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The fact that the residual tracks the orbital frequency is the key diagnostic. An uncorrelated glitch or detector noise would not phase-lock to the inspiral chirp. That coherence pattern is exactly what you'd expect from the residual of true signal minus a slightly wrong model, which points toward incomplete waveform physics or a parameter-estimation mismatch rather than random noise.

The single test I'd run next: an injection-based null distribution

Take the best-fit waveform, inject it into many stretches of real off-source noise, and repeat the extraction-subtraction-coherence pipeline on each realization. Build up the distribution of your residual coherence statistic under the null hypothesis that nothing is present except noise plus a known signal.

This matters because subtracting a best-fit waveform does not leave pure noise — it leaves a source-projection effect that can mimic structure even when nothing new is present…

Start with a coherent null-stream test.

If the residual is a true gravitational wave from the same sky location, it must satisfy the antenna-pattern and timing constraints of the known source. Construct the network null stream — the detector combination that cancels a real GW from that direction — and check whether the residual survives there. Significant power in the null stream points strongly toward correlated noise or an instrumental glitch rather than new physics or missing waveform physics.

If the residual passes the null test, branch the follow-up:

• Missing waveform physics: check whether the residual is absorbed by a more complete model — higher modes, eccentricity, precession, or memory effects. Run a Bayesian model comparison between the baseline and physically motivated extensions.
• New physics: only once systematics are ruled out. Use a parameterized beyond-GR framework to see if the residual structure maps to a specific modification rather than waveform incompleteness…

Reading: you subtracted the best-fit GR BBH waveform and the leftover is a weak, coherently tracked signal in both detectors whose phase/frequency evolution follows the orbital frequency.

Most likely interpretations

• Missing waveform physics (plausible): small mismatches in the template can leave a residual that's still phase-coherent and tracks the same physical frequency evolution — higher-order modes, precession, calibration, or a slight inspiral-merger-ringdown boundary mismatch.
• New physics (possible but less direct): extra radiation channels or deviations from GR can also leave a coherent residual, but "tracks orbital frequency" often looks more like a slightly-wrong template than a wholly different effect.
• Noise (less likely if coherence is strong): generic non-Gaussian noise appearing coherently in both detectors by chance is unlikely, though not impossible if it happens to line up with instrumental artifacts.

What I'd run next

A single best test: waveform-model robustness via controlled re-subtraction, comparing residuals across an extended template family before invoking new physics…