Tidal invariants for compact binaries on quasi-circular orbits

ORAL

Abstract

We extend the gravitational self-force approach to encompass `self-interaction' tidal effects for a compact body of mass $\mu$ on a quasi-circular orbit around a black hole of mass $M \gg \mu$. Specifically, we define and calculate at $O(\mu)$ (conservative) shifts in the eigenvalues of the electric- and magnetic-type tidal tensors, and a (dissipative) shift in a scalar product between their eigenbases. This approach yields four gauge-invariant functions, from which one may construct other tidal quantities such as the curvature scalars and the speciality index. First, we analyze the general case of a geodesic in a regular perturbed vacuum spacetime admitting a helical Killing vector and a reflection symmetry. Next, we specialize to focus on circular orbits in the equatorial plane of Kerr spacetime at $O(\mu)$. We present accurate numerical results for the Schwarzschild case for orbital radii up to the light-ring, calculated via independent implementations in Lorenz and Regge-Wheeler gauges. We show that our results are consistent with leading-order post-Newtonian expansions, and demonstrate the existence of additional structure in the strong-field regime. We anticipate that our strong-field results will inform (e.g.)~effective one-body models for the gravitational two-body probl

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Authors

  • Niels Warburton

    Massachusetts Institute of Technology

  • Ed Wollack

    University of Virginia, California Institute of Technology, Univ of Maryland-College Park, Canadian Institute for Theoretical Astrophysics, West Virginia University, University of Illinois at Urbana-Champaign, Princeton University, Caltech, UC Berkeley, North Carolina State University, UC Berkeley, Lawrence Berkeley National Lab, Cornell, Washington State University, Caltech; Einstein Fellow, North Carolina State University; Hubble Fellow, Theoretical Astrophysics, California Institute of Technology, Center for Radiophysics and Space Research, Cornell University, Dept. of Physics and Astronomy, Washington State University, Albert-Einstein-Institute, Golm, Germany, Lawrence Berkeley National Laboratory, Canadian Institute for Theoretical Astrophysics, University of Toronto, University of Massachusetts, Dartmouth, Univ of Texas, Brownsville, Massachusetts Institute of Technology, Colorado State University, Indiana University, Fermi National Accelerator Laboratory, University of Portsmouth, University of Pennsylvania, Manchester University, University of Barcelona, Indiana Univ - Bloomington, National Institute of Standards and Technology, Oak Ridge National Laboratory, Department of Physics, Princeton University, Princeton, New Jersey 08544, USA, Department of Physics and Astronomy, George Mason University, Fairfax, VA 22030, USA, NIST - Natl Inst of Stds \& Tech, Carnegie Obs, Univ North Texas, Pennsylvania State Univ, Drexel Univ, Univ Michigan, Univ Toronto, HP, Huntingdon Inst, Univ Washington, Harvard CfA, York Univ, Institute for Fundamental Theory, Department of Physics, University of Florida, Mathematical Sciences, University of Southampton, University of British Columbia, Lancaster University, UK, California State University Fullerton, University of Toronto, Cornell University, Oberlin College, Univ. Kentucky, TAMU, St. Mary's Univ., LLNL, Florida State University, Vanderbilt University, Ohio University, Yale University, University of Connecticut, NASA/GSFC, University of Southampton, Penn State University, University of Florida, Univ of Florida - Gainesville, Syracuse University, CITA, Rochester Institute of Technology, Royal Military College of Canada, Virginia Commonwealth University, Univ of California-Santa Cruz, SLAC, Brown University, University of North Florida, University of Chicago, Princeton Univ, Department of Physics, University of Waterloo, Ontario, Canada N2L 3G1, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA, Auburn University, Auburn, Alabama 36849, USA, JINR, Tsinghua University, LBNL, GANIL, Universit\'e Libre de Bruxelles (ULB), Belgium, Mississippi State University, Millersville University, New York Univ NYU, California Nanoscience Center, University of California, Los Angeles, Illinois Institute of Technology, Stanford University, University College Dublin, University Of Sheffield, International Centre for Theoretical Sciences, Chennai Mathematical Institute, Harvard