Recipes for computing radiation from a Kerr black hole using Generalized Sasaki-Nakamura formalism: I. Homogeneous solutions

Central to black hole perturbation theory calculations is the Teukolsky equation that governs the propagation and the generation of radiation emitted by Kerr black holes. However, it is plagued by a long-ranged potential associated to the perturbation equation and hence a direct numerical integration of the equation is challenging. Sasaki and Nakamura devised a formulation that transforms the equation into a new equation that is free from the issue for the case of out-going gravitational radiation. The formulation was later generalized by Hughes to work for any type of radiation. In this work, we revamp the Generalized Sasaki-Nakamura (GSN) formalism and explicitly show the transformations that convert solutions between the Teukolsky and the GSN formalism for both in-going and out-going radiation of scalar, electromagnetic and gravitational type. We derive all necessary ingredients for the GSN formalism to be used in numerical computations. In particular, we describe a new numerical implementation of the formalism, GeneralizedSasakiNakamura.jl, that computes homogeneous solutions to both perturbation equation in the Teukolsky and the GSN formalism. The code works well at low frequencies and is even better at high frequencies by leveraging the fact that black holes are highly permeable to waves at high frequencies. This work lays the foundation for an efficient scheme to compute gravitational radiation from Kerr black holes and an alternative way to compute quasi-normal modes of Kerr black holes.Comment: 31 pages, 12 figure

Identifying strongly lensed gravitational waves through their phase consistency

Strongly lensed gravitational waves (GWs) from binary coalescence manifest as repeated chirps from the original merger. At the detectors, the phase of the lensed GWs and its arrival time differences will be consistent modulo a fixed constant phase shift. We develop a fast and reliable method to efficiently reject event pairs that are not-lensed copies and appropriately rank the most interesting candidates. Our method exploits that detector phases are the best measured GW parameter, with errors only of a fraction of a radian and differences across the frequency band that are better measured than the chirp mass. The arrival time phase differences also avoid the shortcomings of looking for overlaps in highly non-Gaussian sky maps. Our basic statistic determining the consistency with lensing is the distance between the phase posteriors of two events and it directly provides information about the lens-source geometry which helps inform electromagnetic followups. We demonstrate that for simulated signals of not-lensed binaries with many shared parameters none of the pairs have phases closer than $3\sigma$, and most cases reject the lensing hypothesis by $5\sigma$. Looking at the latest catalog, GWTC3, we find that only $6\%$ of the pairs are consistent with lensing at $99\%$ confidence level. Moreover, we reject about half of the pairs that would otherwise favor lensing by their parameter overlaps and demonstrate good correlation with detailed joint parameter estimation results. This reduction of the false alarm rate will be of paramount importance in the upcoming observing runs and the eventual discovery of lensed GWs. Our code is publicly available and could be applied beyond lensing to test possible deviations in the phase evolution from modified theories of gravity and constrain GW birefringence.Comment: 14+7 pages, 12+7 figures, 2 tables, code at https://github.com/ezquiaga/phaza

Finding diamonds in the rough: Targeted Sub-threshold Search for Strongly-lensed Gravitational-wave Events

Strong gravitational lensing of gravitational waves can produce duplicate signals separated in time with different amplitudes. We consider the case in which strong lensing produces identifiable gravitational-wave events and weaker sub-threshold signals hidden in the noise background. We present a search method for the sub-threshold signals using reduced template banks targeting specific confirmed gravitational-wave events. We apply the method to all events from Advanced LIGO's first and second observing run O1/O2. Using GW150914 as an example, we show that the method effectively reduces the noise background and raises the significance of (near-) sub-threshold triggers. In the case of GW150914, we can improve the sensitive distance by $2.0\% - 14.8\%$. Finally, we present the top $5$ possible lensed candidates for O1/O2 gravitational-wave events that passed our nominal significance threshold of False-Alarm-Rate $\leq 1/30$ days

Targeted Sub-threshold Search for Strongly-lensed Gravitational-wave Events

Strong gravitational lensing of gravitational waves can produce duplicated signals that are separated in time and with different amplitudes. We consider the case in which strong lensing produces identifiable gravitational-wave events together with weaker sub-threshold signals that are hidden in the noise background. We present a search method for the sub-threshold signals using reduced template banks targeting specific confirmed gravitational-wave events. We apply the method to an event from Advanced LIGO's first observing run O1, GW151012. We show that the method is effective in reducing the noise background and hence raising the significance of (near-) sub-threshold triggers. In the case of GW151012, we are able to improve the sensitive distance by 10%−25%. Finally, we present the 10 most significant events for GW151012-like signals in O1. Besides the already confirmed gravitational-wave detections, none of the candidates pass our nominal significance threshold of False-Alarm-Rate ≤ 1/30 days

Ranking candidate signals with machine learning in low-latency searches for gravitational waves from compact binary mergers

In the multimessenger astronomy era, accurate sky localization and low latency time of gravitational-wave (GW) searches are keys in triggering successful follow-up observations on the electromagnetic counterpart of GW signals. We, in this work, study the feasibility of adopting a supervised machine learning (ML) method for scoring rank on candidate GW events. We consider two popular ML methods, random forest and neural networks. We observe that the evaluation time of both methods takes tens of milliseconds for ∼45,000 evaluation samples. We compare the classification efficiency between the two ML methods and a conventional low-latency search method with respect to the true positive rate at given false positive rate. The comparison shows that about 10% improved efficiency can be achieved at lower false positive rate ∼2×10⁻⁵ with both ML methods. We also present that the search sensitivity can be enhanced by about 18% at ∼10⁻¹¹  Hz false alarm rate. We conclude that adopting ML methods for ranking candidate GW events is a prospective approach to yield low latency and high efficiency in searches for GW signals from compact binary mergers

Template-based gravitational-wave echoes search using Bayesian model selection

The ringdown of the gravitational-wave signal from a merger of two black holes has been suggested as a probe of the structure of the remnant compact object, which may be more exotic than a black hole. It has been pointed out that there will be a train of echoes in the late-time ringdown stage for different types of exotic compact objects. In this paper, we present a template-based search methodology using Bayesian statistics to search for echoes of gravitational waves. Evidence for the presence or absence of echoes in gravitational-wave events can be established by performing Bayesian model selection. The Occam factor in Bayesian model selection will automatically penalize the more complicated model that echoes are present in gravitational-wave strain data because of its higher degree of freedom to fit the data. We find that the search methodology was able to identify gravitational-wave echoes with Abedi et al.’s echoes waveform model about 82.3% of the time in simulated Gaussian noise in the Advanced LIGO and Virgo network and about 61.1% of the time in real noise in the first observing run of Advanced LIGO with ≥ 5σ significance. Analyses using this method are performed on the data of Advanced LIGO’s first observing run, and we find no statistical significant evidence for the detection of gravitational-wave echoes. In particular, we find < 1σ combined evidence of the three events in Advanced LIGO’s first observing run. The analysis technique developed in this paper is independent of the waveform model used, and can be used with different parametrized echoes waveform models to provide more realistic evidence of the existence of echoes from exotic compact objects