Finn & Lommen (2010) identified a structural limitation of pulsar timing array (PTA) searches for gravitational-wave (GW) bursts: the standard two-step pipeline first fits a timing model to each pulsar's pulse times of arrival and then analyzes the residuals, which 'fits out' any GW contribution whose signature is degenerate with timing-model components; they proposed simultaneous inference of the GW waveform and the timing-model parameters as the remedy, left its realization as future work, and demonstrated the framework only on simulated data with Gaussian, inter-pulsar-uncorrelated noise. The subsequent literature has made joint (simultaneous or analytically marginalized) timing-model inference standard, and real-data burst searches now exist for parametrized burst families — GW memory and cosmic-string cusp signals — all yielding upper limits but no detection. The surviving open core is the fully waveform-agnostic version of the program: detecting, localizing, and reconstructing bursts of a priori unknown morphology in complete real PTA datasets, with timing-model parameters, per-pulsar noise, and inter-pulsar correlated-noise components inferred simultaneously with the signal.

Background

A pulsar timing array (PTA) is a galactic-scale detector that monitors the times of arrival (TOAs) of radio pulses from tens of millisecond pulsars over years to decades, targeting gravitational waves (GWs) in the nanohertz frequency band. For each pulsar, a timing model — a parameterized prediction of every pulse's arrival time incorporating the pulsar's spin period and spin-down, sky position, proper motion, binary orbital elements, and the dispersive delay of the interstellar medium — is fitted to the TOAs, and the differences between observed and predicted arrival times (timing residuals) are searched for GW signatures. The standard pipeline therefore has two steps: fit the timing model first, then analyze the residuals. As Finn & Lommen (2010) emphasized, this has the side-effect of 'fitting out' any GW contribution whose induced residual is degenerate with (i.e. expressible as a linear combination of) timing-model basis functions such as spin period and spin-down. A GW burst is a signal whose duration is much shorter than the observing span; plausible nanohertz burst sources include close parabolic encounters of supermassive black holes, cusps on cosmic strings, and the non-oscillatory GW memory — a permanent change in the metric strain produced by highly energetic events such as supermassive black hole binary mergers. The PTA response to a burst separates into an Earth term (the same wavefront passing the Earth, correlated across pulsars with a quadrupolar sky pattern) and a pulsar term (delayed by the light travel time to each pulsar, typically thousands of years). Finn & Lommen (2010) formulated a Bayesian hierarchy for burst analysis — (1) odds that a burst is present, (2) source localization, (3) waveform reconstruction in the two polarizations, with h_+ and h_x represented as free functions sampled at a set of times rather than drawn from a parametric signal family — and demonstrated it on simulated 30-pulsar data with Gaussian, inter-pulsar-uncorrelated noise, mimicking the timing fit by removing a best-fit linear trend. They identified the timing-model degeneracy as the key limitation and proposed, as future work, extending the Bayesian analysis to infer the timing-model parameters simultaneously with the waveform, applied to TOA data directly. That remedy was realized almost immediately in linear-Gaussian form: van Haasteren & Levin (2010) built a Bayesian search for memory signals in which the full timing model (and measurement-noise rescaling factors) is analytically marginalized jointly with the signal amplitude, and van Haasteren & Vallisneri (2014) systematized this Gaussian-process marginalization into the standard modern PTA likelihood. Building on this machinery, real-data burst searches with joint timing-model treatment now exist for parametrized burst morphologies: memory searches in the Parkes Pulsar Timing Array (Wang et al. 2015), NANOGrav's 5-year (Arzoumanian et al. 2015), 11-year (Aggarwal et al. 2020), 12.5-year (Agazie et al. 2024) and 15-year (Agazie et al. 2025) datasets, and cosmic-string-cusp burst searches in Parkes data (Yonemaru et al. 2021; Xia et al. 2025), plus a combined PPTA/EPTA search with a complete numerical-relativity signal model (Tomson et al. 2025). All report non-detections with upper limits, and the NANOGrav 15-year search attributes its non-improving limits to growth of common (inter-pulsar) red noise — now a confirmed feature of PTA data and the central new degeneracy frontier. For bursts of unknown morphology, dedicated methods exist — Bayesian nonparametrics, in which the number of parameters describing the signal is allowed to grow with the data (Deng 2014), the BayesHopperBurst reversible-jump Markov chain Monte Carlo sampler — one that moves between signal models of different dimensionality — over wavelet decompositions, which samples perturbations of timing-model parameters jointly with the signal and with explicit noise-transient models (Bécsy & Cornish 2021), piecewise-linear burst modeling (Deng et al. 2023), and fast likelihood redefinitions making such searches computationally feasible (Taylor et al. 2025) — but as of the most recent literature these have been applied to real data only for a single pulsar, not to a complete array dataset following Finn & Lommen's full detect-localize-characterize hierarchy.

Problem Statement

Finn & Lommen (2010) asked whether burst-like gravitational waves can be detected, localized, and waveform-characterized in pulsar timing array data when the signal is degenerate with the pulsar timing model, and proposed simultaneous inference of the gravitational waveform and the timing-model parameters as the remedy, with the framework demonstrated only on simulated data with Gaussian, inter-pulsar-uncorrelated noise. That remedy is now standard and has been exercised on real data, but only for bursts of pre-parametrized morphology (memory signals, cosmic-string cusps). The surviving open problem — the part of Finn & Lommen's detect-localize-characterize program that subsequent work has not closed — is: construct and demonstrate on complete real pulsar timing array datasets (i.e. the full multi-pulsar timing data of an existing PTA, rather than a single-pulsar extract) a coherent analysis that (1) detects, (2) localizes on the sky, and (3) reconstructs the waveform of a gravitational-wave burst of a priori unknown morphology — the two polarization waveforms h_+ and h_x treated as free functions of time over the burst duration, not restricted to a pre-parametrized signal family — with the timing-model parameters, per-pulsar noise, and inter-pulsar correlated-noise components inferred simultaneously with the burst signal rather than pre-fit and subtracted. Because no burst of any morphology has yet been confirmed in PTA data, the real-data demonstration consists of the analysis applied end-to-end to a real dataset.

References

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