University, Dept of Physics, North Carolina State U, Raleigh NC, USA \& the Triangle U Nuclear Lab, Durham, NC, USA, Dept of Physics, Indiana U/Purdue U at Indianapolis, Dept of Physics and CEEM, Indiana U/Bloomington, Physics \& Engineering Physics Dept., Tulane U, New Orleans, LA USA, NIST, Gaithersburg, MD USA, IQC, Dept of Physics and Astronomy, UWaterloo, Waterloo, Canada, IQC, Dept of Chemistry, UWaterloo, Perimeter Institute, Waterloo, Canada, Michigan State University, LPC-Caen, Argonne National Lab., University of Washington, Dept of Physics, Florida State University, Physics Division, ORNL, Innosense, LLC, Torrance, CA, Energy Systems Div, ANL, Physics Division, ANL, Earth Systems Science Center, University of Alabama in Huntsville, CSPAR, University of Alabama in Huntsville, ANL, ODU/JLab, University of Manchester, Imperial College, UK, Waikato University, NZ, NASA/Goddard Space Flight Center, University of Hawaii, University of Guelph, Universitat de les Illes Ballears, Brigham Young University, Indiana University Kokomo, Perimeter Institute for Theoretical Physics, UCSD, JPL, Georgia State University, Kansas State Univ, American Association of Physics Teachers, University of Texas -- Brownsville, University of Texas at Arlington, Department of Physics, University of Central Florida, Orlando, USA, CREOL, The College of Optics \& Photonics, University of Central Florida, Orlando, USA, ISET, ULVAC, Susono, Shizuoka, Japan, SISOM Thin Films LLC, Orlando, USA, Sensors Directorate, Air Force Research Laboratory, Wright- Patterson Air Force Base, US, Smithsonian Astrophysical Observatory, Department of Physics and Astronomy, University of Utah, Paul Scherrer Institu, Hartnell College, UCLA, Universite Bordeaux 1, CNRS/IN2P3, INFN / Universita del Politecnico di Bari, Univ of Michigan - Ann Arbor, Korean Astronomy and Space Science Institute, University of Sussex, Columbia University, Argonne National Lab, Jefferson Lab, CSM, UAH, NASA, NASA GSFC, CRESST/UMBC/NASA GSFC, Max-Planck-Institut f\"ur Astrophysik, Bowdoin College, University of Warwick, University of Uppsala, National Astronomical Observatory of Japan and University of Tokyo, National Astronomical Observatory of Japan, Pennsylvania State University, Florida International University, Drake University, Univ. of Maryland, CSNSM, Orsay, France, Bhabha Atomic Research Centre, India, US Naval Academy, Univ. of Notre Dame, Mississippi State Univ., Univ of Richmond, Texas A\&M Univ, Lawrence Livermore National Laboratory, Univ of Kentucky, Cyclotron Institute, Texas A\&M University, University of Kentucky, University of Richmond, University of Notre Dame, University of Maryland, Army Research Laboratory, University of Tennessee, Argonne National Laboratory, University of Liverpool, Daresbury Laboratory, National Superconducting Cyclotron Laboratory, U. of Maryland, Iowa State University, KITP, UC Santa Barbara, Dept. of Astronomy, University of Texas at Austin, NORDITA, Stockholm University and Dept. of Physics, University of Michigan, Department of Physics, Brown University, Physics Department, University of Richmond, Center for Cosmology and Astro-Particle Physics, Ohio State University, Institut d'Astrophysique de Paris, Department of Physics, University of Wisconsin-Madison, the Chinese University of Hong Kong, McGill Univ., Washington University in St. Louis, North Carolina State Univ. and the Triangle Universities Nuclear Laboratory, IUPUI, Tulane Univ., IQC, Univ. of Waterloo, Univ. of Waterloo, NIST, Western University and Algoma University, Fermilab, South Dakota School of Mines and Technology, Colorado School of Mines, Ludwig-Maximilians-Universitat Munchen, MSU/NSCL, Unviersitat Politecnica de Catalunya/Institut d'Estudies Especials de Catalunya, Technische Universitat Munchen, McMaster University, Louisiana State University, Cardiff University, MSLU, George Washington University, Triangle Universities Nuclear Laboratory, US Army Research Laboratory, ORAU/ARL, Los Alamos National Laboratory, None, Nazarbayev University, Kazakhstan, University of Pisa, Carnegie Observatories, Max Planck Institute for Gravitational Physics, Nazarbayev University, George Washington Univ, Undergraduate Physics, Drexel University, Philadelphia, PA, University of Texas Pan American, Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831 USA, Department of Physics, Albion College, Albion, MI 49224, Department of Physics, Pacific Union College, Angwin, CA 94508, Siena