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 $h_0 \geq 2 \times 10^{-26}$ 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 organised by the LIGO Scientific Collaboration, the tracker detects all 50 closed injections ($h_0 \geq 6.84 \times 10^{-26}$), recovering the frequency with a root-mean-square accuracy of $\leq 1.95\times10^{-5}$ Hz. Of the 50 injections, 43 (with $h_0 \geq 1.09 \times 10^{-25}$) 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 $\sim 10^5$ CPU-hours for a typical, broadband (0.5-kHz), LMXB search.