Black Hole Spectroscopy by Mode Cleaning

We formulate a Bayesian framework to analyze ringdown gravitational waves from colliding binary black holes and test the no-hair theorem. The idea hinges on mode cleaning-revealing subdominant oscillation modes by removing dominant ones using newly proposed "rational filters." By incorporating the filter into Bayesian inference, we construct a likelihood function that depends only on the mass and spin of the remnant black hole (no dependence on mode amplitudes and phases) and implement an efficient pipeline to constrain the remnant mass and spin without Markov chain Monte Carlo. We test ringdown models by cleaning combinations of different modes and evaluating the consistency between the residual data and pure noise. The model evidence and Bayes factor are used to demonstrate the presence of a particular mode and to infer the mode starting time. In addition, we design a hybrid approach to estimate the remnant black hole properties exclusively from a single mode using Markov chain Monte Carlo after mode cleaning. We apply the framework to GW150914 and demonstrate more definitive evidence of the first overtone by cleaning the fundamental mode. This new framework provides a powerful tool for black hole spectroscopy in future gravitational-wave events.

Analysis of Ringdown Overtones in GW150914

We analyze GW150914 postmerger data to understand if ringdown overtone detection claims are robust. We find no evidence in favor of an overtone in the data after the waveform peak. Around the peak, the Bayes factor does not indicate the presence of an overtone, while the support for a nonzero amplitude is sensitive to changes in the starting time much smaller than the overtone damping time. This suggests that claims of an overtone detection are noise dominated. We perform GW150914-like injections in neighboring segments of the real detector noise, and we show that noise can indeed induce artificial evidence for an overtone.

Testing General Relativity with Gravitational Waves: An Overview

The detections of gravitational-wave (GW) signals from compact binary coalescence by ground-based detectors have opened up the era of GW astronomy. These observations provide opportunities to test Einstein’s general theory of relativity at the strong-field regime. Here we give a brief overview of the various GW-based tests of General Relativity (GR) performed by the LIGO-Virgo collaboration on the detected GW events to date. After providing details for the tests performed in four categories, we discuss the prospects for each test in the context of future GW detectors. The four categories of tests include the consistency tests, parametrized tests for GW generation and propagation, tests for the merger remnant properties, and GW polarization tests.

Extracting the Gravitational Recoil from Black Hole Merger Signals

Gravitational waves carry energy, angular momentum, and linear momentum. In generic binary black hole mergers, the loss of linear momentum imparts a recoil velocity, or a "kick," to the remnant black hole. We exploit recent advances in gravitational waveform and remnant black hole modeling to extract information about the kick from the gravitational wave signal. Kick measurements such as these are astrophysically valuable, enabling independent constraints on the rate of second-generation merger. Further, we show that kicks must be factored into future ringdown tests of general relativity with third-generation gravitational wave detectors to avoid systematic biases. We find that, although little information can be gained about the kick for existing gravitational wave events, interesting measurements will soon become possible as detectors improve. We show that, once LIGO and Virgo reach their design sensitivities, we will reliably extract the kick velocity for generically precessing binaries-including the so-called superkicks, reaching up to 5000  km/s.

Measuring Spin of the Remnant Black Hole from Maximum Amplitude

Gravitational waves emitted during the merger of two black holes carry information about the remnant black hole, namely its mass and spin. This information is typically found from the ringdown radiation as the black hole settles to a final state. We find that the remnant black hole spin is already known at the peak amplitude of the gravitational wave strain. Using this knowledge, we present a new method for measuring the final spin that is template independent, using only the chirp mass, the instantaneous frequency of the strain, and its derivative at maximum amplitude, all template independent.

Hierarchical Test of General Relativity with Gravitational Waves

We propose a hierarchical approach to testing general relativity with multiple gravitational wave detections. Unlike existing strategies, our method does not assume that parameters quantifying deviations from general relativity are either common or completely unrelated across all sources. We instead assume that these parameters follow some underlying distribution, which we parametrize and constrain. This can be then compared to the distribution expected from general relativity, i.e., no deviation in any of the events. We demonstrate that our method is robust to measurement uncertainties and can be applied to theories of gravity where the parameters beyond general relativity are related to each other, as generally expected. Our method contains the two extremes of common and unrelated parameters as limiting cases. We apply the hierarchical model to the population of 10 binary black hole systems so far detected by LIGO and Virgo. We do this for a parametrized test of gravitational wave generation, by modeling the population distribution of beyond-general-relativity parameters with a Gaussian distribution. We compute the mean and the variance of the population and show that both are consistent with general relativity for all parameters we consider. In the best case, we find that the population properties of the existing binary signals are consistent with general relativity at the ∼1% level. This hierarchical approach subsumes and extends existing methodologies and is more robust at revealing potential subtle deviations from general relativity with increasing number of detections.

Testing the No-Hair Theorem with GW150914

We analyze gravitational-wave data from the first LIGO detection of a binary black-hole merger (GW150914) in search of the ringdown of the remnant black hole. Using observations beginning at the peak of the signal, we find evidence of the fundamental quasinormal mode and at least one overtone, both associated with the dominant angular mode (ℓ=m=2), with 3.6σ confidence. A ringdown model including overtones allows us to measure the final mass and spin magnitude of the remnant exclusively from postinspiral data, obtaining an estimate in agreement with the values inferred from the full signal. The mass and spin values we measure from the ringdown agree with those obtained using solely the fundamental mode at a later time, but have smaller uncertainties. Agreement between the postinspiral measurements of mass and spin and those using the full waveform supports the hypothesis that the GW150914 merger produced a Kerr black hole, as predicted by general relativity, and provides a test of the no-hair theorem at the ∼10% level. An independent measurement of the frequency of the first overtone yields agreement with the no-hair hypothesis at the ∼20% level. As the detector sensitivity improves and the detected population of black-hole mergers grows, we can expect that using overtones will provide even stronger tests.