College, Univ of Minnesota, Washington Univ, Jet Propulaion Laboratory, California Institute of Technology, Pasadena, CA 91109, California Institute of Technology, Pasadena, CA 91125, NASA/Goddard Space Flight Center, Greenbelt, MD 20771, Washington University, St. Louis MO 63146, Florida Atlantic University, LIGO Livingston Observatory, Embry-Riddle University, LIGO Caltech, Univ of Tennessee, Knoxville, University Of Illinois, University Of Kentucky, California Institute Of Technology, Los Alamos National Lab, Juelich Center for Neutron Science, University of Michigan, Ann Arbor, Physikalisch-Technische Bundesanstalt, Technische Universitaet Muenchen, Hobart and William Smith Colleges, Old Dominion University, Jet Propulsion Laboratory, California Institute of Technology, USA, University of Cambridge, United Kingdom, Physics and Astronomy Department, West Virginia University, Jet Propulsion Laboratory, University of Mississippi, Montana State University, Physics Department, Indiana University, Bloomington, Embry-Riddle Aeronautical University, NASA Goddard Space Flight Center Astrophysics Science Division

  • Ed Wollack

    University of Virginia, California Institute of Technology, Univ of Maryland-College Park, Canadian Institute for Theoretical Astrophysics, West Virginia University, University of Illinois at Urbana-Champaign, Princeton University, Caltech, UC Berkeley, North Carolina State University, UC Berkeley, Lawrence Berkeley National Lab, Cornell, Washington State University, Caltech; Einstein Fellow, North Carolina State University; Hubble Fellow, Theoretical Astrophysics, California Institute of Technology, Center for Radiophysics and Space Research, Cornell University, Dept. of Physics and Astronomy, Washington State University, Albert-Einstein-Institute, Golm, Germany, Lawrence Berkeley National Laboratory, Canadian Institute for Theoretical Astrophysics, University of Toronto, University of Massachusetts, Dartmouth, Univ of Texas, Brownsville, Massachusetts Institute of Technology, Colorado State University, Indiana University, Fermi National Accelerator Laboratory, University of Portsmouth, University of Pennsylvania, Manchester University, University of Barcelona, Indiana Univ - Bloomington, National Institute of Standards and Technology, Oak Ridge National Laboratory, Department of Physics, Princeton University, Princeton, New Jersey 08544, USA, Department of Physics and Astronomy, George Mason University, Fairfax, VA 22030, USA, NIST - Natl Inst of Stds \& Tech, Carnegie Obs, Univ North Texas, Pennsylvania State Univ, Drexel Univ, Univ Michigan, Univ Toronto, HP, Huntingdon Inst, Univ Washington, Harvard CfA, York Univ, Institute for Fundamental Theory, Department of Physics, University of Florida, Mathematical Sciences, University of Southampton, University of British Columbia, Lancaster University, UK, California State University Fullerton, University of Toronto, Cornell University, Oberlin College, Univ. Kentucky, TAMU, St. Mary's Univ., LLNL, Florida State University, Vanderbilt University, Ohio University, Yale University, University of Connecticut, NASA/GSFC, University of Southampton, Penn State University, University of Florida, Univ of Florida - Gainesville, Syracuse University, CITA, Rochester Institute of Technology, Royal Military College of Canada, Virginia Commonwealth University, Univ of California-Santa Cruz, SLAC, Brown University, University of North Florida, University of Chicago, Princeton Univ, Department of Physics, University of Waterloo, Ontario, Canada N2L 3G1, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA, Auburn University, Auburn, Alabama 36849, USA, JINR, Tsinghua University, LBNL, GANIL, Universit\'e Libre de Bruxelles (ULB), Belgium, Mississippi State University, Millersville University, New York Univ NYU, California Nanoscience Center, University of California, Los Angeles, Illinois Institute of Technology, Stanford University, University College Dublin, University Of Sheffield, International Centre for Theoretical Sciences, Chennai Mathematical Institute, Harvard University, Dept of Physics, North Carolina State U, Raleigh NC, USA \& the Triangle U Nuclear Lab, Durham, NC, USA, Dept of Physics, Indiana U/Purdue U at Indianapolis, Dept of Physics and CEEM, Indiana U/Bloomington, Physics \& Engineering Physics Dept., Tulane U, New Orleans, LA USA, NIST, Gaithersburg, MD USA, IQC, Dept of Physics and Astronomy, UWaterloo, Waterloo, Canada, IQC, Dept