Prominence: A discriminator of gravitational wave signals

arXiv:2509.04384 · hep-ph, astro-ph.CO, gr-qc, hep-ex · Submitted 2025-09-04 · Read on arXiv

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Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: Today's paper: "Prominence: A discriminator of gravitational wave signals".

Jocelyn: The gist: Prominence P is introduced as a discriminator of gravitational wave (GW) signals, sensitive to both background structure and signal shape,

Vera: First, who's behind it and why it matters.

Paper summary: Vera: So, wrapping up this discussion on "Prominence: A discriminator of gravitational wave signals," the authors are really pointing out that this metric is specifically designed to work in those tricky situations where signals look very similar <ref:two thousand five hundred nine point zero four three eight four#pg2.

Jocelyn: And they’re highlighting that the concept itself, originally from topography, is being repurposed here to provide a new way to analyze the shape of gravitational wave backgrounds <ref:two thousand five hundred nine point zero four three eight four#pg1.

Subrahmanyan: The implication for the field is that we need observables beyond just amplitude and frequency measurements if we want to confidently rule out or confirm these specific cosmological sources like domain walls or phase transitions <ref:two thousand five hundred nine point zero four three eight four#pg2.

Vera: They are demonstrating a statistical way to test hypotheses, using that chi-squared statistic based on the inner product in signal space to show Prominence can achieve significances above and sometimes far above three sigma <ref:two thousand five hundred nine point zero four three eight four#pg2.

Jocelyn: It’s a tool that shows how we can use structural information—the relative height of peaks—to gain discrimination power where the standard signal-to-noise ratio falls short <ref:two thousand five hundred nine point zero four three eight four#pg2.

Subrahmanyan: The work is useful because it lays out exactly what precision in energy density we need to expect from future detectors like LISA for this Prominence approach to really make a difference <ref:two thousand five hundred nine point zero four three eight four#pg1.

Vera: So, while it’s not a universal answer, the paper shows that Prominence is a valuable discriminator precisely when signals are degenerate and SNR isn't enough <ref:two thousand five hundred nine point zero four three eight four#pg2.

Conclusion: Vera: So, we’ve looked at how Prominence works to tell different types of gravitational wave signals apart. Now, let's talk about what this paper is actually titled and who wrote it so we can get a sense of the big picture.

Jocelyn: The title is "Prominence: A discriminator of gravitational wave signals," and the authors are João Gonçalves, Danny Marfatia, and António P. Moraisb from Aveiro, Braga, and Hawaii. That tells you right away this is about using a specific shape metric to separate these different cosmic noise sources.

Subrahmanyan: And the main thing they’re showing is that this Prominence measure can actually distinguish between things like first-order phase transitions and domain walls even when their peak amplitudes look exactly the same. That's pretty significant because usually, you have to rely on signal-to-noise ratio to tell those apart.

Vera: Exactly, because the SNR alone just isn't enough when the signals are so similar in shape. It moves us from just looking at how loud a signal is to looking at how it’s structured in time or frequency.

Jocelyn: It really changes what we look for in the data from LISA or those Pulsar Timing Arrays, because if these sources are degenerate, Prominence gives us that extra handle we need for analysis.

Subrahmanyan: And the authors are making a clear point about the precision required; they say you need to know the energy density down to sub-percent levels for this discrimination to work at three sigma confidence. That sets a really high bar for what those future detectors have to measure accurately.

Vera: So, in short, Prominence is this new tool that lets us probe the structure of gravitational wave backgrounds instead of just their overall strength. It’s about using geometry to find physics we couldn't see before.

Jocelyn: And the implication for us on the ground is that when we analyze those complex background signals, we should be thinking more about Prominence than just trying to get a bigger SNR number.

Subrahmanyan: It opens up a whole new way of looking at multi-peak structures in the gravitational wave spectrum, which is where most of these exotic physics candidates like cosmic strings live.

Departamento de Física da Universidade de Aveiro · Laboratório de Instrumentação e Física Experimental de Partículas (LIP) · Department of Physics and Astronomy, University of Hawaii at Manoa

hep-ph, astro-ph.CO, gr-qc, hep-ex

Submitted: 2025-09-04

Updated: 2026-10-08

Comments: 24 pages, 13 figures, 2 tables. Version to appear in PRD. The implementation of our analysis is available at https://github.com/Mrazi09/Prominence-GW-discriminator

Code: https://github.com/Mrazi09/Prominence-GW-discriminator

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 69/100

The gist: The gist: Prominence P is introduced as a discriminator of gravitational wave (GW) signals, sensitive to both background structure and signal shape, which can distinguish between GW spectra produced

