Application of a hierarchical MCMC follow-up to Advanced LIGO continuous gravitational-wave candidates

Abstract

We present the first application of a hierarchical Markov Chain Monte Carlo (MCMC) follow-up on continuous gravitational-wave candidates from real-data searches. The follow-up uses an MCMC sampler to draw parameter-space points from the posterior distribution, constructed using the matched-filter as a log-likelihood. As outliers are narrowed down, coherence time increases, imposing more restrictive phaseevolution templates. We introduce a novel Bayes factor to compare results from different stages: The signal hypothesis is derived from first principles, while the noise hypothesis uses extreme value theory to derive a background model. The effectiveness of our proposal is evaluated on fake Gaussian data and applied to a set of 30 outliers produced by different continuous wave searches on O2 Advanced LIGO data. The results of our analysis suggest all but five outliers are inconsistent with an astrophysical origin under the standard continuous wave signal model. We successfully ascribe four of the surviving outliers to instrumental artifacts and a strong hardware injection present in the data. The behavior of the fifth outlier suggests an instrumental origin as well, but we could not relate it to any known instrumental cause.

All-sky search for continuous gravitational waves from isolated neutron stars in the early O3 LIGO data

“…Hence this outlier is subjected to the MCMC PyFstat follow-up procedure described in section III D. The resulting (log) Bayes factor comparing signal to empirical noise expectation for the maximum F -statistic in the last stage is found to be log 10 ðB SN Þ ¼ 1.1. Based on the analysis in [41], this value is lower by about 50 than that expected for a standard CW signal of the outlier's putative strain amplitude in the O3a dataset.…”

“…The small number not found to be contaminated by obvious instrumental artifacts are followed up in the full O3 dataset by a search similar to the PowerFlux O3a stage 1, but using much finer spin-down stepping of 1 × 10 −11 Hz=s, and refinement factors of 1=4 for both sky (right ascension and declination each) and frequency stepping, to exploit the improved SNR and parameter resolution possible in the nearly doubled observation span. Any outlier surviving this full-O3 follow-up is explored via a more sensitive method, implemented in PyFstat [38,39] which uses Markov chain Monte Carlo (MCMC) techniques [40,41] to explore small regions of parameter space in successive stages of increasing coherence times.…”

“…Also, a now-known error in the actuation function used for L1 injections led to an unintended time delay of approximately 122 μs, which corresponds to a phase lag in the highest-frequency injection (2991 Hz) of ∼130°and degrades coherent H1-L1 injection recovery. The final follow-up method applied to any survivors of the full-O3 loose-coherence check uses the PYTHON-based PyFstat [38,39] software infrastructure to combine a MCMC approach [40,41] with semicoherent summing of the well known F -statistic detection statistic [42]. In this approach, the parameter space near to those values from a stage-2 outlier is sampled randomly according to a certain probability density function determined by the F -statistic likelihood function.…”

“…In this approach, the parameter space near to those values from a stage-2 outlier is sampled randomly according to a certain probability density function determined by the F -statistic likelihood function. We closely follow an implementation [41] applied to a recent analysis of O2 data to follow up on outliers emerging from several prior O2 continuous wave searches.…”

“…For this O3a analysis we choose five successive stages of follow-up with decreasing values of N seg ¼ 500 (coherence time of 0.36 day), 250, 55, 5 and 1. A random sample of 600 off-source sky locations having the same declination as the putative signal direction, but separated by more than 90 deg from that direction, is used to determine a nonsignal expectation for the background distributions in the same frequency band [41]. A Bayes factor B SN is computed from the change in F -statistic values for a nominal signal compared to the empirical background distribution in the last stage (N seg ¼ 5 to N seg ¼ 1).…”