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 existing HMM analysis pipeline generalized track phase simultaneously, modeling intrastep evolution according a phase-wrapped Ornstein-Uhlenbeck process, calculating emission probability using phase-sensitive version of Bayesian matched filter known as $\mathcal{B}$-statistic, which more sensitive than its predecessors. The tracks signals binary sources with characteristic wave strain ${h}_{0}\ensuremath{\ge}1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}26}$ in Gaussian noise amplitude spectral density $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}\text{ }\text{ }{\mathrm{Hz}}^{\ensuremath{-}1/2}$, simulated observation composed ${N}_{T}=37$ data segments, each ${T}_{\text{drift}}=10\text{ }\mathrm{days}$ long, typical duration low-mass x-ray (LMXB) Sco $\mathrm{X}\ensuremath{-}1$ Laser Interferometer Gravitational Wave Observatory (LIGO). It equally $\ensuremath{\approx}1.5$ times previous pipeline, achieves ${h}_{0}\ensuremath{\ge}2.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}26}$ comparable search. Receiver operating curves (to demonstrate recipe setting detection thresholds) errors recovered parameters are presented range practical ${h}_{0}$ ${N}_{T}$ values. successfully detects every available synthetic signal Stage I Mock Data Challenge convened LIGO Scientific Collaboration, recovering orbital semimajor axis accuracies better $9.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}\text{ }\mathrm{Hz}$ (one part $\ensuremath{\sim}{10}^{8}$) $1.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\text{ }\text{lt}\text{ }\mathrm{s}$ $\ensuremath{\sim}{10}^{3}$) respectively. solver runs $\ensuremath{\approx}2\ifmmode\times\else\texttimes\fi{}{10}^{3}$ CPU-hr source $\ensuremath{\sim}{10}^{5}$ LMXB typical, broadband (0.5-kHz) search, i.e., $\ensuremath{\lesssim}10$ slower pipeline.