We examine various topics involved in the creation of accurate theoretical gravitational waveforms from binary black-hole systems.
\r\n\r\nIn Chapter 2 a pseudospectral numerical code is applied to a set of analytic or near-analytic solutions to Einstein's equations which comprise a testbed for numerical-relativity codes. We then discuss methods for extracting gravitational-wave data from numerical simulations of black-hole binary systems, and introduce a practical technique for obtaining the asymptotic form of that data from finite simulation domains in Chapter 3. A formula is also developed to estimate the size of near-field effects from a compact binary. In Chapter 4 the extrapolated data is then compared to post-Newtonian (PN) approximations. We compare the phase and amplitude of the numerical waveform to a collection of Taylor approximants, cross-validating the numerical and PN waveforms, and investigating the regime of validity of the PN waveforms. Chapter 5 extends that comparison to include Pad\u00e9 and effective-one-body models, and investigates components of the PN models. In each case, a careful accounting is made of errors. Finally, we construct a long post-Newtonian\u2013numerical hybrid waveform and evaluate the performance of LIGO's current data-analysis methods with it. We suggest certain optimizations of those methods, including extending the range of template mass ratios to unphysical ranges for certain values of the total mass, and a simple analytic cutoff frequency for the templates which results in nearly optimal matches for both Initial and Advanced LIGO.
\r\n", "doi": "10.7907/7NSM-RW43", "publication_date": "2009", "thesis_type": "phd", "thesis_year": "2009" }, { "id": "thesis:1987", "collection": "thesis", "collection_id": "1987", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05232007-115433", "primary_object_url": { "basename": "thesisSubmitted.pdf", "content": "final", "filesize": 2306898, "license": "other", "mime_type": "application/pdf", "url": "/1987/1/thesisSubmitted.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Topics in Gravitational-Wave Physics", "author": [ { "family_name": "Lovelace", "given_name": "Geoffrey Mark", "orcid": "0000-0002-7084-1070", "clpid": "Lovelace-Geoffrey-Mark" } ], "thesis_advisor": [ { "family_name": "Thorne", "given_name": "Kip S.", "orcid": "0000-0002-9475-4318", "clpid": "Thorne-K-S" } ], "thesis_committee": [ { "family_name": "Thorne", "given_name": "Kip S.", "orcid": "0000-0002-9475-4318", "clpid": "Thorne-K-S" }, { "family_name": "Libbrecht", "given_name": "Kenneth George", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" }, { "family_name": "Lindblom", "given_name": "Lee A.", "orcid": "0000-0002-3018-1098", "clpid": "Lindblom-L" }, { "family_name": "Phinney", "given_name": "E. Sterl", "orcid": "0000-0002-9656-4032", "clpid": "Phinney-E-S" } ], "local_group": [ { "literal": "TAPIR" }, { "literal": "Astronomy Department" }, { "literal": "LIGO" }, { "literal": "div_pma" } ], "abstract": "Together with ongoing experimental efforts to detect gravitational waves, several fronts of theoretical research are presently being pursued, including second-generation detector design, data analysis, and numerical-relativity simulations of sources. This thesis presents a study in each of these topics: i) The noise in the most sensitive frequency bands in second-generation ground-based gravitational-wave interferometers is dominated by the thermal noise of the test masses. One way to reduce test-mass thermal noise is to modify shape of the laser beam so that it better averages over the thermal fluctuations. When edge effects are neglected, the test-mass thermal noise is related to the beam shape by simple scaling laws. This thesis presents a rigorous derivation of these laws, along with estimates of the errors made by neglecting edge effects. ii) An important class of gravitational-wave sources for space-based gravitational-wave interferometers is extreme-mass-ratio inspirals (EMRIs). These are binaries in which an object of a few solar masses spirals into a (typically million-solar-mass) supermassive black hole (or, if any exist, other type of massive body). Ryan (1995) proved that, under certain simplifying assumptions, the spacetime geometry is redundantly encoded in EMRI waves. One of Ryan's assumptions was negligible tidal coupling. After first finding that only the time-varying part of the induced tide is unambiguously defined when the central body is a black hole, this thesis extends Ryan's theorem by showing that both the spacetime geometry and details of the tidal coupling are encoded in EMRI waves. iii) Merging black holes with comparable masses are important sources of gravitational waves for ground-based detectors. The gravitational waves near the time of merger can only be predicted by numerically solving the Einstein equations. Initial data in numerical simulations must contain the desired physical content but also satisfy the Einstein constraint equations. But conventional binary-black-hole initial data has physical flaws: a nonzero orbital eccentricity and an initial, unphysical pulse of spurious gravitational radiation. Using the Caltech-Cornell pseudospectral code, this thesis develops and implements methods to reduce both of these effects.