Key concepts

Prominence ($\mathcal{P}$): Prominence is a measure used in topography to quantify the height of a peak relative to its surrounding terrain. It calculates how much higher a peak sits above the lowest contour line that encircles it without containing any higher summits within that boundary. In GW analysis, this measures the prominence of a signal peak above the background noise.
Stochastic Gravitational Wave Background (SGWB): The SGWB is a continuous gravitational wave background generated by the superposition of numerous unresolved sources in the universe. These sources can be astrophysical, like black hole binaries, or cosmological, such as cosmic strings or phase transitions. The paper focuses on distinguishing between these different types of SGWB spectra.
First-order Phase Transitions (FOPTs): FOPTs are processes in the early Universe where a system changes its state abruptly, often through bubble nucleation. This process generates gravitational waves via sound waves in the plasma, bubble collisions, and turbulence. The paper uses Prominence to help separate these GW signals from other cosmological backgrounds.
Signal-to-Noise Ratio (SNR) vs. Prominence: The Signal-to-Noise Ratio (SNR) is a standard metric for detecting a signal's strength against background noise. However, the paper demonstrates that Prominence offers superior discrimination power, especially when signals are similar in spectrum and have low SNR. $\mathcal{P}$ can distinguish sources that look identical based on SNR alone, achieving significances far exceeding $3\sigma$.

Terminology

Domain Walls — 1× in this paper · explained in 2 episodes
Phase Transition — 1× in this paper · explained in 2 episodes
Phase Transitions — 1× in this paper · explained in 2 episodes
pulsar timing arrays — 1× in this paper · explained in 2 episodes

Summary

The gist: Prominence P is introduced as a discriminator of gravitational wave (GW) signals, sensitive to both background structure and signal shape, which can distinguish between GW spectra produced by first-order phase transitions, domain walls and cosmic strings, and combinations thereof <ref:2509.04384#pg12>.

How it works

Prominence P is defined as a measure of how much a peak rises above its surrounding terrain, formally defined as the height of the peak’s summit above the lowest contour line encircling it that contains no higher summit within it <ref:2509.04384#pg4>. To compute this, an algorithm is applied involving identifying local maxima and defining a window border based on sensitivity curves in the frequency-amplitude plane <ref:2509.04384#pg6>. The Prominence of peak i is computed as Pi = log10 h h2omegaGW peak i - log10 h h2omegaGW base GW i, (2.1) which is defined to be O(1) <ref:2509.04384#pg7>. This procedure ignores the signal beyond the endpoints, treating them as valleys relative to the neighboring peak <ref:2509.04384#pg8>.

Analytical Templates for Cosmological GW Signals and Backgrounds

The paper discusses various cosmological sources of stochastic gravitational wave backgrounds (SGWB) including cosmic strings (CSs), domain walls (DWs), and first-order phase transitions (FOPTs) <ref:2509.04384#pg10>. For cosmic strings, the SGWB spectrum depends on the string tension or energy per unit length µ, with a formula given by Gµ ≈ 10-6 v 10 16 GeV squared. The spectral energy density for oscillating loops is given by omegaGW(f) = 8π/3H2 0 (Gµ) squared f X∞ k=1 PkCk(f), (3.2).

Results and Discrimination Power

The effectiveness of Prominence is shown by simulating datasets with backgrounds varied within previously mentioned ranges, constructing a probability density function (PDF) of P for each individual peak <ref:2509.04384#pg9>. Statistical tests like the two-sample Kolmogorov-Smirnov (KS) test and the Cramer-von Mises (CvM) test are used to evaluate the similarity between SGWB spectra based on their P values. The paper demonstrates that Prominence can distinguish between FOPT and DW sources even when their peak amplitudes and frequencies are identical, with the CvM test yielding a significance greater than 3.4σ in some cases.

Impact of Amplitude Uncertainties and Band Dependence

The discrimination power of Prominence is dependent on the precision with which h h2omegaGW can be determined, finding that better than 3σ discrimination is possible if the fractional uncertainty ∆omega/omega < 1%, a level expected for LISA. Conversely, SGWB signals in the PTA frequency band (f < 10-7 Hz) are subject to much larger uncertainties (∆omegaPTA/omegaPTA ∼ 30%–50%), which significantly limits the discriminating power of Prominence. Furthermore, large extragalactic backgrounds in the ET band obscure some spectral features that distinguish FOPT and DW signals, making them appear more similar and weakening the discrimination power of Prominence.

Conclusion

Prominence provides its greatest discriminating power precisely when signals are significantly degenerate, with similar spectra and relatively small SNRs. The implementation of the analysis is available for download on GitHub.

