Hidden Markov model tracking of continuous gravitational waves from a binary neutron star with wandering spin. II. Binary orbital phase tracking

A hidden Markov model (HMM) scheme for tracking continuous-wave gravitational radiation from neutron stars in low-mass x-ray binaries (LMXBs) with wandering spin is extended by introducing a frequency-domain matched filter, called the J-statistic, which sums the signal power in orbital sidebands coherently. The J-statistic is similar but not identical to the binary-modulated F-statistic computed by demodulation or resampling. By injecting synthetic LMXB signals into Gaussian noise characteristic of the Advanced Laser Interferometer Gravitational-wave Observatory (Advanced LIGO), it is shown that the J-statistic HMM tracker detects signals with characteristic wave strain h0≥2×10-26 in 370 d of data from two interferometers, divided into 37 coherent blocks of equal length. When applied to data from Stage I of the Scorpius X-1 Mock Data Challenge organized by the LIGO Scientific Collaboration, the tracker detects all 50 closed injections (h0≥6.84×10-26), recovering the frequency with a root-mean-square accuracy of ≤1.95×10-5 Hz. Of the 50 injections, 43 (with h0≥1.09×10-25) are detected in a single, coherent 10 d block of data. The tracker employs an efficient, recursive HMM solver based on the Viterbi algorithm, which requires ∼105 CPU-hours for a typical broadband (0.5 kHz) LMXB search.