", "doi": "10.7907/94TE-3B59", "publication_date": "2007", "thesis_type": "phd", "thesis_year": "2007" }, { "id": "thesis:2073", "collection": "thesis", "collection_id": "2073", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05252007-143511", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 1949530, "license": "other", "mime_type": "application/pdf", "url": "/2073/1/thesis.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Topics in Numerical Relativity: The Periodic Standing-Wave Approximation, the Stability of Constraints in Free Evolution, and the Spin of Dynamical Black Holes", "author": [ { "family_name": "Owen", "given_name": "Robert Philip", "clpid": "Owen-Robert-Philip" } ], "thesis_advisor": [ { "family_name": "Lindblom", "given_name": "Lee A.", "orcid": "0000-0002-3018-1098", "clpid": "Lindblom-L" }, { "family_name": "Price", "given_name": "Richard H.", "orcid": "0000-0001-8955-949X", "clpid": "Price-R-H" }, { "family_name": "Thorne", "given_name": "Kip S.", "orcid": "0000-0002-9475-4318", "clpid": "Thorne-K-S" } ], "thesis_committee": [ { "family_name": "Lindblom", "given_name": "Lee A.", "orcid": "0000-0002-3018-1098", "clpid": "Lindblom-L" }, { "family_name": "Cutler", "given_name": "Curt J.", "orcid": "0000-0002-2080-1468", "clpid": "Cutler-C-J" }, { "family_name": "Libbrecht", "given_name": "Kenneth George", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" }, { "family_name": "Thorne", "given_name": "Kip S.", "orcid": "0000-0002-9475-4318", "clpid": "Thorne-K-S" } ], "local_group": [ { "literal": "Astronomy Department" }, { "literal": "div_pma" } ], "abstract": "This thesis concerns numerical relativity, the attempt to study Einstein's theory of gravitation using numerical discretization. The goal of the field, the study of gravitational dynamics in cases where symmetry reduction or perturbation theory are not possible, finally seems to be coming to fruition, at least for the archetypal problem of the inspiral and coalescence of binary black hole systems. This thesis presents three episodes that each bear some relationship to this story.
\r\n\r\nChapters 2 and 3 present previously published work in collaboration with Richard Price and others on the so-called periodic standing-wave (PSW) approximation for binary inspiral. The approximation is to balance outgoing radiation with incoming radiation, stabilizing the orbit and making the problem stationary in a rotating frame. Chapters 2 and 3 apply the method to the problem of co-orbiting charges coupled to a nonlinear scalar field in three dimensions.
\r\n\r\nChapters 4, 5, and 6 concern the stability of constraint fields in conventional numerical relativity simulations. Chapter 4 (also previously published work, in collaboration with the Caltech numerical relativity group, along with Michael Holst and Lawrence Kidder) presents a method for immediately correcting violations of constraints after they have arisen. Chapters 5 and 6 present methods to \"damp\" away constraint violations dynamically in two specific contexts. Chapter 5 (previously published work in collaboration with the Caltech numerical relativity group and Lawrence Kidder) presents a first-order linearly degenerate symmetric hyperbolic representation of Einstein's equations in generalized harmonic gauge. A representation is presented that stabilizes all constraints, including those that appear when the system is written in first-order form. Chapter 6 presents a generalization of the Kidder-Scheel-Teukolsky evolution systems that provides much-improved stability. This is investigated with numerical simulations of a single black hole spacetime.
\r\n\r\nFinally, chapter 7 presents work in progress to implement code to calculate the spin of black holes in numerical simulations. This requires a well-defined generalization of the concept of \"rotation generators\" on topological two-spheres that may not have any true Killing vectors. I present a new method for defining these fields, and results of a numerical code that computes them.
