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Academic Commons Search Resultsen-usSpinning Black Hole Pairs: Dynamics and Gravitational Waves
https://academiccommons.columbia.edu/catalog/ac:141916
Grossman, Rebecca I.http://hdl.handle.net/10022/AC:P:11791Fri, 11 Nov 2011 12:06:21 +0000Black hole binaries will be an important source of gravitational radiation for both ground-based and future space-based gravitational wave detectors. The study of such systems will offer a unique opportunity to test the dynamical predictions of general relativity when gravity is very strong. To date, most investigations of black hole binary dynamics have focused attention on restricted scenarios in which the black holes do not spin (and thus are confined to move in a plane) and/or in which they stay on quasi-circular orbits. However, spinning black hole pairs in eccentric orbits are now understood to be astrophysically equally important. These spinning binaries exhibit a range of complicated dynamical behaviors, even in the absence of radiation reaction. Their conservative dynamics is complicated by extreme perihelion precession compounded by spin-induced precession. Although the motion seems to defy simple decoding, we are able to quantitatively define and describe the fully three-dimensional motion of arbitrary mass-ratio binaries with at least one black hole spinning and expose an underlying simplicity. To do so, we untangle the dynamics by constructing an instantaneous orbital plane and showing that the motion captured in that plane obeys elegant topological rules. In this thesis, we apply the above prescription to two formal systems used to model black hole binaries. The first is defined by the conservative 3PN Hamiltonian plus spin-orbit coupling and is particularly suitable to comparable-mass binaries. The second is defined by geodesics of the Kerr metric and is used exclusively for extreme mass-ratio binaries. In both systems, we define a complete taxonomy for fully three-dimensional orbits. More than just a naming system, the taxonomy provides unambiguous and quantitative descriptions of the orbits, including a determination of the zoom-whirliness of any given orbit. Through a correspondence with the rational numbers, we are able to show that all of the qualitative features of the well-studied equatorial geodesic motion around Schwarzschild and Kerr black holes are also present in more general black hole binary systems. This includes so-called zoom-whirl behavior, which turns out to be unexpectedly prevalent in comparable-mass binaries in the strong-field regime just as it is for extreme mass-ratio binaries. In each case we begin by thoroughly cataloging the constant radius orbits which generally lie on the surface of a sphere and have acquired the name "spherical orbits". The spherical orbits are significant as they energetically frame the distribution of all orbits. In addition, each unstable spherical orbit is asymptotically approached by an orbit that whirls an infinite number of times, known as a homoclinic orbit. We further catalog the homoclinic trajectories, each of which is the infinite whirl limit of some part of the zoom-whirl spectrum and has a further significance as the separatrix between inspiral and plunge for eccentric orbits. We then show that there exists a discrete set of orbits that are geometrically closed n-leaf clovers in a precessing orbital plane. When viewed in the full three dimensions, these orbits do not close, but they are nonetheless periodic when projected into the orbital plane. Each n-leaf clover is associated with a rational number, q, that measures the degree of perihelion precession in the precessing orbital plane. The rational number q varies monotonically with the orbital energy and with the orbital eccentricity. Since any bound orbit can be approximated as near one of these periodic n-leaf clovers, this special set offers a skeleton that illuminates the structure of all bound orbits in both systems, in or out of the equatorial plane. A first significant conclusion that can be drawn from this analysis is that all generic orbits in the final stages of inspiral under gravitational radiation losses are characterized by precessing clovers with few leaves, and that no orbit will behave like the tightly precessing ellipse of Mercury. We close with a practical application of our taxonomy beyond the illumination of conservative dynamics. The numerical calculation of the first-order (adiabatic) approximation to radiatively evolving inspiral motion in extreme mass-ratio binaries is currently hindered by prohibitive computational cost. Motivated by this limitation, we explain how a judicious use of periodic orbits can dramatically expedite both that calculation and the generation of snapshot gravitational waves from geodesic sources.Physics, Astrophysicsrg420Physics and Astronomy (Barnard College), PhysicsDissertationsResults from the QUIET Q-Band Observing Season
https://academiccommons.columbia.edu/catalog/ac:141910
