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On Aspects of Gravitational-Wave Detection: Detector Characterisation, Data Analysis and Source Modelling for Ground-Based Detectors On aspects of gravitational-wave detection: Detector characterisation, data analysis and source modelling for ground-based detectors Von der Fakult¨at fur¨ Mathematik und Physik der Gottfried Wilhelm Leibniz Universit¨at Hannover zur Erlangung des Grades Doktor der Naturwissenschaften - Dr. rer. nat. - genehmigte Dissertation von M. Sc. Ajith Parameswaran geboren am 27 Mai 1980 in Chemmaniyode, Kerala, Indien. Max-Planck-Institut fur¨ Gravitationsphysik (Albert-Einstein-Institut) und Institut fur¨ Gravitationsphysik, Gottfried Wilhelm Leibniz Universit¨at Hannover 2007 Referent : Prof. B. F. Schutz Koreferent : Prof. K. Danzmann Tag der Promotion : 10 Dezember 2007 To Achan, Amma and Ammu. iv “And how many hours a day did you do lessons?” said Alice, in a hurry to change the subject. “Ten hours the first day”, said the Mock Turtle: “nine the next, and so on.” “What a curious plan!” exclaimed Alice. “That’s the reason they’re called lessons”, the Gryphon remarked: “because they lessen from day to day”. – Lewis Carroll, in Alice’s Adventures in Wonderland. vi Zusammenfassung Die vorliegende Arbeit besch¨aftigt sich mit drei Aspekten der Suche nach Gravitationswellen (GW) mit erdgestutzten¨ Detektoren: Detektorcharakterisierung, Datenanalyse und Modellierung von Quellen. Der erste Teil behandelt die Detektorcharakterisierung und die Entwicklung von Vetostrategien fur¨ die Suche nach transienten unmodellierten GW-Ausbruchen.¨ Der zweite Teil enth¨alt Methoden der Datenanalyse, die zur Suche nach GW-Ausbruchen¨ und verschmelzenden kompakten Doppelsternsystemen angewendet werden. Der dritte Teil befasst sich mit der Mod- ellierung von GW, die von kompakten Bin¨arsystemen erzeugt werden, mit post-Newtonschen (PN) Methoden. Teil I. Kapitel 2 beschreibt die Charakterisierung der Qualit¨at der Parameterabsch¨atzung des mHACR Algorithmus fur¨ GW-Ausbruche.¨ In Kapitel 3 wird eine robuste Strategie zum Auss- chluss bestimmter Klassen von St¨orimpulsen in interferometrischen GW-Detektoren vorgestellt. Dabei wurde die Kenntnis der Kopplung verschiedener Untersystemen des Detektors auf das Ausgangssignal des Interferometers genutzt. Diese Vetomethode wurde durch Einspeisung von St¨orimpulsen in das GEO 600 Interferometer demonstriert (Kapitel 4). Ein Beispiel der An- wendung dieser Vetomethode auf die von GEO 600 aufgenommenen Daten wird pr¨asentiert. Kapitel 5 beschreibt eine weitere Vetomethode, basierend auf dem ‘null stream’, der aus den beiden Ausgangsquadraturen von GEO 600 konstruiert wird. Teil II. Der ‘null stream’, der aus den Ausg¨angen mehrerer Detektoren konstruiert werden kann, kann als Veto zur Vermeidung falscher Alarme bei der Suche nach GW-Ausbruchen¨ verwendet werden. Die gr¨oßte Fehlerquelle in der ‘null stream’ Analyse ist durch Kalibrationsfehler der aufgenommenen Daten gegeben. In Kapitel 6 wird die Einbindung eines ‘null stream’ Vetos in ein Netzwerk von zwei Detektoren, die sich am selben Ort befinden, vorgestellt. Dazu wird ein neues Verfahren zur Vermeidung des Einflusses von Kalibrationsfehlern vorgeschlagen. Ausser- dem wird ein Beispiel der Anwendung auf die Daten des LIGO-Hanford Detektors vorgestellt. Kapitel 7 beschreibt die Konstruktion einer neuen ‘template bank’, die in der Lage ist, die ‘inspi- ral’ Phase, die Verschmelzungsphase und die Abklingphase verschmelzender, nicht rotierender schwarzer L¨ochern zu modellieren. Dadurch wird es m¨oglich eine koh¨arente Suche bezuglich¨ aller drei Phasen eines Bin¨arsystems durchzufuhren,¨ die die Suchempfindlichkeit verbessern und die Ereignisrate der Interferometer steigern wird. Das Kapitel enth¨alt ausserdem eine allge- meine Prozedur, um interpolierte ‘template banks’ zu erstellen. Dabei werden die Wellenformen von Doppelsternsystemen aus nicht-rotierenden schwarzen L¨ochern, wie sie mit Methoden der numerischen Relativit¨at berechnet werden k¨onnen, verwendet. Teil III. In Kapitel 8 wird eine neue vollst¨andig adiabatische Absch¨atzung fur¨ die Berechnung von GW von kompakten einspiralisierenden Bin¨arsystemen unter Benutzung der PN Theorie vorgeschlagen. Sie enth¨alt eine konsistente Behandlung der Beschleunigung des Bin¨arsystems bis zur jeweiligen PN Ordnung, und ihre Ergebnisse liegen deutlich n¨aher an der exakten Wellenform fur¨ den Fall eines Testteilchens, das sich in einer Umlaufbahn um ein Schwarzschild schwarzes Loch befindet. Stichworte: Gravitationswellen, Detektorcharakterisierung, Datenanalyse, Quellenmodellierung. vii viii Abstract This thesis covers three topics related to the search for gravitational waves (GWs) using ground- based interferometric detectors — detector characterisation, data analysis and source modelling. The first part deals with detector characterisation