", "doi": "10.7907/464A-4Y76", "publication_date": "2007", "thesis_type": "phd", "thesis_year": "2007" }, { "id": "thesis:2007", "collection": "thesis", "collection_id": "2007", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05242006-025220", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 3217286, "license": "other", "mime_type": "application/pdf", "url": "/2007/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Topics of LIGO Physics: Template Banks for the Inspiral of Precessing, Compact Binaries, and Design of the Signal-Recycling Cavity for Advanced LIGO", "author": [ { "family_name": "Pan", "given_name": "Yi", "clpid": "Pan-Yi" } ], "thesis_advisor": [ { "family_name": "Thorne", "given_name": "Kip S.", "orcid": "0000-0002-9475-4318", "clpid": "Thorne-K-S" } ], "thesis_committee": [ { "family_name": "Thorne", "given_name": "Kip S.", "orcid": "0000-0002-9475-4318", "clpid": "Thorne-K-S" }, { "family_name": "Weinstein", "given_name": "Alan Jay", "orcid": "0000-0002-0928-6784", "clpid": "Weinstein-Alan-J-Physics" }, { "family_name": "Lindblom", "given_name": "Lee A.", "orcid": "0000-0002-3018-1098", "clpid": "Lindblom-L" }, { "family_name": "Whitcomb", "given_name": "Stanley E.", "clpid": "Whitcomb-S-E" } ], "local_group": [ { "literal": "TAPIR" }, { "literal": "Astronomy Department" }, { "literal": "LIGO" }, { "literal": "div_pma" } ], "abstract": "In the next decade, the detection of gravitational-wave signals by ground-based laser interferometric detectors (e.g., the Laser Interferometer Gravitational-Wave Observatory, or LIGO) will provide new information on the structure and dynamics of compact objects such as neutron stars (NS) and black holes (BH), both isolated and in binary systems. Efforts to detect the intrinsically weak gravitational-wave signals involve the development of high-quality detectors, the precise modeling of expected signals, and the development of efficient data analysis techniques. This thesis concerns two topics in these areas: methods to detect signals from the inspiral of precessing NS-BH and BH-BH binaries, and the design of the signal-recycling cavity for Advanced LIGO (the second generation LIGO detector).
\r\n\r\nThe detection of signals from the inspiral of precessing binaries using the standard matched filter technique, is complicated by the large number (12 at least) of parameters required to describe the complex orbital-precession dynamics of the binary and the consequent modulations of the gravitational-wave signals. To extract these signals from the noisy detector output requires a discrete bank of a huge number of signal templates that cover the 12-dimensional parameter space; and processing data with all these templates requires computational power far exceeding what is available with current technology. To solve this problem, Buonanno, Chen, and Vallisneri (BCV) proposed the use of detection template families (DTFs) --- phenomenological templates that are capable of mimicking rather accurately the inspiral waveform calculated by the post-Newtonian (PN) approach, while having a simpler functional form to reduce the computational cost. In particular, BCV proposed the so called BCV2 DTF for the precessing-binary inspiral, which has 12 parameters (most of them phenomenological). Of these, 8 are extrinsic parameters that can be searched over analytically, and only four of them are intrinsic parameters that need be searched over in a numerical one-by-one manner. The signal-matching efficiency of the BCV2 DTF has been shown to be satisfactory for signals from comparable mass BH-BH binaries.
\r\n\r\nIn Chapter 2 (in collaboration with Alessandra Buonanno, Yanbei Chen, Hideyuki Tagoshi, and Michele Vallisneri), I test the signal-matching efficiency of the BCV2 DTF for signals from a wide sample of precessing BH-BH and NS-BH binaries that covers the parameter range of interest for LIGO and other ground-based gravitational-wave detectors, and I study the mapping between the physical and phenomenological parameters. My colleagues and I calculate the template-match metric, propose the template-placement strategy in the intrinsic parameter space and estimate the number of templates needed (and thus equivalently the computational cost) to cover the parameter space. We also propose a so called BCV2P DTF that replaces the phenomenological parameters in the BCV2 DTF by physical parameters, which can be used to estimate the actual parameters of the binary that emitted any detected signal.
