Observational tests of fundamental physics from gravitational wave detections

With the detection of the signal GW150914 from the collision of two black holes in 2015, observational gravitational wave physics has begun. Many more signals have since been recorded, and new detections are now becoming routine. These observations offer a new window to probe fundamental physics in thus far inaccessible regimes of strong gravity, such as in the regions near black hole horizons. The work presented here pursues this through two approaches, studying predicted signals of either black holes of general relativity, or of proposed alternative objects without horizons. A binary black hole collision creates a single perturbed black hole, which settles to its final state through the ringdown gravitational wave emission. The ringdown consists of a spectrum of modes, which the no-hair theorem in General Relativity predicts to be determined entirely by the black hole mass and angular momentum. Measurement of multiple modes allows to test this prediction but is challenging due to the weak and short-lived nature of the ringdown signal. Two studies are presented on the feasibility of such tests using current and near-future de- tector sensitivities. Large populations of simulated ringdown signals are constructed based on observational models of the binary black hole population. Bayesian parameter estimation techniques are applied to these signals to place bounds on deviations from the no-hair prediction. Detections leading to stringent bounds are unlikely to occur for current instruments but can be found during a few years of operation at their planned future sensitivities. The prospects improve when extending the analysis to combine data from multiple detections into a single bound on deviations. At the sensitivity planned for the next observation run of current instruments, the detections from one year of data can be combined into stringent bounds. Solutions are provided to limitations uncovered for this type of study. In a further study, strong evidence is found for the presence of a subdominant mode in the data of the event GW190521. A new method is employed to allow the analysis of only the ringdown part of the signal, without contamination from outside the analysis window and preventing windowing artefacts and signal loss. Tests of the no-hair theorem are performed, yielding unexpectedly tight constraints on deviations. Two phenomenologically distinct signals from horizonless compact objects are studied, both following after the primary signal which is otherwise unchanged compared to that of a black hole binary. One takes the form of repeated pulses after the ringdown, called gravitational wave echoes, while the other consists of a very long-lived damped sinusoid with a small amplitude. Using a simplified waveform model for echoes, evidence for such signals in the data of several detections is evaluated. Previous results from the first search for these are replicated, and the methods tested thoroughly. Through improved estimation methods, low statistical significance is established for these results, yet the presence of such signals cannot be ruled out by the analysis. An independent Bayesian analysis is performed for the same waveform model, with results for each event either preferring the absence of echoes in the data or being consistent with it. Bounds on the echo amplitudes ruled out by the data are produced. The long-lived mode signal for a broad class of horizonless objects is considered in a Bayesian analysis. Methods are developed to accommodate the long duration of the signal, and their performance is tested with simulated signals and off-source data. They are then applied to the data of the event GW150914, yielding stringent bounds on the deviations from the Kerr geometry exhibited by such objects.Mit der Detektion des Signals GW150914 von der Kollision zweier schwarzer Löcher im Jahr 2015 begann die beobachtungsbasierte Gravitationswellenphysik. Viele