saif Ali, Tamanjyot Singh.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic depictions of the sky and source coordinate [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Evolution of the spherical coordinates [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The ratio of the GW amplitude [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The evolution of the polarization phase and phase correction term [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Mismatches between RP GW sources and NP tem [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Mismatches between RP GW sources and NP templates minimized over [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Signal-to-noise ratios [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. The quantity [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. The mismatch [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. The quantity [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Dimensionless precession parameters [PITH_FULL_IMAGE:figures/full_fig_p023_11.png] view at source ↗

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    This sky location implies a beam-pattern amplitude C = 3 /4and phase α = 0according to Eq. (4). The left, middle, and right columns correspond to the three different choices of the direction of the total angular mo- mentumJlisted as Systems 1, 2, and 3 in Table I. We plot the ratio of the regularly precessing (RP) to the non-precessing (NP) amplitude to f...

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