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Register a new userHidden Markov model tracking of continuous gravitational waves from young supernova remnants
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Searches for persistent gravitational radiation from nonpulsating neutron stars in young supernova remnants (SNRs) are computationally challenging because of rapid stellar braking. We describe a practical, efficient, semi-coherent search based on a hidden Markov model (HMM) tracking scheme, solved by the Viterbi algorithm, combined with a maximum likelihood matched filter, the $mathcal{F}$-statistic. The scheme is well suited to analyzing data from advanced detectors like the Advanced Laser Interferometer Gravitational Wave Observatory (Advanced LIGO). It can track rapid phase evolution from secular stellar braking and stochastic timing noise torques simultaneously without searching second- and higher-order derivatives of the signal frequency, providing an economical alternative to stack-slide-based semi-coherent algorithms. One implementation tracks the signal frequency alone. A second implementation tracks the signal frequency and its first time derivative. It improves the sensitivity by a factor of a few upon the first implementation, but the cost increases by two to three orders of magnitude.
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Gravitational wave searches for continuous-wave signals from neutron stars are especially challenging when the stars 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.
We describe directed searches for continuous gravitational waves in data from the sixth LIGO science data run. The targets were nine young supernova remnants not associated with pulsars; eight of the remnants are associated with non-pulsing suspected neutron stars. One targets parameters are uncertain enough to warrant two searches, for a total of ten. Each search covered a broad band of frequencies and first and second frequency derivatives for a fixed sky direction. The searches coherently integrated data from the two LIGO interferometers over time spans from 5.3-25.3 days using the matched-filtering F-statistic. We found no credible gravitational-wave signals. We set 95% confidence upper limits as strong (low) as $4times10^{-25}$ on intrinsic strain, $2times10^{-7}$ on fiducial ellipticity, and $3times10^{-6}$ on r-mode amplitude. These beat the indirect limits from energy conservation and are within the range of theoretical predictions for neutron-star ellipticities and r-mode amplitudes.
A hidden Markov model (HMM) scheme for tracking continuous-wave gravitational radiation from neutron stars in low-mass X-ray binaries (LMXBs) with wandering spin is extended by introducing a frequency-domain matched filter, called the J-statistic, which sums the signal power in orbital sidebands coherently. The J-statistic is similar but not identical to the binary-modulated F-statistic computed by demodulation or resampling. By injecting synthetic LMXB signals into Gaussian noise characteristic of the Advanced Laser Interferometer Gravitational-wave Observatory (Advanced LIGO), it is shown that the J-statistic HMM tracker detects signals with characteristic wave strain $h_0 geq 2 times 10^{-26}$ in 370 d of data from two interferometers, divided into 37 coherent blocks of equal length. When applied to data from Stage I of the Scorpius X-1 Mock Data Challenge organised by the LIGO Scientific Collaboration, the tracker detects all 50 closed injections ($h_0 geq 6.84 times 10^{-26}$), recovering the frequency with a root-mean-square accuracy of $leq 1.95times10^{-5}$ Hz. Of the 50 injections, 43 (with $h_0 geq 1.09 times 10^{-25}$) are detected in a single, coherent 10-d block of data. The tracker employs an efficient, recursive HMM solver based on the Viterbi algorithm, which requires $sim 10^5$ CPU-hours for a typical, broadband (0.5-kHz), LMXB search.
Persistent gravitational waves from rapidly rotating neutron stars, such as those found in some young supernova remnants, may fall in the sensitivity band of the advanced Laser Interferometer Gravitational-wave Observatory (aLIGO). Searches for these signals are computationally challenging, as the frequency and frequency derivative are unknown and evolve rapidly due to the youth of the source. A hidden Markov model (HMM), combined with a maximum-likelihood matched filter, tracks rapid frequency evolution semi-coherently in a computationally efficient manner. We present the results of an HMM search targeting 12 young supernova remnants in data from Advanced LIGOs second observing run. Six targets produce candidates that are above the search threshold and survive pre-defined data quality vetoes. However, follow-up analyses of these candidates show that they are all consistent with instrumental noise artefacts.
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 an existing HMM analysis pipeline is generalized to track rotational phase and frequency simultaneously, by modeling the intra-step rotational evolution according to a phase-wrapped Ornstein-Uhlenbeck process, and by calculating the emission probability using a phase-sensitive version of the Bayesian matched filter known as the $mathcal{B}$-statistic. The generalized algorithm tracks signals from isolated and binary sources with characteristic wave strain $h_0 geq 1.3times 10^{-26}$ in Gaussian noise with amplitude spectral density $4times 10^{-24},{rm Hz^{-1/2}}$, for a simulated observation composed of $N_T=37$ data segments, each $T_{rm drift}=10,{rm days}$ long, the typical duration of a search for the low-mass X-ray binary (LMXB) Sco X$-$1 with the Laser Interferometer Gravitational Wave Observatory (LIGO). It is equally sensitive to isolated and binary sources and $approx 1.5$ times more sensitive than the previous pipeline. Receiver operating characteristic curves and errors in the recovered parameters are presented for a range of practical $h_0$ and $N_T$ values. The generalized algorithm successfully detects every available synthetic signal in Stage I of the Sco X$-$1 Mock Data Challenge convened by the LIGO Scientific Collaboration, recovering the frequency and orbital semimajor axis with accuracies of better than $9.5times 10^{-7},{rm Hz}$ and $1.6times 10^{-3},{rm lt,s}$ respectively. The Viterbi solver runs in $approx 2times 10^3$ CPU-hr for an isolated source and $sim 10^5$ CPU-hr for a LMXB source in a typical, broadband ($0.5$-${rm kHz}$) search.
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