\r\n\r\nIn Chapters 3 and 4 (in collaboration with Alessandra Buonanno, Yanbei Chen, and Michele Vallisneri), I investigate a physical template family (PTF) suggested by BCV. This PTF uses the most accurate known waveforms for inspiraling, precessing binaries (the adiabatic PN waveforms), formulated using a new precessing convention such that five parameters become extrinsic. PTF has the obvious advantages over the DTFs of a perfect match with target signals, a lower false-alarm rate at fixed threshold, and an ability to directly estimate the physical parameters of any detected signal.
\r\n\r\nIn Chapter 3, we focus on the simpler single-spin binaries in which only four parameters out of nine remain intrinsic. We propose a two-stage scheme to search over the five extrinsic parameters quickly, and investigate the false-alarm statistics in each of the two stages. We define and calculate the metric of the full template space, and the projected metric and average metric of the intrinsic parameter subspace, and use these metrics to develop the method of template placement. Finally, we estimate that the number of templates needed to detect single-spin binary inspirals is within the reach of the current available computational power.
\r\n\r\nIn Chapter 4, we generalize the use of the single-spin PTF to double-spin binaries, based on the fact that most double-spin binaries have similar dynamics to the single-spin ones. Since the PTF in this case is, strictly speaking, only quasi-physical, we test and eventually find satisfactory signal-matching performance. We also investigate, both analytically and numerically, the difference between the single-spin and double-spin dynamics, and gain an intuition into where in the parameter space the PTF works well. We estimate the number of templates needed to cover all BH-BH and NS-BH binaries of interest to ground-based detectors, which turns out to be roughly at the limit of currently available computational power. Since the PTF is not exactly physical for double-spin binaries, it introduces systematic errors in parameter estimation. We investigate these, and find that they are either comparable to or overwhelmed by statistical errors, for events with moderate signal-to-noise ratio. BCV and I are currently systematically investigating parameter estimation with the PTF.
\r\n\r\nThe second part of this thesis concerns the design of the signal-recycling cavity for Advanced LIGO. In the planned Advanced-LIGO-detector upgrades from the first-generation LIGO, a signal-recycling mirror (SRM) is introduced at the dark output port. This SRM forms a signal-recycling cavity (SRC) with the input test masses. This signal-recycling design offers several advantages and brings new physics to LIGO. However, there is a problem in the current design of the SRC: the SRC is nearly degenerate, i.e., it does not distinguish transverse optical modes; and as a result, mode coupling due to mirror deformation will strongly reduce the optical power in the fundamental mode, and thus reduce the signal strength, which is roughly proportional to it.
\r\n\r\nIn Chapter 5, I investigate this problem using a numerical simulation of the propagation of the optical field in an Advanced LIGO interferometer. I find that if the current degenerate design for the SRC is used, there will be a serious and perhaps unattainable constraint on the magnitude of mirror deformations, in order to keep the reduction of signal-to-noise ratio below a few percent. This conclusion is consistent with previous order of magnitude estimates. This constraint poses practical difficulties on the quality of mirror polishing and the control of thermal aberration of the mirrors. Based on my simulation results, for a range of degeneracies of the SRC, I find the optimal level of degeneracy, which minimizes the reduction of signal-to-noise ratio. That optimum is nearly non-degenerate. I also discuss possible modifications to the current design that can achieve this optimal degeneracy.