weitere Signale wurden seither aufgezeichnet und neue Detektionen werden zur Routine. Diese Beobachtungen eröffnen einen neuen Weg, fundamentale Physik im bisher unzugänglichen Regime starker Gravitation zu untersuchen, zum Beispiel in der Umgebung der Horizonte schwarzer Löcher. Die hier präsentierten Studien verfolgen dies durch zwei Ansätze, indem sie entweder die vorhergesagten Signale schwarzer Löcher in der Allgemeinen Relativitätstheorie oder vorgeschlagener alternativer Objekte ohne Horizonte untersuchen. Die Kollision zweier schwarzer Löcher erzeugt ein einzelnes gestörtes schwarzes Loch, welches durch Emission der Abkling-Gravitationswellen schließlich in einen ungestörten Zustand übergeht. Die Abkling-Strahlung besteht aus einem Spektrum von Moden, welche dem Keine- Haare-Theorem der Allgemeinen Relativitätstheorie nach gänzlich durch Masse und Drehimpuls des schwarzen Loches bestimmt werden. Die Messung mehrerer Moden ermöglicht die Prüfung dieser Vorhersage, ist jedoch wegen des schwachen und kurzlebigen Abklingsignals schwierig. Zwei Studien zur Durchführbarkeit solcher Tests mithilfe aktuell und in naher Zukunft verfügbarer Detektor-Empfindlichkeiten werden dargelegt. Große Populationen simulierter Abklingsignale werden konstruiert, basierend auf beobachtungsgestützten Modellen der Population von Binärsystemen schwarzer Löcher. Bayessche Parameterabschätzung wird auf diese Signale angewendet, um Abweichungen von der Keine-Haare-Vorhersage zu beschränken. Detektionen, die zu strikter Begrenzung führen, sind mit aktuellen Instrumenten unwahrscheinlich, können aber innerhalb weniger Jahre des Betriebs mit ihren geplanten zukünftigen Empfindlichkeiten erreicht werden. Diese Aussichten verbessern sich, wenn Daten mehrerer Detektionen in der Begrenzung kombiniert werden. Mit der geplanten Empfindlichkeit aktueller Instrumente im nächsten Beobachtungslauf können die in einem Jahr gesammelten Daten zu strikten Begrenzungen kombiniert werden. Lösungen für die entdeckten Limitationen dieser Art Analyse werden vorgestellt. In einer weiteren Studie wird starke Evidenz für die Existenz einer subdominanten Mode in den Daten des Signals GW190521 gefunden. Eine neue Methode wird eingesetzt, welche die Analyse des Abkling-Signals ermöglicht, ohne Kontamination von außerhalb des Analyse- Fensters, Artefakte oder Signalverlust zu verursachen. Tests des Keine-Haare-Theorems werden durchgeführt und liefern unerwartet strikte Beschränkungen für Abweichungen. Zwei phänomenologisch verschiedene Signale horizontfreier kompakter Objekte werden untersucht. Beide folgen dem Primärsignal, das ansonsten gegenüber dem schwarzer Löcher un- verändert ist. Eines besteht aus wiederholten Pulsen, als Gravitationswellen-Echos bezeichnet, während das zweite die Form einer langlebigen, gedämpften Sinuswelle geringer Amplitude hat. Anhand eines vereinfachten Modells der Echo-Wellenform wird die Evidenz solcher Signale in den Daten mehrerer Detektionen bewertet. Frühere Ergebnisse der ersten Suche nach Echos werden repliziert und die Methoden ausführlich geprüft. Durch verbesserte Abschätzungsmethoden wird eine geringe statistische Signifikanz der Ergebnisse etabliert, allerdings kann die Anwesenheit solcher Signale nicht durch diese Untersuchung ausgeschlossen werden. Eine unabhängige Bayessche Analyse wird mit derselben Wellenform durchgeführt, wobei die Ergebnisse die Abwesenheit des Signals bevorzugen oder mit Rauschen vereinbar sind. Grenzen für die von den Daten ausgeschlossenen Amplituden der Echos werden gefunden. Das Signal einer langlebigen Mode von einer großen Klasse horizontfreier Objekte wird in einer Bayesschen Analyse betrachtet. Methoden werden entwickelt, um die lange Dauer des Signals handhaben zu können, und ihre Leistungsfähigkeit wird an simulierten Signalen und signalfreien Daten getestet. Auf die Daten des Signals GW150914 angewendet, liefern sie strikte Beschränkungen für die Abweichungen solcher Objekte von der Kerr-Geometrie

