Simulated detector network sharpens the search for neutron stars’ faint internal vibrations

A faint signal beneath the tides

As two neutron stars orbit each other, each star’s gravity deforms its companion. The resulting tidal effects influence the gravitational waves emitted during their approach. These effects can carry information about the equation of state: the relationship between pressure, density and other properties of dense matter.

Mengfei Sun and colleagues examine an additional contribution from internal oscillations called g modes. These are supported by buoyancy and are sensitive to properties such as composition gradients and superfluidity. When tidal driving matches a mode’s natural frequency, a resonance can transfer orbital energy into the oscillation, slightly changing the timing, or phase, of the gravitational-wave signal.

This extra phase change is weak compared with the broader tidal response. Identifying it would be a step toward probing stellar interiors, not itself a measurement of their composition.

Building an artificial observing experiment

The researchers generated eccentric binary-neutron-star waveforms using the TEOBResumS-Dalí model. Unlike a circular orbit, an eccentric orbit supplies tidal driving at multiple harmonics—different multiples of the orbital frequency. The team calculated resonant phase corrections and mapped them separately onto the radiation harmonics before reconstructing time-domain signals.

The resonance prescription neglects stellar spin and uses a Newtonian tidal-orbital coupling model restricted to quadrupolar tides. Only resonances satisfying an approximate one-orbit coherence condition were retained. That condition determines where the adopted modeling prescription applies; it is not a general detection threshold.

Simulated component masses ranged from 1.2 to 2.0 solar masses. Eccentricities at a 10-hertz reference frequency ranged from zero to 0.5, mode frequencies from 50 to 300 hertz, and the dimensionless mode-coupling parameter from 0.03 to 0.30. Source orientations were randomized and redshifts extended to two.

Signals were projected onto modeled responses for the proposed Einstein Telescope, or ET, and Cosmic Explorer, or CE. The researchers added colored Gaussian noise based on their design sensitivity curves. These were synthetic observations, not measurements from operating ET or CE instruments.

Four classes, two seconds at a time

The development dataset contained 200,000 examples, equally divided among four classes: signals without tidal effects, signals with adiabatic tides, signals with tides plus a g-mode resonance correction, and pure noise. Training used 180,000 examples and validation used 20,000. A separate 10,000-example dataset was reserved for final evaluation.

Although waveforms began at 20 hertz, the classifiers received only the final two seconds before merger, sampled at 2,048 hertz. They did not directly use the earlier inspiral information that future detectors could access at lower frequencies.

The neural networks used one-dimensional convolutional layers, residual connections and attention across successive representation levels. For joint observations, separate detector-specific encoders extracted features before combining them for classification.

What improved—and what remained difficult

Overall neural-network accuracy was 65.0% for ET, 80.9% for CE and 87.5% for ET+CE. A matched-filtering comparison on the same evaluation samples achieved 53.4%, 70.3% and 71.8%, respectively. These are four-class classification accuracies, not astronomical detection probabilities.

The joint neural model correctly recovered 94.3% of examples containing the resonant correction. Its precision for that class was 84.0%, meaning some examples assigned a resonance label belonged to other classes. Both figures matter, and both depend on the simulated evaluation population.

That distinction is especially important for ET alone. Its resonant-class recall reached 95.7%, but its recall for adiabatic-tide signals without the correction was nearly zero. The joint model produced more balanced results, recovering 73.1% of that difficult nonresonant tidal class.

Two alternative ET+CE networks achieved approximately 84.3% overall accuracy, compared with 87.5% for the separate-encoder model. One alternative nevertheless had higher resonant-class recall, illustrating why recall alone is insufficient to judge performance.

Stronger mode coupling generally improved separation. Joint-model resonant recall rose from 89.6% at coupling 0.03 to 98.5% at 0.30. There was no clear monotonic trend with eccentricity, and dependence on the tested mode frequencies was weaker than the overall coupling dependence.

A classification result, not a detection forecast

The neural networks outperformed the particular matched-filtering classifier implemented here: a template-bank comparison within the same fixed, short time window, with a separately calibrated threshold for assigning the noise class. This does not demonstrate superiority over every matched-filtering search or a full Bayesian analysis. Learning subtle waveform features is the authors’ interpretation of the advantage, rather than a separately established physical explanation.

Real detector noise, waveform uncertainties, broader source populations and longer observations remain important tests. The study does not infer mode parameters or constrain neutron-star microphysics; the authors identify Bayesian parameter inference as a next step.

Source and publication status

The study is published in Physical Review D 114, 103011 (2026). This article uses arXiv:2606.11959v2, which the source record identifies as the final accepted version. The arXiv submission history verifies the original posting on June 10, 2026, at 11:40:08 UTC, and the v2 revision on November 6, 2026, at 03:53:56 UTC. The original posting timestamp is not the journal publication date.