", "doi": "10.7907/TJB1-PQ24", "publication_date": "2006", "thesis_type": "phd", "thesis_year": "2006" }, { "id": "thesis:3017", "collection": "thesis", "collection_id": "3017", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-08052003-161044", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 1513234, "license": "other", "mime_type": "application/pdf", "url": "/3017/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Topics in Gravitational-Wave Astronomy", "author": [ { "family_name": "O'Shaughnessy", "given_name": "Richard William", "orcid": "0000-0001-5832-8517", "clpid": "O'Shaughnessy-Richard-William" } ], "thesis_advisor": [ { "family_name": "Thorne", "given_name": "Kip S.", "orcid": "0000-0002-9475-4318", "clpid": "Thorne-K-S" } ], "thesis_committee": [ { "family_name": "Thorne", "given_name": "Kip S.", "orcid": "0000-0002-9475-4318", "clpid": "Thorne-K-S" }, { "family_name": "Libbrecht", "given_name": "Kenneth George", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" }, { "family_name": "Lindblom", "given_name": "Lee A.", "orcid": "0000-0002-3018-1098", "clpid": "Lindblom-L" }, { "family_name": "Kamionkowski", "given_name": "Marc P.", "orcid": "0000-0001-7018-2055", "clpid": "Kamionkowski-M-P" }, { "family_name": "Phinney", "given_name": "E. Sterl", "orcid": "0000-0002-9656-4032", "clpid": "Phinney-E-S" } ], "local_group": [ { "literal": "TAPIR" }, { "literal": "Astronomy Department" }, { "literal": "LIGO" }, { "literal": "div_pma" } ], "abstract": "Both the Laser Interferometer Gravitational Wave Observatory (LIGO) and the Laser Interferometer Space Antenna (LISA) will over the next decade detect gravitational waves emitted by the motion of compact objects (e.g. black hole and neutron star binaries). This thesis presents methods to improve (i) LIGO detector quality, (ii) our knowledge of waveforms for certain LIGO and LISA sources, and (iii) models for the rate of detectability of a particular LISA source.
\r\n\t\t\t\t\t\t\t\t\t \r\n1) Plunge of compact object into a supermassive black hole: LISA should detect many inspirals of compact objects into supermassive black holes (~ 10\u2075-10\u2077 M\u2299). Since the inspiral of each compact object terminates shortly after the inspiralling object reaches its last stable orbit, the late-stage inspiral waveform provides insight into the location of the last stable orbit and strong-field relativity. I discovered that while LISA will easily see the overall inspiral (consisting of many cycles before plunge), the present LISA design will just miss detecting the waves emitted from the transition from inspiral to plunge.
\r\n\r\n2) Scheme to reduce thermoelastic noise in advanced LIGO: After its first upgrade, LIGO will have its sensitivity limited by thermoelastic noise. [Thermoelastic noise occurs because milimeter-scale thermal fluctuations in the mirror bulk expand and contract, causing the mirror surface to shimmer.] The interferometer's sensitivity could be enhanced substantially by reducing thermoelastic noise. In collaboration with Kip Thorne, Erika d'Ambrosio, Sergey Vyatchanin, and Sergey Strigin, I developed a proposal to reduce thermoelastic noise in advanced-LIGO by switching the LIGO cavity optics from simple spherical mirrors to a new, Mexican-hat shape.
\r\n\t\t\t\t\t\t\t\t\t \r\n3) Geometric-optics-based analysis of stability of symmetric-hyperbolic formulations of Einstein's equations: Einstein's equations must be evolved numerically to predict accurate waveforms for the late stages of binary black hole inspiral and merger. But no matter which representation of Einstein's equations is used, numerical simulations rarely run long. For examle, for first-order symmetric-hyperbolic (FOSH) formulations of Einstein's evolution equations, sometimes exact but unphysical solutions grow so large that the evolution fails. For FOSH formulations, I found easily-understood solutions (wave packets) and used them to predict which formulations will be particularly ill-behaved.
", "doi": "10.7907/4C1K-VZ17", "publication_date": "2004", "thesis_type": "phd", "thesis_year": "2004" }, { "id": "thesis:8122", "collection": "thesis", "collection_id": "8122", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:03112014-101628149", "type": "thesis", "title": "Dynamical Stability of Nascent Neutron Stars", "author": [ { "family_name": "Liu", "given_name": "Yuk Tung", "clpid": "Liu-Yuk-Tung" } ], "thesis_advisor": [ { "family_name": "Thorne", "given_name": "Kip S.", "orcid": "0000-0002-9475-4318", "clpid": "Thorne-K-S" } ], "thesis_committee": [ { "family_name": "Thorne", "given_name": "Kip S.", "orcid": "0000-0002-9475-4318", "clpid": "Thorne-K-S" }, { "family_name": "Blandford", "given_name": "Roger D.", "clpid": "Blandford-R-D" }, { "family_name": "Libbrecht", "given_name": "Kenneth George", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" }, { "family_name": "Lindblom", "given_name": "Lee A.", "orcid": "0000-0002-3018-1098", "clpid": "Lindblom-L" } ], "local_group": [ { "literal": "TAPIR" }, { "literal": "Astronomy Department" }, { "literal": "div_pma" } ], "abstract": "This thesis presents a study of the dynamical stability of nascent neutron stars resulting from the\r\naccretion induced collapse of rapidly rotating white dwarfs.