Dumoulin, Robert Nicolashttp://hdl.handle.net/10022/AC:P:11789Fri, 11 Nov 2011 11:43:46 +0000The Q/U Imaging ExperimenT (QUIET) is a ground-based telescope located in the high Atacama Desert in Chile, and is designed to measure the polarization of the Cosmic Microwave Background (CMB) in the Q and W frequency bands (43 and 95 GHz respectively) using coherent polarimeters. From 2008 October to 2010 December, data from more than 10,000 observing hours were collected, first with the Q-band receiver (2008 October to 2009 June) and then with the W-band receiver (until the end of the 2010 observing season). The QUIET data analysis effort uses two independent pipelines, one consisting of a maximum likelihood framework and the other consisting of a pseudo-C` framework. Both pipelines employ blind analysis methods, and each provides analysis of the data using large suites of null tests specific to the pipeline. Analysis of the Q-band receiver data was completed in November of 2010, confirming the only previous detection of the first acoustic peak of the EE power spectrum and setting competitive limits on the scalar-totensor ratio, r. In this dissertation, the results from the Q-band observing season using the maximum likelihood pipeline will be presented.Physics, AstrophysicsPhysicsDissertationsHEFT measurement of the hard X-ray size of the Crab Nebula and the hard X-ray optics of the Nuclear Spectroscopic Telescope Array (NuSTAR)
https://academiccommons.columbia.edu/catalog/ac:141649
An, Hongjunhttp://hdl.handle.net/10022/AC:P:11786Wed, 09 Nov 2011 16:55:00 +0000In this thesis, I discuss two topics: The High Energy Focusing Telescope (HEFT) and the Nuclear Spectroscopic Telescope Array (NuSTAR). HEFT is the first experiment done with imaging telescopes in the hard X-ray energy band (~20-70 keV). I briefly describe the instrument and the balloon campaign. The inflight calibration of the Point Spread Function (PSF) is done with a point source observation (~50 minutes of Cyg X-1 observation). With the PSF calibrated, I attempt to measuring the size of the Crab Nebula in this energy band. Analysis for aspect reconstruction, optical axis determination and the size measurement are described in detail. The size of the Crab Nebula is energy dependent due to synchrotron burn-off. The measurement of the size at different energies can provide us with important parameters for the pulsar wind nebula (PWN) model such as the magnetization parameter. With ~60 minutes of observation of the Crab Nebula with HEFT, I measure the size of the Crab Nebula at energies of 25-58 keV. The analysis technique I used for the size measurement here can be used for measuring the size of astrophysical objects whose sizes are comparable to the width of the PSF. NuSTAR is a satellite version of the HEFT experiment although the spatial and spectral resolution of the optics are improved significantly. And thus, the fabrication technique for the HEFT optics needed to be modified. I describe the fabrication technique for the NuSTAR optics, focusing on the epoxy selection and process development and the metrology systems for characterizing the figure of the glass surfaces.Physics, Astrophysicsha2153PhysicsDissertationsFrom Measure Zero to Measure Hero: Periodic Kerr Orbits and Gravitational Wave Physics
https://academiccommons.columbia.edu/catalog/ac:137822
Perez-Giz, Gabehttp://hdl.handle.net/10022/AC:P:11008Mon, 29 Aug 2011 12:13:35 +0000A direct observational detection of gravitational waves - perhaps the most fundamental prediction of a theory of curved spacetime - looms close at hand. Stellar mass compact objects spiraling into supermassive black holes have received particular attention as sources of gravitational waves detectable by space-based gravitational wave observatories. A well-established approach models such an extreme mass ratio inspirals (EMRI) as an adiabatic progression through a series of Kerr geodesics. Thus, the direct detection of gravitational radiation from EMRIs and the extraction of astrophysical information from those waveforms require a thorough knowledge of the underlying geodesic dynamics. This dissertation adopts a dynamical systems approach to the study of Kerr orbits, beginning with equatorial orbits. We deduce a topological taxonomy of orbits that hinges on a correspondence between periodic orbits and rational numbers. The taxonomy defines the entire dynamics, including aperiodic motion, since every orbit is in or near the periodic set. A remarkable implication of this periodic orbit taxonomy is that the simple precessing ellipse familiar from planetary orbits is not allowed in the strong-field regime. Instead, eccentric orbits trace out precessions of multi-leaf clovers in the final stages of inspiral. Furthermore, for any black hole, there is some orbital angular momentum value in the strong-field regime below which zoom-whirl behavior becomes unavoidable. We then generalize the taxonomy to help identify nonequatorial orbits whose radial and polar frequencies are rationally related, or in resonance. The thesis culminates by describing how those resonant orbits can be leveraged for an order of magnitude or more reduction in the computational cost of adiabatic order EMRI trajectories, which are so prohibitively expensive that no such relativistically correct inspirals have been generated to date.Physics, Astrophysics, Applied mathematicsgep1PhysicsDissertations