of Chemistry, UWaterloo, Perimeter Institute, Waterloo, Canada, Michigan State University, LPC-Caen, Argonne National Lab., University of Washington, Dept of Physics, Florida State University, Physics Division, ORNL, Innosense, LLC, Torrance, CA, Energy Systems Div, ANL, Physics Division, ANL, Earth Systems Science Center, University of Alabama in Huntsville, CSPAR, University of Alabama in Huntsville, ANL, ODU/JLab, University of Manchester, Imperial College, UK, Waikato University, NZ, NASA/Goddard Space Flight Center, University of Hawaii, University of Guelph, Universitat de les Illes Ballears, Brigham Young University, Indiana University Kokomo, Perimeter Institute for Theoretical Physics, UCSD, JPL, Georgia State University, Kansas State Univ, American Association of Physics Teachers, University of Texas -- Brownsville, University of Texas at Arlington, Department of Physics, University of Central Florida, Orlando, USA, CREOL, The College of Optics \& Photonics, University of Central Florida, Orlando, USA, ISET, ULVAC, Susono, Shizuoka, Japan, SISOM Thin Films LLC, Orlando, USA, Sensors Directorate, Air Force Research Laboratory, Wright- Patterson Air Force Base, US, Smithsonian Astrophysical Observatory, Department of Physics and Astronomy, University of Utah, Paul Scherrer Institu, Hartnell College, UCLA, Universite Bordeaux 1, CNRS/IN2P3, INFN / Universita del Politecnico di Bari, Univ of Michigan - Ann Arbor, Korean Astronomy and Space Science Institute, University of Sussex, Columbia University, Argonne National Lab, Jefferson Lab, CSM, UAH, NASA, NASA GSFC, CRESST/UMBC/NASA GSFC, Max-Planck-Institut f\"ur Astrophysik, Bowdoin College, University of Warwick, University of Uppsala, National Astronomical Observatory of Japan and University of Tokyo, National Astronomical Observatory of Japan, Pennsylvania State University, Florida International University, Drake University, Univ. of Maryland, CSNSM, Orsay, France, Bhabha Atomic Research Centre, India, US Naval Academy, Univ. of Notre Dame, Mississippi State Univ., Univ of Richmond, Texas A\&M Univ, Lawrence Livermore National Laboratory, Univ of Kentucky, Cyclotron Institute, Texas A\&M University, University of Kentucky, University of Richmond, University of Notre Dame, University of Maryland, Army Research Laboratory, University of Tennessee, Argonne National Laboratory, University of Liverpool, Daresbury Laboratory, National Superconducting Cyclotron Laboratory, U. of Maryland, Iowa State University, KITP, UC Santa Barbara, Dept. of Astronomy, University of Texas at Austin, NORDITA, Stockholm University and Dept. of Physics, University of Michigan, Department of Physics, Brown University, Physics Department, University of Richmond, Center for Cosmology and Astro-Particle Physics, Ohio State University, Institut d'Astrophysique de Paris, Department of Physics, University of Wisconsin-Madison, the Chinese University of Hong Kong, McGill Univ., Washington University in St. Louis, North Carolina State Univ. and the Triangle Universities Nuclear Laboratory, IUPUI, Tulane Univ., IQC, Univ. of Waterloo, Univ. of Waterloo, NIST, Western University and Algoma University, Fermilab, South Dakota School of Mines and Technology, Colorado School of Mines, Ludwig-Maximilians-Universitat Munchen, MSU/NSCL, Unviersitat Politecnica de Catalunya/Institut d'Estudies Especials de Catalunya, Technische Universitat Munchen, McMaster University, Louisiana State University, Cardiff University, MSLU, George Washington University, Triangle Universities Nuclear Laboratory, US Army Research Laboratory, ORAU/ARL, Los Alamos National Laboratory, None, Nazarbayev University, Kazakhstan, University of Pisa, Carnegie Observatories, Max Planck Institute for Gravitational Physics, Nazarbayev University, George Washington Univ, Undergraduate Physics, Drexel University, Philadelphia, PA, University of Texas Pan American, Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831 USA, Department of Physics, Albion College, Albion, MI 49224, Department of Physics, Pacific Union College, Angwin, CA 94508, Siena College, Univ of Minnesota, Washington Univ, Jet Propulaion Laboratory, California Institute of Technology, Pasadena, CA 91109, California Institute of Technology, Pasadena, CA 91125, NASA/Goddard Space Flight Center, Greenbelt, MD 20771, Washington University, St. Louis MO 63146, Florida Atlantic University, LIGO Livingston Observatory, Embry-Riddle University, LIGO