Topics in Gravitational-Wave Physics

While the astrophysics community is on the brink of detecting the first gravitational-wave signal [1, 2, 3], efforts continue to improve the existing detectors and develop new technologies for future-generation detectors. In parallel, the need is rapidly growing for improved analyzes and interpretations of the science data that comes from the detectors. This thesis contributes to these issues with research results related to (i) the design of possible upgrades for the Advanced detectors for the ground-based Laser Interferometer Gravitational-wave Observatory (AdvLIGO) [4, 5, 6, 7] (i.e. for improved versions of the initial LIGO detectors [9, 10]), and (ii) future data analysis techniques for the Laser Interferometer Space Antenna (LISA) [11, 12] (a planned space-based gravitational-wave mission). More specifically: Currently, an international array of first-generation ground-based, laser-interferometer gravitational-wave detectors (consisting of LIGO, VIRGO [13, 14], GEO600 [15, 16] and TAMA300 [17]) is actively searching for gravitational waves in the frequency band (10 Hz { 10 kHz), with peak sensitivity at a few hundred Hertz. On September the 30th, 2007, the initial LIGO interferometers finished their Science Run 5 (S5) [18], which collected one year of triple coincidence data at the interferometers' design sensitivity. The next version of LIGO's interferometers, called Enhanced LIGO [19], with amplitude sensitivity improved by a factor about 2 (event rate increased by a factor 2³≃10), is being implemented and will collect data in science mode in 2009-10. Advanced LIGO is expected to begin operations around 2013. At the end of commissioning, it will have a factor ten better amplitude sensitivity than initial LIGO, which translates to a thousand-fold increase in event rate. Therefore, just a few hours of observations by AdvLIGO will be worth the entire lifetime of initial LIGO. Another significant advantage of the Advanced LIGO design is that it will allow tuning of the sensitivity as a function of frequency, so as to optimize searches for specific astrophysical sources with specific expected spectra. LISA, the first system of space-based gravitational-wave interferometers, is planned for launch and science operation in 2018 or perhaps somewhat later, depending on political developments. It will operate with peak sensitivity around a few milliHertz and should detect galore of signals simultaneously. The lifetime of the mission is expected to be around five years. This thesis consists of four chapters: this introductory chapter, two chapters (2 and 3) dealing with research relevant to the technology for a possible upgrade of Advanced LIGO, and one chapter (4) relevant to data analysis for LISA. Specifically: Chapter 2 elucidates the influence of the shape (power profile) of an interferometer's arm-cavity light beams on a tilt instability, in which the tilt of an arm cavity mirror is driven by light pressure. Chapter 3 proves a duality relation between arm cavities with almost at mirrors (as originally planned for AdvLIGO) and cavities with almost concentric spherical mirrors (a design change that has been made, to control the tilt instability). I discovered and used this duality relation numerically in the research reported in Chapter 2, but only later, in collaboration with others, did I prove the duality relation analytically (Chapter 3). Chapter 4 reports details of and results from a Mock LISA Data Challenge in which gravitational wave signals from (mock) supermassive black-hole binaries were sought and found in simulated LISA data.</p

Estimate of Tilt Instability of Mesa-Beam and Gaussian-Beam Modes for Advanced LIGO

Sidles and Sigg have shown that advanced LIGO interferometers will encounter a serious tilt instability, in which symmetric tilts of the mirrors of an arm cavity cause the cavity's light beam to slide sideways, so its radiation pressure exerts a torque that increases the tilt. Sidles and Sigg showed that the strength T of this torque is 26.2 times greater for advanced LIGO's baseline cavities -- nearly flat spherical mirrors which support Gaussian beams (``FG'' cavities), than for nearly concentric spherical mirrors which support Gaussian beams with the same diffraction losses as the baseline case -- ``CG'' cavities: T^{FG}/T^{CG} = 26.2. This has motivated a proposal to change the baseline design to nearly concentric, spherical mirrors. In order to reduce thermoelastic noise in advanced LIGO, O'Shaughnessy and Thorne have proposed replacing the spherical mirrors and their Gaussian beams by ``Mexican-Hat'' (MH) shaped mirrors which support flat-topped, ``mesa'' shaped beams. In this paper we compute the tilt-instability torque for advanced-LIGO cavities with nearly flat MH mirrors and mesa beams (``FM'' cavities) and nearly concentric MH mirrors and mesa beams (``CM'' cavities), with the same diffraction losses as in the baseline FG case. We find that the relative sizes of the restoring torques are T^{CM}/T^{CG} = 0.91, T^{FM}/T^{CG} = 96, T^{FM}/T^{FG} = 3.67. Thus, the nearly concentric MH mirrors have a weaker tilt instability than any other configuration. Their thermoelastic noise is the same as for nearly flat MH mirrors, and is much lower than for spherical mirrors.Comment: 10 pages, 3 figures, 4 table

