Theoretical and computational research will be carried out in support of LIGO, the Laser Interferometer Gravitational Wave Observatory: (1) Research close to experiment, e.g. analysis of and methods to reduce thermal noise, light scattering noise, and opto- mechanical instabilities. (2) Development of numerical-relativity tools for simulating gravitational-wave sources, especially a computer code based on pseudo-spectral methods that is robust, highly accurate, and very efficient. (3) Use of this code and other theoretical methods to develop insights into gravitational wave sources, and especially predict their emitted waveforms. Among the sources to be studied are (a) the slow inspiral of neutron stars and small black holes into intermedicate-mass black holes ("Extreme mass ratio inspirals" or EMRIs), (b) the late inspiral of black-hole binaries including spin-orbit and spin-spin interactions and possible spin flips, (c) the transition from inspiral to plunge in black-hole binaries, (d) the merger of black-hole binaries, and (d) rotating neutron stars. (4) Use of the insights about sources developed in this work to construct better template families for searching for the waves, and improved techniques for extracting information carried by the waves. (5) Participation in the LIGO Scientific Collaboration's gravitational wave searches, using these templates and techniques as well as others. This research is designed to help make LIGO a success by (i) increasing its prospects of detecting gravitational waves from a wide variety of sources, and (ii) improving its ability to extract from observed waves the rich information that the waves should carry. It will also contribute to the advance of technology and techniques for high-precision measurement, contribute to our understanding of astrophysical systems, and contribute to the development of numerical methods and computer codes capable of carrying out robust and accurate simulations of highly dynamical spacetimes. This research will be carried out in large measure by about ten graduate students and six postdoctoral students. This program's diversity of types of research and research tools will provide a rich training ground for these students.

Project Report

This grant supported theoretical and computational research by 5 senior investigators, 15 postdoctoral students and 20 graduate students. Here are a few highlights: A. Interface between theory and experimental design A1. Under the leadership of Professor Yanbei Chen, we showed that LIGO's gravitational-wave detectors can be used to explore the quantum mechanical behavior of 40 kilogram mirrors. This brings experimental quantum physics, for the first time, into the domain of human sized objects. A2. Professor Chen invented the Double Optical Spring for use in LIGO and other physics experiments. It was demonstrated experimentally by the research group of Professor Nergis Malvalvala at MIT. A3. We devised and scoped out several possible enhancements for the Advanced LIGO gravitational-wave detectors. A4. We developed a deeper understanding of several noise sources and dangerous effects in Advanced LIGO, and devised ways to control them. B. Numerical relativity research tools B1. Under the leadership of Drs. Mark Scheel and Lee Lindblom, and in collaboration with Professor Saul Teukolsky's group at Cornell, we developed and perfected the Spectral Einstein Code (SpEC) for solving Einstein's general relativity equations numerically, on a computer. By using spectral methods, SpEC achieves higher accuracy and speed than any other numerical relativity code. B2. We brought SpEC into a form that (i) can simulate the evolution of binary systems made of two generic spinning black holes, as they spiral together, collide and merge, and (ii) can compute with high accuracy the gravitational waveforms (wave shapes) that these binaries emit. C. New analytical relativity research tools C1. Under the leadership of Professor Kip Thorne, we invented tidal tendex lines and frame-drag vortex lines, for visualizing all aspects of the curvature of spacetime. These are analogs of electric and magnetic field lines. The tendex lines describe stretching and squeezing forces exerted by spacetime curvature. The frame-drag vortex lines describe twisting forces and guide the whirling of space. C2. We incorporated into SpEC an ability to compute tendex and vortex lines, and thereby visualize spacetime curvature. D. Gravitational wave sources D1. A spinning black hole has two vortexes (concentrations of frame-drag vortex lines) sticking out of it. Using SpEC, we discovered that, when two spinning black holes collide and merge, they deposit their four vortexes on the merged hole's horizon. As the merged hole rotates, its vortexes spiral outward like water from a turning sprinkler, becomng gravitational waves. See attached Image. D2. Our SpEC simulations also revealed tendexes (concentrations of tendex lines) that stick out of a merged black hole and spiral outward becoming graviational waves. D3. We discovered that the waves from the merged hole's rotating vortexes and those from its tendexes superpose constructively in some directions and destructively in others. The merged hole recoils like a fired gun, from this anisotropic wave emission, acquiring a huge kick. Professor Manuella Campanelli's group at Rochester Institute of Technology, discovered these kicks; our simulations revealed the cause. D4. Using SpEC (and collaborating with others), we initiated a project to compute the gravitational waveforms from ~1000 binary black holes with different masses and spins. Our waveforms will underpin templates for use in LIGO's searches for gravitational waves. D5. We identified, and scoped out, a new class of gravitational wave sources for LIGO: Intermediate Mass Ratio Inspirals (IMRIs), in which a neutron star or small black hole spirals into an intermediate mass black hole or other body (one with mass between 50 and 1000 suns). D7. We proved that the gravitational waves from an IMRI, and those from an Extreme Mass Ratio Inspiral (EMRI), carry: (i) a complete map of the spacetime geometry of the massive central body, (ii) the details of the inspiral orbit, and (iii) details of the tidal coupling between the central body and the inspiraling object. E. LIGO's Searches for Gravitational Waves E1. Most of the searches, by the LIGO Scientific Collaboration (LSC), for gravitational waves from binary black holes have used templates produced by our research group and our collaborators. E2. Cutler devised two new techniques that will improve the LSC's searches for gravitational waves from spinning neutron stars (pulsars): the Bayesian F-statistic, and the phase-relaxed frequentist F-statistic. E3. Chen devised a new technique, called the infinite impulse response filter that will help find gravitational waves in LIGO's noisy data quickly, as they arrive, rather than the waves being identified by data analysis days or weeks after arrival. ******* Under this grant, 15 postdoctoral students and 20 graduate students received research training. We trained them broadly, in research ranging from experimental design to data analysis to astrophysical modeling to numerical simulation. We made great effort to disseminate information about this grant's science, and related science carried out by others --- via our website (joint with Teukolsky's Cornell group) www.black-holes.org, via university-wide lectures for undergraduate students at 6 universities, and via 26 public lectures.

Agency
National Science Foundation (NSF)
Institute
Division of Physics (PHY)
Application #
0601459
Program Officer
Beverly K. Berger
Project Start
Project End
Budget Start
2006-06-01
Budget End
2011-05-31
Support Year
Fiscal Year
2006
Total Cost
$2,210,002
Indirect Cost
Name
California Institute of Technology
Department
Type
DUNS #
City
Pasadena
State
CA
Country
United States
Zip Code
91125