Caltech, Univ of Tennessee, Knoxville, University Of Illinois, University Of Kentucky, California Institute Of Technology, Los Alamos National Lab, Juelich Center for Neutron Science, University of Michigan, Ann Arbor, Physikalisch-Technische Bundesanstalt, Technische Universitaet Muenchen, Hobart and William Smith Colleges, Old Dominion University, Jet Propulsion Laboratory, California Institute of Technology, USA, University of Cambridge, United Kingdom, Physics and Astronomy Department, West Virginia University, Jet Propulsion Laboratory, University of Mississippi, Montana State University, Physics Department, Indiana University, Bloomington, Embry-Riddle Aeronautical University, NASA Goddard Space Flight Center Astrophysics Science Division

  • Ed Wollack

    University of Virginia, California Institute of Technology, Univ of Maryland-College Park, Canadian Institute for Theoretical Astrophysics, West Virginia University, University of Illinois at Urbana-Champaign, Princeton University, Caltech, UC Berkeley, North Carolina State University, UC Berkeley, Lawrence Berkeley National Lab, Cornell, Washington State University, Caltech; Einstein Fellow, North Carolina State University; Hubble Fellow, Theoretical Astrophysics, California Institute of Technology, Center for Radiophysics and Space Research, Cornell University, Dept. of Physics and Astronomy, Washington State University, Albert-Einstein-Institute, Golm, Germany, Lawrence Berkeley National Laboratory, Canadian Institute for Theoretical Astrophysics, University of Toronto, University of Massachusetts, Dartmouth, Univ of Texas, Brownsville, Massachusetts Institute of Technology, Colorado State University, Indiana University, Fermi National Accelerator Laboratory, University of Portsmouth, University of Pennsylvania, Manchester University, University of Barcelona, Indiana Univ - Bloomington, National Institute of Standards and Technology, Oak Ridge National Laboratory, Department of Physics, Princeton University, Princeton, New Jersey 08544, USA, Department of Physics and Astronomy, George Mason University, Fairfax, VA 22030, USA, NIST - Natl Inst of Stds \& Tech, Carnegie Obs, Univ North Texas, Pennsylvania State Univ, Drexel Univ, Univ Michigan, Univ Toronto, HP, Huntingdon Inst, Univ Washington, Harvard CfA, York Univ, Institute for Fundamental Theory, Department of Physics, University of Florida, Mathematical Sciences, University of Southampton, University of British Columbia, Lancaster University, UK, California State University Fullerton, University of Toronto, Cornell University, Oberlin College, Univ. Kentucky, TAMU, St. Mary's Univ., LLNL, Florida State University, Vanderbilt University, Ohio University, Yale University, University of Connecticut, NASA/GSFC, University of Southampton, Penn State University, University of Florida, Univ of Florida - Gainesville, Syracuse University, CITA, Rochester Institute of Technology, Royal Military College of Canada, Virginia Commonwealth University, Univ of California-Santa Cruz, SLAC, Brown University, University of North Florida, University of Chicago, Princeton Univ, Department of Physics, University of Waterloo, Ontario, Canada N2L 3G1, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA, Auburn University, Auburn, Alabama 36849, USA, JINR, Tsinghua University, LBNL, GANIL, Universit\'e Libre de Bruxelles (ULB), Belgium, Mississippi State University, Millersville University, New York Univ NYU, California Nanoscience Center, University of California, Los Angeles, Illinois Institute of Technology, Stanford University, University College Dublin, University Of Sheffield, International Centre for Theoretical Sciences, Chennai Mathematical Institute, Harvard University, Dept of Physics, North Carolina State U, Raleigh NC, USA \& the Triangle U Nuclear Lab, Durham, NC, USA, Dept of Physics, Indiana U/Purdue U at Indianapolis, Dept of Physics and CEEM, Indiana U/Bloomington, Physics \& Engineering Physics Dept., Tulane U, New Orleans, LA USA, NIST, Gaithersburg, MD USA, IQC, Dept of Physics and Astronomy, UWaterloo, Waterloo, Canada, IQC, Dept of Chemistry, UWaterloo, Perimeter Institute, Waterloo, Canada, Michigan State University, LPC-Caen, Argonne National Lab., University of Washington, Dept of Physics, Florida State University, Physics Division, ORNL, Innosense, LLC, Torrance, CA, Energy Systems Div, ANL, Physics Division, ANL, Earth Systems Science Center, University of Alabama in Huntsville, CSPAR, University