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Register a new userComparison of Signals from Gravitational Wave Detectors with Instantaneous Time-Frequency Maps
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Gravitational wave astronomy relies on the use of multiple detectors, so that coincident detections may distinguish real signals from instrumental artifacts, and also so that relative timing of signals can provide the sky position of sources. We show that the comparison of instantaneous time-frequency and time- amplitude maps provided by the Hilbert-Huang Transform (HHT) can be used effectively for relative signal timing of common signals, to discriminate between the case of identical coincident signals and random noise coincidences, and to provide a classification of signals based on their time-frequency trajectories. The comparison is done with a chi-square goodness-of-fit method which includes contributions from both the instantaneous amplitude and frequency components of the HHT to match two signals in the time domain. This approach naturally allows the analysis of waveforms with strong frequency modulation.
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General Relativity predicts only two tensor polarization modes for gravitational waves while at most six possible polarization modes of gravitational waves are allowed in the general metric theory of gravity. The number of polarization modes is totally determined by the specific modified theory of gravity. Therefore, the determination of polarization modes can be used to test gravitational theory. We introduce a concrete data analysis pipeline for a single space-based detector such as LISA to detect the polarization modes of gravitational waves. Apart from being able to detect mixtures of tensor and extra polarization modes, this method also has the added advantage that no waveform model is needed and monochromatic gravitational waves emitted from any compact binary system with known sky position and frequency can be used. We apply the data analysis pipeline to the reference source J0806.3+1527 of TianQin with 90-days simulation data, and we show that $alpha$ viewed as an indicative of the intrinsic strength of the extra polarization component relative to the tensor modes can be limited below 0.5 for LISA and below 0.2 for Taiji. We investigate the possibility to detect the nontensorial polarization modes with the combined network of LISA, TianQin and Taiji and find that $alpha$ can be limited below 0.2.
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