Operational significance assignment for continuous gravitational-wave detections from known pulsars: signal-agnostic sky-bin excision, extreme-tail inference, and cross-pipeline validation of the sky-shifting method

No continuous gravitational wave (CW) has yet been detected, so the procedure by which the first detection claim will be assigned a statistically valid significance is itself an open methodological problem. Isi, Mastrogiovanni, Pitkin and Piccinni (Phys. Rev. D 102, 123027, 2020) showed that 'sky-shifting' (off-sourcing) — re-analyzing detector data time-corrected for shifted sky locations — empirically estimates the noise-only background of targeted CW searches from known pulsars in real, non-Gaussian detector noise, but they identified three unresolved limitations: (i) no general-purpose, signal-presence-agnostic rule for excising sky bins contaminated by a loud putative signal, nor quantification of how excision degrades the attainable minimum empirical $p$-value; (ii) unquantified statistical robustness of the exponential-decay extrapolation used for extreme on-source detection-statistic values; (iii) validation only for monochromatic line disturbances and two pipelines (Bayesian heterodyne and 5-vector), leaving realistic coherent noise-line mixtures, $\mathcal{F}$-statistic implementations, other preprocessing choices, detector states and longer datasets untested. Extreme-value-theory estimators for the loudest candidate have since been developed and adopted in follow-up contexts (ref. 2), but the flagship targeted known-pulsar searches through O4a still use off-source-frequency backgrounds, Gaussian chi-square thresholds, and exponential tail fits, and no systematic treatment of excision rules, $p$-value floors, coherent line mixtures, or cross-pipeline validation is known in the literature to date. The problem of completing and validating a rigorous, operational significance-assignment framework for targeted CW searches therefore remains open.

Background

Continuous gravitational waves (CWs) are long-lived, nearly monochromatic gravitational-wave signals expected from rapidly rotating neutron stars with a non-axisymmetric mass distribution. Unlike the short compact-binary-coalescence signals routinely detected by the LIGO, Virgo and KAGRA interferometers, a CW from a known pulsar can be searched for coherently over months of data because the star's sky position and rotational phase evolution are known from electromagnetic timing, so only a small parameter space (essentially the strain amplitude $h_0$ and polarization geometry) remains unknown. Three families of targeted-search statistics are standard: the time-domain Bayesian heterodyne method, which reports a signal-versus-noise Bayes factor $\mathcal{B}^{\rm S}_{\rm N}$ (the probability ratio of the data under a coherent-signal model versus noise-only models); the $\mathcal{F}$-statistic (and variants such as the $\mathcal{G}$- and $\mathcal{D}$-statistics), matched-filter statistics analytically maximized over the signal's amplitude parameters, whose Gaussian-noise false-alarm rates follow chi-square distributions; and the 5-vector method, a frequency-domain matched filter built from the five spectral components of the signal's sidereal amplitude modulation. All of these assume the detector noise is Gaussian and stationary, which real interferometer data are not: the data contain persistent narrow spectral disturbances ('lines') whose origin is often poorly understood and whose frequency distribution drifts as the instruments evolve. Because a coherent analysis has extremely fine frequency resolution, even weak lines falling inside the Doppler-modulated band of a targeted pulsar can produce loud false outliers, invalidating analytic false-alarm formulas. The standard remedy, borrowed from compact-binary searches where time slides generate artificial background data, is to estimate the background empirically. For CW targeted searches the data cannot be usefully time-slid or time-shuffled without scrambling the very line structure one is trying to characterize. Isi et al. (2020) therefore proposed and systematically studied sky-shifting (also called off-sourcing): the same data are re-analyzed after applying the detector's timing correction for a different sky location, which decoheres any real astrophysical signal while preserving the statistical character of the noise. They showed the shifted analyses yield valid independent background draws provided the shifted sky locations are (i) resolvably different from the source location and (ii) drawn from the same ecliptic hemisphere as the source, because the dominant timing effect (the Rømer delay from Earth's orbital motion) leaves strong residual correlations along lines of fixed ecliptic latitude. A loud putative signal leaks power into sky bins neighboring the source through exactly this timing footprint. Very loud signals are self-protecting (the on-source statistic exceeds any contaminated background value), but at intermediate amplitudes the contamination biases the estimated background and hence the significance. The paper's remedy — excising contaminated sky regions from the background estimation — carries two costs that it left unresolved: excision reduces the number $N$ of background draws, raising the floor of empirically attainable $p$-values (roughly $1/N$), and justifying excision around the on-source location implicitly presumes a signal is present, which is circular when the analysis is supposed to test that very hypothesis. In addition, the significance of very large on-source statistic values had to be assigned by extrapolating the empirical background tail with an exponential-decay fit, whose bias and alternatives were not quantified, and the method's line-robustness was demonstrated only against simulated monochromatic lines with two pipelines. These gaps matter because a credible first CW detection claim will require empirically calibrated significance in exactly the non-Gaussian, line-affected regime the claim will be made in.

Problem Statement

Establish a complete, operationally validated significance-assignment procedure for targeted continuous gravitational-wave searches from known pulsars using sky-shifted (off-sourced) backgrounds, resolving the limitations left open by Isi et al. (2020) as one coherent objective — a valid detection claim in real detector noise. Specifically, deliver and validate: (1) a robust, general-purpose decision rule for when and how to excise potentially contaminated sky-shifted sky regions from background estimation that does not presuppose the presence of a signal in the on-source data, together with a quantification of how the excised area trades against the number of remaining background draws and hence the attainable minimum empirical $p$-value; (2) a statistically calibrated method for assigning significances to very large on-source detection-statistic values that fall beyond the empirical background support, replacing the ad hoc exponential-decay tail extrapolation, with its bias and coverage quantified (for example along extreme-value-theoretic lines) for the targeted-search setting with a finite number of sky-shift draws; and (3) a systematic extension and validation of sky-shifting beyond monochromatic line disturbances and beyond the Bayesian-heterodyne and 5-vector pipelines — validating, at minimum, for each of: (a) a realistic coherent combination of instrumental lines, (b) an $\mathcal{F}$-statistic implementation, (c) two or more differing preprocessing choices, (d) two or more detector states, and (e) at least one dataset longer than those analysed by Isi et al. (2020) — demonstrating when the method's false-alarm and false-dismissal performance holds and when it fails. Additional pipelines, preprocessing choices, detector states and dataset durations beyond this minimum are optional. The common objective uniting these components is that a future candidate from a targeted known-pulsar search can be assigned a significance whose validity under realistic non-Gaussian noise is established rather than assumed; the components are jointly needed because an operational procedure fails at the weakest of these links.

References

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