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Register a new userComputational Techniques for Parameter Estimation of Gravitational Wave Signals
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Since the very first detection of gravitational waves from the coalescence of two black holes in 2015, Bayesian statistical methods have been routinely applied by LIGO and Virgo to extract the signal out of noisy interferometric measurements, obtain point estimates of the physical parameters responsible for producing the signal, and rigorously quantify their uncertainties. Different computational techniques have been devised depending on the source of the gravitational radiation and the gravitational waveform model used. Prominent sources of gravitational waves are binary black hole or neutron star mergers, the only objects that have been observed by detectors to date. But also gravitational waves from core collapse supernovae, rapidly rotating neutron stars, and the stochastic gravitational wave background are in the sensitivity band of the ground-based interferometers and expected to be observable in future observation runs. As nonlinearities of the complex waveforms and the high-dimensional parameter spaces preclude analytic evaluation of the posterior distribution, posterior inference for all these sources relies on computer-intensive simulation techniques such as Markov chain Monte Carlo methods. A review of state-of-the-art Bayesian statistical parameter estimation methods will be given for researchers in this cross-disciplinary area of gravitational wave data analysis.
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Unlike ground-based gravitational wave detectors, space-based gravitational wave detectors can detect the ringdown signals from massive black hole binary mergers with large signal-to-noise ratio, and help to extract the source parameters and localize the source. To reduce the computation time in Fisher information matrix, we derive the analytical formulas of frequency-domain ringdown signals for heliocentric detectors and geocentric detectors by considering the effect of the harmonic phases, the rotation period of the geocentric detector, and the detector arm length. We explore the median errors of parameter estimation and source localization with ringdown singals from binaries with different masses and different redshifts. Using a binary source with the total mass $M=10^7 M_odot$ at the redshift $z=1$, we analyze the dependence of these errors on the sky position. We find that the network of space-based gravitational wave detectors can significantly improve the source localization at the ringdown stage.
Compact binary systems with neutron stars or black holes are one of the most promising sources for ground-based gravitational wave detectors. Gravitational radiation encodes rich information about source physics; thus parameter estimation and model selection are crucial analysis steps for any detection candidate events. Detailed models of the anticipated waveforms enable inference on several parameters, such as component masses, spins, sky location and distance that are essential for new astrophysical studies of these sources. However, accurate measurements of these parameters and discrimination of models describing the underlying physics are complicated by artifacts in the data, uncertainties in the waveform models and in the calibration of the detectors. Here we report such measurements on a selection of simulated signals added either in hardware or software to the data collected by the two LIGO instruments and the Virgo detector during their most recent joint science run, including a blind injection where the signal was not initially revealed to the collaboration. We exemplify the ability to extract information about the source physics on signals that cover the neutron star and black hole parameter space over the individual mass range 1 Msun - 25 Msun and the full range of spin parameters. The cases reported in this study provide a snap-shot of the status of parameter estimation in preparation for the operation of advanced detectors.
Third-generation gravitational wave detectors, such as the Einstein Telescope and Cosmic Explorer, will detect a bunch of gravitational-wave (GW) signals originating from the coalescence of binary neutron star (BNS) and binary black hole (BBH) systems out to the higher redshifts, $zsim 5-10$. There is a potential concern that some of the GW signals detected at a high statistical significance eventually overlap with each other, and the parameter estimation of such an overlapping system can differ from the one expected from a single event. Also, there are certainly overlapping systems in which one of the overlapping events has a low signal-to-noise ratio $lesssim 4$, and is thus unable to be clearly detected. Those system will potentially be misidentified with a single GW event, and the estimated parameters of binary GWs can be biased. We estimate the occurrence rate of those overlapping events. We find that the numbers of overlapping events are $sim 200$ per day for BNSs and a few per hour for BBHs. Then we study the statistical impacts of these overlapping GWs on a parameter estimation based on the Fisher matrix analysis. Our finding is that the overlapping signals produce neither large statistical errors nor serious systematic biases on the parameters of binary systems, unless the coalescence time and the redshifted chirp masses of the two overlapping GWs are very close to each other, i.e., $|mathcal{M}_{z1}-mathcal{M}_{z2}|lesssim10^{-4} ,(10^{-1}),M_odot$ and $|t_{rm c1}-t_{rm c2}|lesssim10^{-2},(10^{-1})$,s for BNSs (BBHs). The occurrence rate of such a closely overlapping event is shown to be much smaller than one per year with the third-generation detectors.
Inspiraling binaries of compact objects are primary targets for current and future gravitational-wave observatories. Waveforms computed in General Relativity are used to search for these sources, and will probably be used to extract source parameters from detected signals. However, if a different theory of gravity happens to be correct in the strong-field regime, source-parameter estimation may be affected by a fundamental bias: that is, by systematic errors induced due to the use of waveforms derived in the incorrect theory. If the deviations from General Relativity are not large enough to be detectable on their own and yet these systematic errors remain significant (i.e., larger than the statistical uncertainties in parameter estimation), fundamental bias cannot be corrected in a single observation, and becomes stealth bias. In this article we develop a scheme to determine in which cases stealth bias could be present in gravitational-wave astronomy. For a given observation, the answer depends on the detection signal-to-noise ratio and on the strength of the modified-gravity correction. As an example, we study three representative stellar-mass binary systems that will be detectable with second-generation ground-based observatories. We find that significant systematic bias can occur whether or not modified gravity can be positively detected, for correction strengths that are not currently excluded by any other experiment. Thus, stealth bias may be a generic feature of gravitational-wave detections, and it should be considered and characterized, using expanded models such as the parametrized post-Einstein framework, when interpreting the results of parameter-estimation analyses.
In the past few years, the detection of gravitational waves from compact binary coalescences with the Advanced LIGO and Advanced Virgo detectors has become routine. Future observatories will detect even larger numbers of gravitational-wave signals, which will also spend a longer time in the detectors sensitive band. This will eventually lead to overlapping signals, especially in the case of Einstein Telescope (ET) and Cosmic Explorer (CE). Using realistic distributions for the merger rate as a function of redshift as well as for component masses in binary neutron star and binary black hole coalescences, we map out how often signal overlaps of various types will occur in an ET-CE network over the course of a year. We find that a binary neutron star signal will typically have tens of overlapping binary black hole and binary neutron star signals. Moreover, it will happen up to tens of thousands of times per year that two signals will have their end times within seconds of each other. In order to understand to what extent this would lead to measurement biases with current parameter estimation methodology, we perform injection studies with overlapping signals from binary black hole and/or binary neutron star coalescences. Varying the signal-to-noise ratios, the durations of overlap, and the kinds of overlapping signals, we find that in most scenarios the intrinsic parameters can be recovered with negligible bias. However, biases do occur for a short binary black hole or a quieter binary neutron star signal overlapping with a long and louder binary neutron star event when the merger times are sufficiently close. Hence our studies show where improvements are required to ensure reliable estimation of source parameters for all detected compact binary signals as we go from second-generation to third-generation detectors.
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