and veto development for the search for transient, unmodelled GW bursts. The second part is related to data-analysis methods used in the search for GW bursts and coalescing compact binaries. The third part addresses some theoretical challenges related to the post-Newtonian (PN) modelling of GWs from inspiralling compact binaries. Part I. Chapter 2 describes the studies carried out for characterising the parameter-estimation quality of the mHACR burst-detection algorithm. Chapter 3 presents a robust strategy to veto certain classes of instrumental glitches that appear at the output of interferometric GW detectors, making use of the knowledge of the coupling of different detector subsystems to the main detector output. This veto method is demonstrated by injecting instrumental glitches in the hardware of the GEO 600 detector (Chapter 4). An example application of the veto method to the data of GEO 600 is also presented. Another instrumental veto method making use of the null stream constructed from the two output quadratures of GEO 600 is described in Chapter 5. Part II. The null stream constructed from multiple GW detectors can be used as a powerful veto against spurious instrumental triggers in the search for GW bursts. The biggest source of error in the null-stream analysis comes from the calibration errors in the data. Chapter 6 presents an implementation of the null-stream veto in a network of two co-located detectors, proposing a new formulation to overcome the effect of calibration errors. An example application to the data of the two LIGO-Hanford detectors is also presented. Chapter 7 constructs a new template bank which can model the inspiral, merger and ring down stages of the coalescence of non- spinning binary black holes. This will allow us to coherently search for all the three stages of the binary black hole coalescence, improving the sensitivity of the search and potentially bringing remarkable improvement in the event-rate for ground-based interferometers. This Chapter also prescribes a general procedure to construct interpolated template banks using non-spinning binary-black-hole waveforms produced by numerical relativity. Part III. Chapter 8 proposes a new complete adiabatic approximation for the computation of gravitational waveforms from inspiralling compact binaries using PN theory. This approximation provides a consistent treatment of the acceleration of the binary up to the respective PN order. The new approximants are found to be much closer (than the standard adiabatic approximants) to the exact waveform in the case of a test particle orbiting a Schwarzschild black hole. Key words: Gravitational waves, detector characterisation, data analysis, source modelling. ix x Contents List of Figures xv List of Tables xxiii 1. Gravitational-wave astronomy: Opening a new window onto the Universe 1 1.1. Introduction.................................. 1 1.2. Expected sources of gravitational waves . ...... 2 1.2.1. Coalescingcompactbinaries. 3 1.2.2. Sources of gravitational-wave bursts . ... 3 1.2.3. Sources of periodic gravitational waves . ..... 4 1.2.4. Stochastic gravitational-wave background . ..... 5 1.3. Gravitational-wave astronomy . ... 5 1.3.1. Testingtheoriesofgravity . 6 1.3.2. Astrophysics using gravitational waves . ..... 6 1.3.3. Cosmology using gravitational waves . ... 7 1.4. The search for gravitational waves . .... 7 1.4.1. Detecting gravitational waves . 8 1.4.2. Worldwide network of gravitational-wave detectors . ....... 8 1.4.3. Current observational results . 10 1.4.4. Challenges in the search for gravitational waves . ....... 11 1.5. Overviewandsummaryofthisthesis . ... 14 I. Detector characterisation and veto development for ground-based interferometers 19 2. Improving and characterising the hierarchical algorithm for curves and ridges 21 2.1. The burst detection algorithm mHACR . 21 2.1.1. Detectionalgorithm . 22 2.1.2. Parameterestimation . 23 2.2. Quality of the parameter estimation . .... 24 2.3. Application of mHACR in the detector characterisation of GEO 600 . 26 3. Physical instrumental vetoes for gravitational-wave burst triggers 29 3.1. The search for transient, unmodelled gravitational-wave bursts . 29 3.2. Vetoes using known instrumental couplings . ...... 30 3.2.1. Noisetransfer............................. 30 3.2.2. A veto strategy using known instrumental couplings . ...... 31 xi Contents 3.2.3. Test statistic: using null-stream . ... 32 3.2.4. Test statistic: using cross-correlation . ...... 33 3.2.5. Implementation. 34 3.3. Softwareinjections . 35 3.3.1. Causalinjections . 36 3.3.2. Randominjections . 37 3.4. An alternative method: ‘trigger mapping’ . ...... 37 3.4.1. Mappingthebursttriggers . 38 3.4.2. Identifying consistent events . ... 40 3.4.3. Softwareinjections . 41 3.5. Summary ................................... 42
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