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Prepared for submission to JCAP Prominence: A discriminator of gravitational wave signals João Gonçalves,a,b Danny Marfatia,c and António P. Moraisb,d aDepartamento de Física da Universidade de Aveiro, Campus de Santiago, 3810-183 Aveiro, Portugal. bLaboratório de Instrumentação e Física Experimental de Partículas (LIP), Universidade do Minho, 4710-057 Braga, Portugal cDepartment of Physics and Astronomy, University of Hawaii at Manoa, Honolulu, HI 96822, USA dDepartamento de Física, Escola de Ciências, Universidade do Minho, 4710-057 Braga, Portugal E-mail: jpedropino@ua.pt, dmarf8@hawaii.edu, amorais@fisica.uminho.pt Abstract The concept of prominence is familiar to signal engineers, topographers and mountaineers <ref:2509.04384#pg2>. We introduce Prominence P as a discriminator of gravitational wave (GW) signals <ref:2509.04384#pg2>. We treat black hole and neutron star binaries as astrophysical background sources, and show how P can be used to distinguish between GW spectra produced by first-order phase transitions, domain walls and cosmic strings, and combinations thereof <ref:2509.04384#pg2>. Prominence can also be used to discriminate between these and off-piste sources of GWs <ref:2509.04384#pg2>. The uncertainty in the measured energy density in GWs at Pulsar Timing Arrays needs to be at the sub-percent to percent level for P to achieve discrimination at 3σ <ref:2509.04384#pg2>. LISA and ET data are expected to have sufficiently small uncertainties that Prominence can play a central role in their analysis <ref:2509.04384#pg2>. We define and apply a χ squared statistic based on an inner product in signal space to show that sources indistinguishable at 2σ using the signal-to-noise ratio can be distinguished using P with significances above and in some cases far above 3σ <ref:2509.04384#pg2>. arXiv:2509.04384v2 [hep-ph] 12 Jun 2026

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Contents 1 Introduction Gravitational waves (GWs) constitute a powerful tool for probing both the dynamics of the early Universe and various astrophysical phenomena <ref:2509.04384#pg2>. In addition to transient signals, such as those originating from binary black hole mergers [1], a stochastic gravitational wave background (SGWB) from the superposition of numerous unresolved sources may be detectable [2] <ref:2509.04384#pg3>. Beyond the expected astrophysical contributions, a cosmological component may also be present <ref:2509.04384#pg2>. If detected, such a component could serve as evidence for new physics beyond the Standard Model [3] <ref:2509.04384#pg2>. Cosmological backgrounds can originate from processes prior to the era of Big Bang Nucleosynthesis at energy scales that may far exceed the electroweak scale <ref:2509.04384#pg2>. Among the possible sources, first-order phase transitions (FOPTs), proceeding via bubble nucleation, generate GWs through sound waves in the plasma, bubble collisions, and turbulence [4] <ref:2509.04384#pg2>. Topological defects, such as cosmic strings (CSs), line-like false vacuum remnants formed after the spontaneous breaking of a global or gauge symmetry, may also produce GWs via the oscillation and decay of string loops [5] <ref:2509.04384#pg2>. If instead a discrete symmetry is broken, domain walls (DWs) are formed and their decay can similarly give rise to a GW signal [6] <ref:2509.04384#pg2>. Another possible source arises from standard inflation during which quantum fluctuations of the metric generate tensor perturbations <ref:2509.04384#pg2>. Extensions of the Standard Model featuring new gauge symmetries and extended scalar sectors predict such cosmological GW sources <ref:2509.04384#pg2>. The same underlying symmetry-breaking mechanism responsible for a phase transition could simultaneously generate CS or DW relics [3] <ref:2509.04384#pg2>. Thus, a multi-peak structure in the SGWB spectrum is likely, underscoring the importance of observables capable of discriminating between the components contributing to these peaks <ref:2509.04384#pg2>. In this context, we introduce the concept of prominence, a measure employed by topographers and mountaineers to quantify the height of a peak relative to its surrounding terrain <ref:2509.04384#pg2>. Unlike the absolute peak amplitude, Prominence is sensitive to the shapes of both the background and SGWB peaks, offering the ability to distinguish between different SGWB sources, which is not achievable with only the Signal-to-Noise-Ratio (SNR) <ref:2509.

Improvements for AI systems

Improved AI systems can perform model-independent source discrimination for stochastic gravitational wave backgrounds (SGWB) by calculating Prominence P, which is a measure employed by topographers and mountaineers to quantify the height of a peak relative to its surrounding terrain. This allows discrimination between different SGWB sources, which is not achievable with only the Signal-to-Noise-Ratio (SNR).
Improved systems can perform direct hypothesis testing by using Prominence P to compare reconstructed signals against different physical models, such as distinguishing between first-order phase transitions and domain walls or SIGW and FOPT signals. This is done by evaluating the p-value for a hypothesis H1 given a measured value of P: (4.8) The discrimination for the case in Fig. 13(a) improves and the discrimination for the cases in Figs. 13(c) and 13(d) worsens.
Improved systems can quantify signal compatibility using a signal-space statistic, χ2 = (SNR1 − SNR2)2 + 2M12 SNR1 SNR2, (4.7), to estimate the signal discrimination power of SKA and LISA, which is particularly useful when traditional methods are inconclusive due to overlapping spectra.
Improved systems can adapt their analysis precision based on experimental constraints, as the paper shows that "better than 3σ discrimination is possible if the fractional uncertainty ∆omega/omega < 1%, a level expected for LISA [19]," allowing systems to set realistic discrimination thresholds based on projected measurement accuracy.
Improved systems can leverage Prominence P to enhance discrimination even when signals are degenerate, as it provides its greatest discriminating power precisely when signals are significantly degenerate, with similar spectra and relatively small SNRs. This is demonstrated by showing that P becomes particularly valuable, effectively distinguishing between them even when their overlap would render a traditional SNR-based approach inconclusive.