\r\n\r\nChapter 2 and part of Chapter 3 study the equilibrium models for these neutron stars. They are\r\nconstructed by assuming that the neutron stars have the same masses, angular momenta, and specific\r\nangular momentum distributions as the pre-collapse white dwarfs. If the pre-collapse white dwarf is\r\nrapidly rotating, the collapsed object will contain a high density central core of size about 20 km,\r\nsurrounded by a massive accretion torus extending to hundreds of kilometers from the rotation axis.\r\nThe ratio of the rotational kinetic energy to gravitational binding energy, \u03b2, of these neutron stars\r\nis all found to be less than 0.27.
\r\n\r\nChapter 3 studies the dynamical stability of these neutron stars by numerically evolving the\r\nlinearized hydrodynamical equations. A dynamical bar-mode instability is observed when the \u03b2 of\r\nthe star is greater than the critical value \u03b2d \u2248 0.25. It is expected that the unstable mode will\r\npersist until a substantial amount of angular momentum is carried away by gravitational radiation.\r\nThe detectability of these sources is studied and it is estimated that LIGO II is unlikely to detect\r\nthem unless the event rate is greater than 10-6/year/galaxy.
\r\n\r\nAll the calculations on the structure and stability of the neutron stars in Chapters 2 and 3\r\nare carried out using Newtonian hydrodynamics and gravity. Chapter 4 studies the relativistic\r\neffects on the structure of these neutron stars. New techniques are developed and used to construct\r\nneutron star models to the first post-Newtonian (1PN) order. The structures of the 1PN models\r\nare qualitatively similar to the corresponding Newtonian models, but the values of \u03b2 are somewhat\r\nsmaller. The maximum \u03b2 for these 1PN neutron stars is found to be 0.24, which is 8% smaller than\r\nthe Newtonian result (0.26). However, relativistic effects will also change the critical value \u03b2d. A\r\ndetailed post-Newtonian stability analysis has yet to be carried out to study the relativistic effects\r\non the dynamical stability of these neutron stars.
", "doi": "10.7907/61ZS-XQ28", "publication_date": "2003", "thesis_type": "phd", "thesis_year": "2003" }, { "id": "thesis:8122", "collection": "thesis", "collection_id": "8122", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:03112014-101628149", "type": "thesis", "title": "Dynamical Stability of Nascent Neutron Stars", "author": [ { "family_name": "Liu", "given_name": "Yuk Tung", "clpid": "Liu-Yuk-Tung" } ], "thesis_advisor": [ { "family_name": "Thorne", "given_name": "Kip S.", "orcid": "0000-0002-9475-4318", "clpid": "Thorne-K-S" } ], "thesis_committee": [ { "family_name": "Thorne", "given_name": "Kip S.", "orcid": "0000-0002-9475-4318", "clpid": "Thorne-K-S" }, { "family_name": "Blandford", "given_name": "Roger D.", "clpid": "Blandford-R-D" }, { "family_name": "Libbrecht", "given_name": "Kenneth George", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" }, { "family_name": "Lindblom", "given_name": "Lee A.", "orcid": "0000-0002-3018-1098", "clpid": "Lindblom-L" } ], "local_group": [ { "literal": "TAPIR" }, { "literal": "Astronomy Department" }, { "literal": "div_pma" } ], "abstract": "This thesis presents a study of the dynamical stability of nascent neutron stars resulting from the\r\naccretion induced collapse of rapidly rotating white dwarfs.