of Alabama in Huntsville, ANL, ODU/JLab, University of Manchester, Imperial College, UK, Waikato University, NZ, NASA/Goddard Space Flight Center, University of Hawaii, University of Guelph, Universitat de les Illes Ballears, Brigham Young University, Indiana University Kokomo, Perimeter Institute for Theoretical Physics, UCSD, JPL, Georgia State University, Kansas State Univ, American Association of Physics Teachers, University of Texas -- Brownsville, University of Texas at Arlington, Department of Physics, University of Central Florida, Orlando, USA, CREOL, The College of Optics \& Photonics, University of Central Florida, Orlando, USA, ISET, ULVAC, Susono, Shizuoka, Japan, SISOM Thin Films LLC, Orlando, USA, Sensors Directorate, Air Force Research Laboratory, Wright- Patterson Air Force Base, US, Smithsonian Astrophysical Observatory, Department of Physics and Astronomy, University of Utah, Paul Scherrer Institu, Hartnell College, UCLA, Universite Bordeaux 1, CNRS/IN2P3, INFN / Universita del Politecnico di Bari, Univ of Michigan - Ann Arbor, Korean Astronomy and Space Science Institute, University of Sussex, Columbia University, Argonne National Lab, Jefferson Lab, CSM, UAH, NASA, NASA GSFC, CRESST/UMBC/NASA GSFC, Max-Planck-Institut f\"ur Astrophysik, Bowdoin College, University of Warwick, University of Uppsala, National Astronomical Observatory of Japan and University of Tokyo, National Astronomical Observatory of Japan, Pennsylvania State University, Florida International University, Drake University, Univ. of Maryland, CSNSM, Orsay, France, Bhabha Atomic Research Centre, India, US Naval Academy, Univ. of Notre Dame, Mississippi State Univ., Univ of Richmond, Texas A\&M Univ, Lawrence Livermore National Laboratory, Univ of Kentucky, Cyclotron Institute, Texas A\&M University, University of Kentucky, University of Richmond, University of Notre Dame, University of Maryland, Army Research Laboratory, University of Tennessee, Argonne National Laboratory, University of Liverpool, Daresbury Laboratory, National Superconducting Cyclotron Laboratory, U. of Maryland, Iowa State University, KITP, UC Santa Barbara, Dept. of Astronomy, University of Texas at Austin, NORDITA, Stockholm University and Dept. of Physics, University of Michigan, Department of Physics, Brown University, Physics Department, University of Richmond, Center for Cosmology and Astro-Particle Physics, Ohio State University, Institut d'Astrophysique de Paris, Department of Physics, University of Wisconsin-Madison, the Chinese University of Hong Kong, McGill Univ., Washington University in St. Louis, North Carolina State Univ. and the Triangle Universities Nuclear Laboratory, IUPUI, Tulane Univ., IQC, Univ. of Waterloo, Univ. of Waterloo, NIST, Western University and Algoma University, Fermilab, South Dakota School of Mines and Technology, Colorado School of Mines, Ludwig-Maximilians-Universitat Munchen, MSU/NSCL, Unviersitat Politecnica de Catalunya/Institut d'Estudies Especials de Catalunya, Technische Universitat Munchen, McMaster University, Louisiana State University, Cardiff University, MSLU, George Washington University, Triangle Universities Nuclear Laboratory, US Army Research Laboratory, ORAU/ARL, Los Alamos National Laboratory, None, Nazarbayev University, Kazakhstan, University of Pisa, Carnegie Observatories, Max Planck Institute for Gravitational Physics, Nazarbayev University, George Washington Univ, Undergraduate Physics, Drexel University, Philadelphia, PA, University of Texas Pan American, Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831 USA, Department of Physics, Albion College, Albion, MI 49224, Department of Physics, Pacific Union College, Angwin, CA 94508, Siena College, Univ of Minnesota, Washington Univ, Jet Propulaion Laboratory, California Institute of Technology, Pasadena, CA 91109, California Institute of Technology, Pasadena, CA 91125, NASA/Goddard Space Flight Center, Greenbelt, MD 20771, Washington University, St. Louis MO 63146, Florida Atlantic University, LIGO Livingston Observatory, Embry-Riddle University, LIGO Caltech, Univ of Tennessee, Knoxville, University Of Illinois, University Of Kentucky, California Institute Of Technology, Los Alamos National Lab, Juelich Center for Neutron Science, University of Michigan, Ann Arbor, Physikalisch-Technische Bundesanstalt, Technische Universitaet Muenchen, Hobart and William Smith Colleges, Old Dominion University, Jet Propulsion Laboratory, California Institute of Technology, USA, University of Cambridge, United Kingdom, Physics and Astronomy Department, West Virginia University, Jet Propulsion Laboratory, University of Mississippi, Montana State University, Physics Department, Indiana University, Bloomington, Embry-Riddle Aeronautical University, NASA Goddard Space Flight Center Astrophysics Science Division

