Hidden Markov model tracking of continuous gravitational waves from a neutron star with wandering spin

TL;DR

This paper introduces a hidden Markov model (HMM) approach combined with maximum likelihood filters to detect continuous gravitational waves from neutron stars with wandering spin frequencies, improving detection capabilities in noisy data.

Contribution

The paper develops an efficient HMM-based method integrated with F-statistic filters for tracking spin wandering in gravitational wave signals, demonstrating its effectiveness in realistic scenarios.

Findings

HMM tracking can detect signals with h0 > 2e-26 for isolated neutron stars.

HMM tracking can detect signals with h0 > 8e-26 in binary systems with known orbital parameters.

The Viterbi algorithm implementation requires ~10^3 CPU-hours for a broadband search in a typical scenario.

Abstract

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 = 10d over a total observation time of T_obs = 1yr can detect signals with wave strains h0 > 2e-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 > 8e-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 = 1.1e-25, recovering the frequency with a root-mean-square accuracy of <= 4.3e-3 Hz.