\r\n\r\nChapter 2 and part of Chapter 3 study the equilibrium models for these neutron stars. They are\r\nconstructed by assuming that the neutron stars have the same masses, angular momenta, and specific\r\nangular momentum distributions as the pre-collapse white dwarfs. If the pre-collapse white dwarf is\r\nrapidly rotating, the collapsed object will contain a high density central core of size about 20 km,\r\nsurrounded by a massive accretion torus extending to hundreds of kilometers from the rotation axis.\r\nThe ratio of the rotational kinetic energy to gravitational binding energy, \u03b2, of these neutron stars\r\nis all found to be less than 0.27.
\r\n\r\nChapter 3 studies the dynamical stability of these neutron stars by numerically evolving the\r\nlinearized hydrodynamical equations. A dynamical bar-mode instability is observed when the \u03b2 of\r\nthe star is greater than the critical value \u03b2d \u2248 0.25. It is expected that the unstable mode will\r\npersist until a substantial amount of angular momentum is carried away by gravitational radiation.\r\nThe detectability of these sources is studied and it is estimated that LIGO II is unlikely to detect\r\nthem unless the event rate is greater than 10-6/year/galaxy.
\r\n\r\nAll the calculations on the structure and stability of the neutron stars in Chapters 2 and 3\r\nare carried out using Newtonian hydrodynamics and gravity. Chapter 4 studies the relativistic\r\neffects on the structure of these neutron stars. New techniques are developed and used to construct\r\nneutron star models to the first post-Newtonian (1PN) order. The structures of the 1PN models\r\nare qualitatively similar to the corresponding Newtonian models, but the values of \u03b2 are somewhat\r\nsmaller. The maximum \u03b2 for these 1PN neutron stars is found to be 0.24, which is 8% smaller than\r\nthe Newtonian result (0.26). However, relativistic effects will also change the critical value \u03b2d. A\r\ndetailed post-Newtonian stability analysis has yet to be carried out to study the relativistic effects\r\non the dynamical stability of these neutron stars.
", "doi": "10.7907/61ZS-XQ28", "publication_date": "2003", "thesis_type": "phd", "thesis_year": "2003" }, { "id": "thesis:2226", "collection": "thesis", "collection_id": "2226", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05292002-113750", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 2118011, "license": "other", "mime_type": "application/pdf", "url": "/2226/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Modeling and Detecting Gravitational Waves from Compact Stellar Objects", "author": [ { "family_name": "Vallisneri", "given_name": "Michele", "orcid": "0000-0002-4162-0033", "clpid": "Vallisneri-Michele" } ], "thesis_advisor": [ { "family_name": "Thorne", "given_name": "Kip S.", "orcid": "0000-0002-9475-4318", "clpid": "Thorne-K-S" } ], "thesis_committee": [ { "family_name": "Thorne", "given_name": "Kip S.", "orcid": "0000-0002-9475-4318", "clpid": "Thorne-K-S" }, { "family_name": "Libbrecht", "given_name": "Kenneth George", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" }, { "family_name": "Lindblom", "given_name": "Lee A.", "orcid": "0000-0002-3018-1098", "clpid": "Lindblom-L" }, { "family_name": "Kamionkowski", "given_name": "Marc P.", "orcid": "0000-0001-7018-2055", "clpid": "Kamionkowski-M-P" } ], "local_group": [ { "literal": "TAPIR" }, { "literal": "Astronomy Department" }, { "literal": "LIGO" }, { "literal": "div_pma" } ], "abstract": "In the next few years, the first detections of gravity-wave signals using Earth-based interferometric detectors will begin to provide precious new information about the structure, dynamics, and evolution of compact bodies, such as neutron stars and black holes, both isolated and in binary systems. The intrinsic weakness of gravity-wave signals requires a proactive approach to modeling the prospective sources and anticipating the shape of the signals that we seek to detect. Full-blown 3-D numerical simulations of the sources are playing and will play an important role in planning the gravity-wave data-analysis effort. This thesis explores the interplay between numerical source modeling and data analysis, looking closely at three case studies.
\r\n\r\n1. I evaluate the prospects for extracting equation-of-state information from neutron-star tidal disruption in neutron-star\u2013black-hole binaries with LIGO-II, and I estimate that the observation of disrupting systems at distances that yield about one event per year should allow the determination of the neutron-star radius to about 15%, which compares favorably to the currently available electromagnetic determinations.