  • Ed Wollack

    University of Virginia, California Institute of Technology, Univ of Maryland-College Park, Canadian Institute for Theoretical Astrophysics, West Virginia University, University of Illinois at Urbana-Champaign, Princeton University, Caltech, UC Berkeley, North Carolina State University, UC Berkeley, Lawrence Berkeley National Lab, Cornell, Washington State University, Caltech; Einstein Fellow, North Carolina State University; Hubble Fellow, Theoretical Astrophysics, California Institute of Technology, Center for Radiophysics and Space Research, Cornell University, Dept. of Physics and Astronomy, Washington State University, Albert-Einstein-Institute, Golm, Germany, Lawrence Berkeley National Laboratory, Canadian Institute for Theoretical Astrophysics, University of Toronto, University of Massachusetts, Dartmouth, Univ of Texas, Brownsville, Massachusetts Institute of Technology, Colorado State University, Indiana University, Fermi National Accelerator Laboratory, University of Portsmouth, University of Pennsylvania, Manchester University, University of Barcelona, Indiana Univ - Bloomington, National Institute of Standards and Technology, Oak Ridge National Laboratory, Department of Physics, Princeton University, Princeton, New Jersey 08544, USA, Department of Physics and Astronomy, George Mason University, Fairfax, VA 22030, USA, NIST - Natl Inst of Stds \& Tech, Carnegie Obs, Univ North Texas, Pennsylvania State Univ, Drexel Univ, Univ Michigan, Univ Toronto, HP, Huntingdon Inst, Univ Washington, Harvard CfA, York Univ, Institute for Fundamental Theory, Department of Physics, University of Florida, Mathematical Sciences, University of Southampton, University of British Columbia, Lancaster University, UK, California State University Fullerton, University of Toronto, Cornell University, Oberlin College, Univ. Kentucky, TAMU, St. Mary's Univ., LLNL, Florida State University, Vanderbilt University, Ohio University, Yale University, University of Connecticut, NASA/GSFC, University of Southampton, Penn State University, University of Florida, Univ of Florida - Gainesville, Syracuse University, CITA, Rochester Institute of Technology, Royal Military College of Canada, Virginia Commonwealth University, Univ of California-Santa Cruz, SLAC, Brown University, University of North Florida, University of Chicago, Princeton Univ, Department of Physics, University of Waterloo, Ontario, Canada N2L 3G1, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA, Auburn University, Auburn, Alabama 36849, USA, JINR, Tsinghua University, LBNL, GANIL, Universit\'e Libre de Bruxelles (ULB), Belgium, Mississippi State University, Millersville University, New York Univ NYU, California Nanoscience Center, University of California, Los Angeles, Illinois Institute of Technology, Stanford University, University College Dublin, University Of Sheffield, International Centre for Theoretical Sciences, Chennai Mathematical Institute, Harvard University, Dept of Physics, North Carolina State U, Raleigh NC, USA \& the Triangle U Nuclear Lab, Durham, NC, USA, Dept of Physics, Indiana U/Purdue U at Indianapolis, Dept of Physics and CEEM, Indiana U/Bloomington, Physics \& Engineering Physics Dept., Tulane U, New Orleans, LA USA, NIST, Gaithersburg, MD USA, IQC, Dept of Physics and Astronomy, UWaterloo, Waterloo, Canada, IQC, Dept of Chemistry, UWaterloo, Perimeter Institute, Waterloo, Canada, Michigan State University, LPC-Caen, Argonne National Lab., University of Washington, Dept of Physics, Florida State University, Physics Division, ORNL, Innosense, LLC, Torrance, CA, Energy Systems Div, ANL, Physics Division, ANL, Earth Systems Science Center, University of Alabama in Huntsville, CSPAR, University of Alabama in Huntsville, ANL, ODU/JLab, University of Manchester, Imperial College, UK, Waikato University, NZ, NASA/Goddard Space Flight Center, University of Hawaii, University of Guelph, Universitat de les Illes Ballears, Brigham Young University, Indiana University Kokomo, Perimeter Institute for Theoretical Physics, UCSD, JPL, Georgia State University, Kansas