Tracking continuous gravitational waves from a neutron star at once and twice the spin frequency with a hidden Markov model

Abstract

Searches for continuous gravitational waves from rapidly spinning neutron stars normally assume that the star rotates about one of its principal axes of moment of inertia, and hence the gravitational radiation emits only at twice the spin frequency of the star, 2f . The superfluid interior of a star pinned to the crust along an axis nonaligned with any of its principal axes allows the star to emit gravitational waves at both f and 2f , even without free precession, a phenomenon not clearly observed in known pulsars. The dual-harmonic emission mechanism motivates searches combining the two frequency components of a signal to improve signal-to-noise ratio. We describe an economical, semicoherent, dual-harmonic search method, combined with a maximum likelihood coherent matched filter, F-statistic, and improved from an existing hidden Markov model (HMM) tracking scheme to track two frequency components simultaneously. We validate the method and demonstrate its performance through Monte Carlo simulations. We find that for sources emitting gravitational waves at both f and 2f , the rate of correctly recovering synthetic signals (i.e., detection efficiency), at a given false alarm probability, can be improved by ∼ 10%-70% by tracking two frequencies simultaneously compared to tracking a single component only. For sources emitting at 2f only, dual-harmonic tracking only leads to minor sensitivity loss, producing 10% lower detection efficiency than tracking a single component. In directed continuous-wave searches where f is unknown and hence the full frequency band is searched, the computationally efficient HMM tracking algorithm provides an option of conducting both the dual-harmonic search and the conventional single frequency tracking to obtain optimal sensitivity, with a typical run time of ∼ 10 3 core-hr for one year's observation.

Searches for Continuous Gravitational Waves from Young Supernova Remnants in the Early Third Observing Run of Advanced LIGO and Virgo

“…The dual-harmonic emission mechanism motivates searches combining the two frequency components of a signal to improve signal-to-noise ratio. The HMM tracking scheme described in Section 4.2 has been extended to track two frequency components simultaneously (Sun et al 2019). The signal model considered in this section consists of both f å and 2f å components, given by (Jaranowski et al 1998;Sun et al 2019)…”

“…The HMM tracking scheme described in Section 4.2 has been extended to track two frequency components simultaneously (Sun et al 2019). The signal model considered in this section consists of both f å and 2f å components, given by (Jaranowski et al 1998;Sun et al 2019)…”

“…Given that the condition N T = N Q is generally satisfied with the choices of T coh in this method, the issue described in Section 4.2 with short T coh ∼ 1 hr does not happen. The full mathematical definition of S is given in Sun et al (2019). We determine a threshold corresponding to 1% false-alarm probability S th = 5.47 and S th = 5.33 for T coh = 12 hr and T coh = 9 hr, respectively, obtained from Monte Carlo simulations in Gaussian noise and verified in real O3a data.…”

“…Here we assume the special scenario θ = 45°and i = cos 0, i.e., signals at both f å and 2f å are linearly polarized. In this scenario, tracking the two frequency bands simultaneously offers the most significant sensitivity improvement from searching a single band, compared to other choices of θ and i cos (Sun et al 2019).…”

“…We apply three semicoherent methods to search for signals from 15 known young SNRs in the data collected in the first half (6 months) of O3: the directed Band-Sampled-Data (BSD) pipeline (Piccinni et al 2018), based on the FrequencyHough (FH) transform (Astone et al 2014b;Antonucci et al 2008), and the single-harmonic Viterbi and dual-harmonic Viterbi pipelines, both based on a hidden Markov model (HMM) tracking scheme (Sun et al 2018(Sun et al , 2019. The two Viterbi methods achieve a lower sensitivity compared to the BSD pipeline but take into consideration the uncertainties associated with the star's stochastic spin evolution, with one of them tracking two harmonics of the star's spin frequency simultaneously (Sun et al 2018(Sun et al , 2019, making the three methods complementary to each other.…”