Gravitational wave searches for continuous-wave signals from neutron stars are especially challenging when the star's spin frequency is unknown a priori from electromagnetic observations and wanders stochastically under the action of internal (e.g. superfluid or magnetospheric) or external (e.g. accretion) torques. It is shown that frequency tracking by hidden Markov model (HMM) methods can be combined with existing maximum likelihood coherent matched filters like the F-statistic to surmount some of the challenges raised by spin wandering. Specifically it is found that, for an isolated, biaxial rotor whose spin frequency walks randomly, HMM tracking of the F-statistic output from coherent segments with duration T drift = 10 d over a total observation time of T obs = 1 yr can detect signals with wave strains h0 > 2 × 10 −26 at a noise level characteristic of the Advanced Laser Interferometer Gravitational Wave Observatory (Advanced LIGO). For a biaxial rotor with randomly walking spin in a binary orbit, whose orbital period and semi-major axis are known approximately from electromagnetic observations, HMM tracking of the Bessel-weighted F-statistic output can detect signals with h0 > 8 × 10 −26 . An efficient, recursive, HMM solver based on the Viterbi algorithm is demonstrated, which requires ∼ 10 3 CPU-hours for a typical, broadband (0.5-kHz) search for the low-mass X-ray binary Scorpius X-1, including generation of the relevant F-statistic input. In a "realistic" observational scenario, Viterbi tracking successfully detects 41 out of 50 synthetic signals without spin wandering in Stage I of the Scorpius X-1 Mock Data Challenge convened by the LIGO Scientific Collaboration down to a wave strain of h0 = 1.1×10 −25 , recovering the frequency with a root-mean-square accuracy of ≤ 4.3 × 10 −3 Hz.

Results are presented from a semicoherent search for continuous gravitational waves from the brightest low-mass X-ray binary, Scorpius X-1, using data collected during the first Advanced LIGO observing run. The search combines a frequency domain matched filter (Bessel-weighted F-statistic) with a hidden Markov model to track wandering of the neutron star spin frequency. No evidence of gravitational waves is found in the frequency range 60–650 Hz. Frequentist 95% confidence strain upper limits, h95%0=4.0×10−25, 8.3×10−25, and 3.0×10−25 for electromagnetically restricted source orientation, unknown polarization, and circular polarization, respectively, are reported at 106 Hz. They are ≤10 times higher than the theoretical torque-balance limit at 106 Hz

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We present results from a semicoherent search for continuous gravitational waves from the low-mass x-ray binary Scorpius X-1, using a hidden Markov model (HMM) to track spin wandering. This search improves on previous HMM-based searches of LIGO data by using an improved frequency domain matched filter, the J-statistic, and by analyzing data from Advanced LIGO's second observing run. In the frequency range searched, from 60 to 650 Hz, we find no evidence of gravitational radiation. At 194.6 Hz, the most sensitive search frequency, we report an upper limit on gravitational wave strain (at 95% confidence) of h 95% 0 ¼ 3.47 × 10 −25 when marginalizing over source inclination angle. This is the most sensitive search for Scorpius X-1, to date, that is specifically designed to be robust in the presence of spin wandering.