State Univ, American Association of Physics Teachers, University of Texas -- Brownsville, University of Texas at Arlington, Department of Physics, University of Central Florida, Orlando, USA, CREOL, The College of Optics \& Photonics, University of Central Florida, Orlando, USA, ISET, ULVAC, Susono, Shizuoka, Japan, SISOM Thin Films LLC, Orlando, USA, Sensors Directorate, Air Force Research Laboratory, Wright- Patterson Air Force Base, US, Smithsonian Astrophysical Observatory, Department of Physics and Astronomy, University of Utah, Paul Scherrer Institu, Hartnell College, UCLA, Universite Bordeaux 1, CNRS/IN2P3, INFN / Universita del Politecnico di Bari, Univ of Michigan - Ann Arbor, Korean Astronomy and Space Science Institute, University of Sussex, Columbia University, Argonne National Lab, Jefferson Lab, CSM, UAH, NASA, NASA GSFC, CRESST/UMBC/NASA GSFC, Max-Planck-Institut f\"ur Astrophysik, Bowdoin College, University of Warwick, University of Uppsala, National Astronomical Observatory of Japan and University of Tokyo, National Astronomical Observatory of Japan, Pennsylvania State University, Florida International University, Drake University, Univ. of Maryland, CSNSM, Orsay, France, Bhabha Atomic Research Centre, India, US Naval Academy, Univ. of Notre Dame, Mississippi State Univ., Univ of Richmond, Texas A\&M Univ, Lawrence Livermore National Laboratory, Univ of Kentucky, Cyclotron Institute, Texas A\&M University, University of Kentucky, University of Richmond, University of Notre Dame, University of Maryland, Army Research Laboratory, University of Tennessee, Argonne National Laboratory, University of Liverpool, Daresbury Laboratory, National Superconducting Cyclotron Laboratory, U. of Maryland, Iowa State University, KITP, UC Santa Barbara, Dept. of Astronomy, University of Texas at Austin, NORDITA, Stockholm University and Dept. of Physics, University of Michigan, Department of Physics, Brown University, Physics Department, University of Richmond, Center for Cosmology and Astro-Particle Physics, Ohio State University, Institut d'Astrophysique de Paris, Department of Physics, University of Wisconsin-Madison, the Chinese University of Hong Kong, McGill Univ., Washington University in St. Louis, North Carolina State Univ. and the Triangle Universities Nuclear Laboratory, IUPUI, Tulane Univ., IQC, Univ. of Waterloo, Univ. of Waterloo, NIST, Western University and Algoma University, Fermilab, South Dakota School of Mines and Technology, Colorado School of Mines, Ludwig-Maximilians-Universitat Munchen, MSU/NSCL, Unviersitat Politecnica de Catalunya/Institut d'Estudies Especials de Catalunya, Technische Universitat Munchen, McMaster University, Louisiana State University, Cardiff University, MSLU, George Washington University, Triangle Universities Nuclear Laboratory, US Army Research Laboratory, ORAU/ARL, Los Alamos National Laboratory, None, Nazarbayev University, Kazakhstan, University of Pisa, Carnegie Observatories, Max Planck Institute for Gravitational Physics, Nazarbayev University, George Washington Univ, Undergraduate Physics, Drexel University, Philadelphia, PA, University of Texas Pan American, Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831 USA, Department of Physics, Albion College, Albion, MI 49224, Department of Physics, Pacific Union College, Angwin, CA 94508, Siena College, Univ of Minnesota, Washington Univ, Jet Propulaion Laboratory, California Institute of Technology, Pasadena, CA 91109, California Institute of Technology, Pasadena, CA 91125, NASA/Goddard Space Flight Center, Greenbelt, MD 20771, Washington University, St. Louis MO 63146, Florida Atlantic University, LIGO Livingston Observatory, Embry-Riddle University, LIGO Caltech, Univ of Tennessee, Knoxville, University Of Illinois, University Of Kentucky, California Institute Of Technology, Los Alamos National Lab, Juelich Center for Neutron Science, University of Michigan, Ann Arbor, Physikalisch-Technische Bundesanstalt, Technische Universitaet Muenchen, Hobart and William Smith Colleges, Old Dominion University, Jet Propulsion Laboratory, California Institute of Technology, USA, University of Cambridge, United Kingdom, Physics and Astronomy Department, West Virginia University, Jet Propulsion Laboratory, University of Mississippi, Montana State University, Physics Department, Indiana University, Bloomington, Embry-Riddle Aeronautical University, NASA Goddard Space Flight Center Astrophysics Science Division