\r\n\r\n2. In collaboration with Lee Lindblom and Joel Tohline, I perform numerical simulations of the nonlinear dynamics of the r-mode instability in young, rapidly spinning neutron stars, and I find evidence that nonlinear couplings to other modes will not pose a significant limitation to the growth of the r-mode amplitude.
\r\n\r\n3. In collaboration with Alessandra Buonanno and Yanbei Chen, I study the problem of detecting gravity waves from solar-mass black-hole\u2013black-hole binaries with LIGO-I, and I construct two families of detection templates that address the inadequacy of standard post-Newtonian theory to predict reliable waveforms for these systems.
\r\n", "doi": "10.7907/JN6M-BW40", "publication_date": "2002", "thesis_type": "phd", "thesis_year": "2002" }, { "id": "thesis:6771", "collection": "thesis", "collection_id": "6771", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:01202012-112836824", "primary_object_url": { "basename": "Alvi_k_2002.pdf", "content": "final", "filesize": 21554023, "license": "other", "mime_type": "application/pdf", "url": "/6771/1/Alvi_k_2002.pdf", "version": "v6.0.0" }, "type": "thesis", "title": "Topics in General Relativity: Binary Black Holes and Hyperbolic Formulations of Einstein's Equations", "author": [ { "family_name": "Alvi", "given_name": "Kashif Siddiq", "clpid": "Alvi-Kashif-Siddiq" } ], "thesis_advisor": [ { "family_name": "Thorne", "given_name": "Kip S.", "orcid": "0000-0002-9475-4318", "clpid": "Thorne-K-S" } ], "thesis_committee": [ { "family_name": "Thorne", "given_name": "Kip S.", "orcid": "0000-0002-9475-4318", "clpid": "Thorne-K-S" }, { "family_name": "Kamionkowski", "given_name": "Marc P.", "orcid": "0000-0001-7018-2055", "clpid": "Kamionkowski-M-P" }, { "family_name": "Lindblom", "given_name": "Lee A.", "orcid": "0000-0002-3018-1098", "clpid": "Lindblom-L" }, { "family_name": "Mabuchi", "given_name": "Hideo", "orcid": "0000-0002-5156-7678", "clpid": "Mabuchi-H" } ], "local_group": [ { "literal": "TAPIR" }, { "literal": "Astronomy Department" }, { "literal": "div_pma" } ], "abstract": "This thesis consists of three projects in general relativity on topics related to binary black holes\r\nand the gravitational waves they emit. The first project involves calculating a four-metric that is an approximate solution to Einstein's equations representing two widely separated nonrotating black holes in a circular orbit. This metric is constructed by matching a post-Newtonian metric to\r\ntwo tidally distorted Schwarzschild metrics using the framework of matched asymptotic expansions. The four-metric presented here provides physically realistic initial data that are tied to the binary's inspiral phase and can be evolved numerically to determine the gravitational wave output during the late stages of inspiral as well as the merger.
\r\n\r\nThe second project is on the tidal interaction of binary black holes during the inspiral phase. The holes' tidal distortion results in the flow of energy and angular momentum into or out of the holes in a process analogous to Newtonian tidal friction in a planet-moon system. The changes in the black holes' masses, spins, and horizon areas during inspiral are calculated for a circular binary with holes of possibly comparable masses. The absorption or emission of energy and angular momentum by the holes is shown to have a negligible influence on the binary 's orbital evolution when the holes have comparable masses. The tidal-interaction analysis presented in this thesis is applicable to a black hole in a binary with any companion body (e.g., a neutron star) that is well separated from\r\nthe hole.
\r\n\r\nThe final project is on first-order hyperbolic formulations of Einstein's equations, which are promising as a basis for numerical simulation of binary black holes. This thesis presents two first-order symmetrizable hyperbolic systems that include the lapse and shift as dynamical fields and have only physical characteristic speeds. The first system may be useful in numerical work; the second system allows one to show that any solution to Einstein's equations in any gauge can be obtained\r\nusing hyperbolic evolution of the entire metric, including the gauge fields.
", "doi": "10.7907/5S0S-MF65", "publication_date": "2002", "thesis_type": "phd", "thesis_year": "2002" } ]