Discovery of a 270 Hz X-Ray Burst Oscillation in the X-Ray Dipper 4U 1916-053

We report the discovery of a highly coherent oscillation in a type-I X-ray burst observed from 4U 1916-053 by the Rossi X-ray Timing Explorer (RXTE). The oscillation was most strongly detected approx. 1 s after the burst onset at a frequency of 269.3 Hz, and it increased in frequency over the following 4 seconds of the burst decay to a maximum of around 272 Hz. The total measured drift of 3.58 +/- 0.41 Hz (1 sigma) represents the largest fractional change in frequency (1.32 +/- 0.15 %) yet observed in any burst oscillation. If the asymptotic frequency of the oscillation is interpreted in terms of a decoupled surface burning layer, the implied neutron star spin period is around 3.7 ms. However, the expansion of the burning layer required to explain frequency drift during the burst is around 80 m, substantially larger than expected theoretically (assuming rigid rotation). The oscillation was not present in the persistent emission before the burst, nor in the initial rise. When detected its amplitude was 6-12% (RMS) with a roughly sinusoidal profile. The burst containing the oscillation showed no evidence for photospheric radius expansion, while at least 5 of the other 9 bursts observed from the source by RXTE during 1996 and 1998 did. No comparable oscillations were detected in the other bursts. A pair of kilohertz quasi-periodic oscillations (QPOs) has been previously reported from this source with a mean separation of 348 +/- 12 Hz. 4U 1916-053 is the first example of a source where the burst oscillation frequency is significantly smaller than the frequency separation of the kHz QPOs.Comment: 8 pages, 2 figures, 2 tables; accepted for ApJ Letter

A duality relation between non-spherical mirror optical cavities and its application to gravitational-wave detectors

In this paper, we analytically prove a unique duality relation between the eigenspectra of paraxial optical cavities with non-spherical mirrors: a one-to-one mapping between eigenmodes and eigenvalues of cavities deviating from flat mirrors by $h(\vec{r})$ and cavities deviating from concentric mirrors by $-h(\vec{r})$, where $h$ need not be a small perturbation. We then illustrate its application to optical cavities, proposed for advanced interferometric gravitational-wave detectors, where the mirrors are designed to support beams with rather flat intensity profiles over the mirror surfaces. This unique mapping might be very useful in future studies of alternative optical designs for advanced gravitational waves interferometers or experiments employing optical cavities with non-standard mirrors.Comment: 26 pages, 5 figures, minor changes matching the published versio

The Mock LISA Data Challenges: from Challenge 1B to Challenge 3

The Mock LISA Data Challenges are a programme to demonstrate and encourage the development of LISA data-analysis capabilities, tools and techniques. At the time of this workshop, three rounds of challenges had been completed, and the next was about to start. In this article we provide a critical analysis of entries to the latest completed round, Challenge 1B. The entries confirm the consolidation of a range of data-analysis techniques for Galactic and massive--black-hole binaries, and they include the first convincing examples of detection and parameter estimation of extreme--mass-ratio inspiral sources. In this article we also introduce the next round, Challenge 3. Its data sets feature more realistic waveform models (e.g., Galactic binaries may now chirp, and massive--black-hole binaries may precess due to spin interactions), as well as new source classes (bursts from cosmic strings, isotropic stochastic backgrounds) and more complicated nonsymmetric instrument noise.Comment: 20 pages, 3 EPS figures. Proceedings of the 12th Gravitational Wave Data Analysis Workshop, Cambridge MA, 13--16 December 2007. Typos correcte

Discovery of a 270 Hz X-ray burst oscillation in the X-ray dipper 4U 1916-053

Submitted to ApJ LettersConsiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7 Rome; International School for Advanced Studies, Via Beirut, 7 Trieste / CNR - Consiglio Nazionale delle RichercheSIGLEITItal