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

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 = 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.

Search for ultralight bosons in Cygnus X-1 with Advanced LIGO

“…Hence we use G(f ) = F(f ) ⊗ B(f ), a Bessel-weighted F-statistic, in Eqn. (S6) for a source in a binary orbit, where B(f ) is given by [24] B(f ) = [J n (2πf a 0 )] 2 δ(f − n/P ). (S15) * lssun@caltech.edu † richard.brito@roma1.infn.it ‡ maxisi@mit.edu; NHFP Einstein fellow…”

“…Like for the stochastic background, such constraints are contingent on BH populations. Isi et al [21] modeled the signal waveforms for individual sources with a known sky location, and demonstrated the suitability of a specific search algorithm based on a hidden Markov model (HMM) to efficiently search for such signals [21,[24][25][26]. Two primary types of sources are of interests for such directed searches: remnants from compact binary coalescences (CBCs) [27], and known BHs in X-ray binaries [11,28,29].…”

“…In the search, we take advantage of the frequency-domain matched filter of Refs. [24,25] to account for the Doppler modulation.…”

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

“…In a HMM, the emission probability at discrete time t n is defined as the likelihood of hidden state q i being observed in state o j , given by [37]…”

“…Here we leverage the existing frequency domain estimator F-statistic described in Sec. III, and define log emission probability computed over each interval [t, t+T coh ], given by [37,42,45] ln…”