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Published August 15, 2021 | Accepted Version + Published
Journal Article Open

Hidden Markov model tracking of continuous gravitational waves from a binary neutron star with wandering spin. III. Rotational phase tracking


A hidden Markov model (HMM) solved recursively by the Viterbi algorithm can be configured to search for persistent, quasimonochromatic gravitational radiation from an isolated or accreting neutron star, whose rotational frequency is unknown and wanders stochastically. Here an existing HMM analysis pipeline is generalized to track rotational phase and frequency simultaneously, by modeling the intrastep rotational evolution according to a phase-wrapped Ornstein-Uhlenbeck process, and by calculating the emission probability using a phase-sensitive version of the Bayesian matched filter known as the B-statistic, which is more sensitive than its predecessors. The generalized algorithm tracks signals from isolated and binary sources with characteristic wave strain h₀ ≥ 1.3 × 10⁻²⁶ in Gaussian noise with amplitude spectral density 4 × 10⁻²⁴ Hz^(−1/2), for a simulated observation composed of N_T = 37 data segments, each T_(drift) = 10 days long, the typical duration of a search for the low-mass x-ray binary (LMXB) Sco X−1 with the Laser Interferometer Gravitational Wave Observatory (LIGO). It is equally sensitive to isolated and binary sources and ≈1.5 times more sensitive than the previous pipeline, which achieves h₀ ≥ 2.0 × 10⁻²⁶ for a comparable search. Receiver operating characteristic curves (to demonstrate a recipe for setting detection thresholds) and errors in the recovered parameters are presented for a range of practical h₀ and N_T values. The generalized algorithm successfully detects every available synthetic signal in Stage I of the Sco X−1 Mock Data Challenge convened by the LIGO Scientific Collaboration, recovering the frequency and orbital semimajor axis with accuracies of better than 9.5 × 10⁻⁷ Hz (one part in ∼10⁸) and 1.6 × 10⁻³ lt s (one part in ∼10³) respectively. The Viterbi solver runs in ≈2 × 10³ CPU-hr for an isolated source and ∼10⁵ CPU-hr for a LMXB source in a typical, broadband (0.5-kHz) search, i.e., ≲10 times slower than the previous pipeline.

Additional Information

© 2021 American Physical Society. (Received 15 June 2020; accepted 22 July 2021; published 18 August 2021) We would like to thank Paul Lasky, Chris Messenger, Keith Riles, Karl Wette, Letizia Sammut, John Whelan, Grant Meadors and the LIGO Scientific Collaboration Continuous Wave Working Group for detailed comments and informative discussions. We especially thank Karl Wette for alerting us to the existence of the phase extraction tool XLALEstimatePulsarAmplitudeParams in the LAL suite and Grant Meadors for pointing us to the phase-sensitive formulation of the B -statistic in Ref. [23]. The synthetic data for Stage I of the Sco X-1 MDC were prepared primarily by Chris Messenger with the assistance of members of the MDC team [20]. We thank Chris Messenger and Paul Lasky for their assistance in handling the MDC data. We thank the anonymous referees for their constructive feedback. P. Clearwater and L. Sun have been supported by Australian Postgraduate Awards. P. Clearwater was also a recipient of a scholarship from the Commonwealth Scientific and Industrial Research Organisation, Australia. L. Sun has been a member of the LIGO Laboratory. LIGO was constructed by the California Institute of Technology and Massachusetts Institute of Technology with funding from the National Science Foundation and operates under cooperative agreement PHY-1764464. Advanced LIGO was built under Grant No. PHY-0823459. The research is supported by the Australian Research Council (ARC) Centre of Excellence for Gravitational Wave Discovery (OzGrav), Grant No. CE170100004.

Attached Files

Published - PhysRevD.104.042003.pdf

Accepted Version - 2107.12822.pdf


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August 20, 2023
October 20, 2023