Citation
Pan, Yi (2006) Topics of LIGO physics: Template banks for the inspiral of precessing, compact binaries, and design of the signalrecycling cavity for Advanced LIGO. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd05242006025220
Abstract
In the next decade, the detection of gravitationalwave signals by groundbased laser interferometric detectors (e.g., the Laser Interferometer GravitationalWave 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 gravitationalwave signals involve the development of highquality 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 NSBH and BHBH binaries, and the design of the signalrecycling cavity for Advanced LIGO (the second generation LIGO detector).
The 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 orbitalprecession dynamics of the binary and the consequent modulations of the gravitationalwave signals. To extract these signals from the noisy detector output requires a discrete bank of a huge number of signal templates that cover the 12dimensional 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 postNewtonian (PN) approach, while having a simpler functional form to reduce the computational cost. In particular, BCV proposed the so called BCV2 DTF for the precessingbinary 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 onebyone manner. The signalmatching efficiency of the BCV2 DTF has been shown to be satisfactory for signals from comparable mass BHBH binaries.
In Chapter 2 (in collaboration with Alessandra Buonanno, Yanbei Chen, Hideyuki Tagoshi, and Michele Vallisneri), I test the signalmatching efficiency of the BCV2 DTF for signals from a wide sample of precessing BHBH and NSBH binaries that covers the parameter range of interest for LIGO and other groundbased gravitationalwave detectors, and I study the mapping between the physical and phenomenological parameters. My colleagues and I calculate the templatematch metric, propose the templateplacement 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.
In 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 falsealarm rate at fixed threshold, and an ability to directly estimate the physical parameters of any detected signal.
In Chapter 3, we focus on the simpler singlespin binaries in which only four parameters out of nine remain intrinsic. We propose a twostage scheme to search over the five extrinsic parameters quickly, and investigate the falsealarm 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 singlespin binary inspirals is within the reach of the current available computational power.
In Chapter 4, we generalize the use of the singlespin PTF to doublespin binaries, based on the fact that most doublespin binaries have similar dynamics to the singlespin ones. Since the PTF in this case is, strictly speaking, only quasiphysical, we test and eventually find satisfactory signalmatching performance. We also investigate, both analytically and numerically, the difference between the singlespin and doublespin 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 BHBH and NSBH binaries of interest to groundbased detectors, which turns out to be roughly at the limit of currently available computational power. Since the PTF is not exactly physical for doublespin 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 signaltonoise ratio. BCV and I are currently systematically investigating parameter estimation with the PTF.
The second part of this thesis concerns the design of the signalrecycling cavity for Advanced LIGO. In the planned AdvancedLIGOdetector upgrades from the firstgeneration LIGO, a signalrecycling mirror (SRM) is introduced at the dark output port. This SRM forms a signalrecycling cavity (SRC) with the input test masses. This signalrecycling 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.
In 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 signaltonoise 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 signaltonoise ratio. That optimum is nearly nondegenerate. I also discuss possible modifications to the current design that can achieve this optimal degeneracy.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  data analysis; false alarm; Gaussian mode 
Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Physics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  19 May 2006 
Record Number:  CaltechETD:etd05242006025220 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd05242006025220 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  2007 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  31 May 2006 
Last Modified:  26 Dec 2012 02:45 
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