Low significance of evidence for black hole echoes in gravitational wave data

Recent detections of merging black holes allow observational tests of the nature of these objects. In some proposed models, non-trivial structure at or near the black hole horizon could lead to echo signals in gravitational wave data. Recently, Abedi et al. claimed tentative evidence for repeating damped echo signals following the gravitational-wave signals of the binary black hole merger events recorded in the first observational period of the Advanced LIGO interferometers. We reanalyse the same data, addressing some of the shortcomings of their method using more background data and a modified procedure. We find a reduced statistical significance for the claims of evidence for echoes, calculating increased p-values for the null hypothesis of echo-free noise. The reduced significance is entirely consistent with noise, and so we conclude that the analysis of Abedi et al. does not provide any observational evidence for the existence of Planck-scale structure at black hole horizons.Comment: As accepted by Physical Review

Sub-atomic constraints on the Kerr geometry of GW150914

We obtain stringent constraints on near-horizon deviations of a black hole from the Kerr geometry by performing a long-duration Bayesian analysis of the gravitational-wave data immediately following GW150914. GW150914 was caused by a binary system that merged to form a final compact object. We parameterize deviations of this object from a Kerr black hole by modifying its boundary conditions from full absorption to full reflection, thereby modeling it as a horizonless ultracompact object. Such modifications result in the emission of long-lived monochromatic quasinormal modes after the merger. These modes would extract energy on the order of a few solar masses from the final object, making them observable by LIGO. By putting bounds on the existence of these modes, we show that the Kerr geometry is not modified down to distances as small as $4 \times 10^{-16}$ meters away from the horizon. Our results indicate that the post-merger object formed by GW150914 is a black hole that is well described by the Kerr geometry

Model systematics in time domain tests of binary black hole evolution

We perform several consistency tests between different phases of binary black hole dynamics; the inspiral, the merger, and the ringdown on the gravitational wave events GW150914 and GW170814. These tests are performed explicitly in the time domain, without any spectral leakage between the different phases. We compute posterior distributions on the mass and spin of the initial black holes and the final black hole. We also compute the initial areas of the two individual black holes and the final area from the parameters describing the remnant black hole. This facilitates a test of Hawking's black hole area theorem. We use different waveform models to quantify systematic waveform uncertainties for the area increase law with the two events. We find that these errors may lead to overstating the confidence with which the area theorem is confirmed. For example, we find $>99\%$ agreement with the area theorem for GW150914 if a damped sinusoid consisting of a single-mode is used at merger to estimate the final area. This is because this model overestimates the final mass. Including an overtone of the dominant mode decreases the confidence to $\sim94\%$; using a full merger-ringdown model further decreases the confidence to $\sim 85-90\%$. We find that comparing the measured change in the area to the expected change in area yields a more robust test, as it also captures over estimates in the change of area. We find good agreement with GR when applying this test to GW150914 and GW170814

A frequency-domain perspective on GW150914 ringdown overtone

We revisit the recent debate on the evidence for an overtone in the black hole ringdown of GW150914. By gating and inpainting the data, we discard the contamination from earlier parts of the gravitational wave signal before ringdown. This enables the parameter estimation to be conducted in the frequency domain, which is mathematically equivalent to the time domain method. We keep the settings as similar as possible to the previous studies by \textcite{Cotesta:2022pci} and Isi \textit{et al.}\cite{Isi:2019aib,Isi:2022mhy} which yielded conflicting results on the Bayes factor of the overtone. We examine the spectral contents of the matched-filtering in the frequency domain, and propose a convergence test to assess the validity of an overtone model. Our results find the Bayes factors for the overtone fall within $10$ and $26$ around a range of times centered at the best-fit merger time of GW150914, which supports the existence of an overtone in agreement with the conclusions of Isi \textit{et al.}\cite{Isi:2019aib,Isi:2022mhy}. Our work contributes to the understanding of how various methods affect the statistical significance of overtones.Comment: 8 pages, 7 figures. Data release at https://github.com/gwastro/gw150914-overtone. Comments welcome

Statistical validation of the detection of a sub-dominant quasi-normal mode in GW190521

One of the major aims of gravitational wave astronomy is to observationally test the Kerr nature of black holes. The strongest such test, with minimal additional assumptions, is provided by observations of multiple ringdown modes, also known as black hole spectroscopy. For the gravitational wave merger event GW190521, we have previously claimed the detection of two ringdown modes emitted by the remnant black hole. In this paper we provide further evidence for the detection of multiple ringdown modes from this event. We analyse the recovery of simulated gravitational wave signals designed to replicate the ringdown properties of GW190521. We quantify how often our detection statistic reports strong evidence for a sub-dominant $(\ell,m,n)=(3,3,0)$ ringdown mode, even when no such mode is present in the simulated signal. We find this only occurs with a probability $\sim 0.02$, which is consistent with a Bayes factor of $56 \pm 1$ (1$\sigma$ uncertainty) found for GW190521. We also quantify our agnostic analysis of GW190521, in which no relationship is assumed between ringdown modes, and find that only 1 in 250 simulated signals without a $(3,3,0)$ mode yields a result as significant as GW190521. Conversely, we verify that when simulated signals do have an observable $(3,3,0)$ mode they consistently yield a strong evidence and significant agnostic results. We also find that constraints on deviations from the $(3,3,0)$ mode on GW190521-like signals with a $(3,3,0)$ mode are consistent with what was obtained from our previous analysis of GW190521. Our results strongly support our previous conclusion that the gravitational wave signal from GW190521 contains an observable sub-dominant $(\ell,m,n)=(3,3,0)$ mode.Comment: 16 pages, 10 figure

