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Register a new userMethod for estimation of gravitational-wave transient model parameters in frequency-time maps
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A common technique for detection of gravitational-wave signals is searching for excess power in frequency-time maps of gravitational-wave detector data. In the event of a detection, model selection and parameter estimation will be performed in order to explore the properties of the source. In this paper, we develop a Bayesian statistical method for extracting model-dependent parameters from observed gravitational-wave signals in frequency-time maps. We demonstrate the method by recovering the parameters of model gravitational-wave signals added to simulated advanced LIGO noise. We also characterize the performance of the method and discuss prospects for future work.
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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.
A method is described for the detection and estimation of transient chirp signals that are characterized by smoothly evolving, but otherwise unmodeled, amplitude envelopes and instantaneous frequencies. Such signals are particularly relevant for gravitational wave searches, where they may arise in a wide range of astrophysical scenarios. The method uses splines with continuously adjustable breakpoints to represent the amplitude envelope and instantaneous frequency of a signal, and estimates them from noisy data using penalized least squares and model selection. Simulations based on waveforms spanning a wide morphological range show that the method performs well in a signal-to-noise ratio regime where the time-frequency signature of a signal is highly degraded, thereby extending the coverage of current unmodeled gravitational wave searches to a wider class of signals.
Data from gravitational wave detectors are recorded as time series that include contributions from myriad noise sources in addition to any gravitational wave signals. When regularly sampled data are available, such as for ground based and future space based interferometers, analyses are typically performed in the frequency domain, where stationary (time invariant) noise processes can be modeled very efficiently. In reality, detector noise is not stationary due to a combination of short duration noise transients and longer duration drifts in the power spectrum. This non-stationarity produces correlations across samples at different frequencies, obviating the main advantage of a frequency domain analysis. Here an alternative time-frequency approach to gravitational wave data analysis is proposed that uses discrete, orthogonal wavelet wavepackets. The time domain data is mapped onto a uniform grid of time-frequency pixels. For locally stationary noise - that is, noise with an adiabatically varying spectrum - the time-frequency pixels are uncorrelated, which greatly simplifies the calculation of quantities such as the likelihood. Moreover, the gravitational wave signals from binary systems can be compactly represented as a collection of lines in time-frequency space, resulting in a computational cost for computing waveforms and likelihoods that scales as the square root of the number of time samples, as opposed to the linear scaling for time or frequency based analyses. Key to this approach is having fast methods for computing binary signals directly in the wavelet domain. Multiple fast transform methods are developed in detail.
Employing the Fisher information matrix analysis, we estimate parameter errors of TianQin and LISA for monochromatic gravitational waves. With the long-wavelength approximation we derive analytical formulas for the parameter estimation errors. We separately analyze the effects of the amplitude modulation due to the changing orientation of the detector plane and the Doppler modulation due to the translational motion of the center of the detector around the Sun. We disclose that in the low frequency regime there exist different patterns in angular resolutions and estimation errors of sources parameters between LISA and TianQin, the angular resolution falls off as $S_n(f)/f^2$ for TianQin but $S_n(f)$ for LISA, and the estimation errors of the other parameters fall off as $sqrt{S_n(f)}/f$ for TianQin but $sqrt{S_n(f)}$ for LISA. In the medium frequency regime we observe the same pattern where the angular resolution falls off as $S_n(f)/f^2$ and the estimation errors of the other parameters fall off as $sqrt{S_n(f)}$ for both TianQin and LISA. In the high frequency regime, the long-wavelength approximation fails, we numerically calculate the parameter estimation errors for LISA and TianQin and find that the parameter estimation errors measured by TianQin are smaller than those by LISA.
Searches for continuous gravitational waves from unknown sources attempt to detect long-lasting gravitational radiation by identifying Doppler-modulated signatures in the data. Semicoherent methods allow for wide parameter space surveys, identifying interesting regions to be followed up using more sensitive (and computationally expensive) tools. Thus, it is required to properly understand the parameter space structure under study, as failing to do so could significantly affect the effectiveness of said strategies. We introduce a new measure for distances in parameter space suited for semicoherent continuous wave searches. This novel approach, based on comparing time-frequency tracks, can be applied to any kind of quasi-monochromatic continuous wave signals and adapts itself to the underlying structure of the parameter space under study. In a first application to the post-processing stage of an all-sky search for continuous waves from neutron stars in binary systems, we demonstrate a search sensitivity improvement by solely replacing previous ad hoc distance measures in the candidate clustering procedure by the new proposal.
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