Observation of a multimode quasi-normal spectrum from a perturbed black hole

We provide strong observational evidence for a multimode black hole ringdown spectrum, using the gravitational wave event GW190521. We show strong evidence for the presence of at least two ringdown modes, with a Bayes factor of $43.4^{+8.1}_{-6.8}$ preferring two modes over one. The dominant mode is the fundamental $\ell=m=2$ harmonic, and the sub-dominant mode corresponds to the fundamental $\ell=m=3$ harmonic. We estimate the redshifted mass and dimensionless spin of the final black hole as $332^{+31}_{-35}\,M_\odot$ and $0.871^{+0.052}_{-0.096}$ respectively. The detection of the two modes disfavors a binary progenitor with equal masses, and the mass ratio is constrained to $0.45^{+0.22}_{-0.29}$. General relativity predicts that the frequency and damping time of each mode in the spectrum depends only on two parameters, the black hole mass and angular momentum. Consistency between the different modes thus provides a test of general relativity. As a test of the black hole no-hair theorem, we constrain the fractional deviation of the sub-dominant mode frequency from the Kerr prediction to $\delta f_{330} = -0.010^{+0.073}_{-0.121}

Statistical validation of the detection of a sub-dominant quasi-normal mode in GW190521

One of the major aims of gravitational wave astronomy is to observationally test the Kerr nature of black holes. The strongest such test, with minimal additional assumptions, is provided by observations of multiple ringdown modes, also known as black hole spectroscopy. For the gravitational wave merger event GW190521, we have previously claimed the detection of two ringdown modes emitted by the remnant black hole. In this paper we provide further evidence for the detection of multiple ringdown modes from this event. We analyze the recovery of simulated gravitational wave signals designed to replicate the ringdown properties of GW190521. We quantify how often our detection statistic reports strong evidence for a sub-dominant $(\ell,m,n)=(3,3,0)$ ringdown mode, even when no such mode is present in the simulated signal. We find this only occurs with a probability $\sim 0.02$, which is consistent with a Bayes factor of $56 \pm 1$ (1$\sigma$ uncertainty) found for GW190521. We also quantify our agnostic analysis of GW190521, in which no relationship is assumed between ringdown modes, and find that less than 1 in 500 simulated signals without a $(3,3,0)$ mode yield a result as significant as GW190521. Conversely, we verify that when simulated signals do have an observable $(3,3,0)$ mode they consistently yield a strong evidence and significant agnostic results. We also find that simulated GW190521-like signals with a $(3,3,0)$ mode present yield tight constraints on deviations of that mode from Kerr, whereas constraints on the $(2,2,1)$ overtone of the dominant mode yield wide constraints that are not consistent with Kerr. These results on simulated signals are similar to what we find for GW190521. Our results strongly support our previous conclusion that the gravitational wave signal from GW190521 contains an observable sub-dominant $(\ell,m,n)=(3,3,0)$ mode

Spectroscopy for asymmetric binary black hole mergers

We study Bayesian inference of black hole ringdown modes for simulated binary black hole signals. We consider to what extent different fundamental ringdown modes can be identified in the context of black hole spectroscopy. Our simulated signals are inspired by the high-mass event GW190521. We find strong correlation between mass ratio and Bayes factors of the subdominant ringdown modes. The Bayes factor values and time dependency, and the peak time of the (3,3,0) mode align with those found analyzing the real event GW190521, particularly for high-mass ratio systems