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Title: Gravitomagnetic resonant excitation of Rossby modes in coalescing neutron star binaries

Abstract

In coalescing neutron star binaries, r-modes in one of the stars can be resonantly excited by the gravitomagnetic tidal field of its companion. This post-Newtonian gravitomagnetic driving of these modes dominates over the Newtonian tidal driving previously computed by Ho and Lai. To leading order in the tidal expansion parameter R/r (where R is the radius of the neutron star and r is the orbital separation), only the l=2, |m|=1, and |m|=2 r-modes are excited. The tidal work done on the star through this driving has an effect on the evolution of the inspiral and on the phasing of the emitted gravitational wave signal. For a neutron star of mass M, radius R, spin frequency f{sub spin}, modeled as a {gamma}=2 polytrope, with a companion also of mass M, the gravitational wave phase shift for the m=2 mode is {approx}0.1 radians (R/10 km){sup 4}(M/1.4M{sub {center_dot}}){sup -10/3}(f{sub spin}/100 Hz){sup 2/3} for optimal spin orientation. For canonical neutron star parameters this phase shift will likely not be detectable by gravitational wave detectors such as LIGO, but if the neutron star radius is larger it may be detectable if the signal-to-noise ratio is moderately large. The energy transfer is large enough to drivemore » the mode into the nonlinear regime if f{sub spin} > or approx. 100 Hz. For neutron star--black hole binaries, the effect is smaller; the phase shift scales as companion mass to the -4/3 power for large companion masses. The net energy transfer from the orbit into the star is negative corresponding to a slowing down of the inspiral. This occurs because the interaction reduces the spin of the star, and occurs only for modes which satisfy the Chandrasekhar-Friedman-Schutz instability criterion. A large portion of the paper is devoted to developing a general formalism to treat mode driving in rotating stars to post-Newtonian order, which may be useful for other applications. We also correct some conceptual errors in the literature on the use of energy conservation to deduce the effect of the mode driving on the gravitational wave signal.« less

Authors:
 [1];  [1]
  1. Center for Radiophysics and Space Research, Cornell University, Ithaca, New York, 14853 (United States)
Publication Date:
OSTI Identifier:
21011066
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 75; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.75.044001; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BLACK HOLES; COSMOLOGICAL MODELS; COSMOLOGY; ENERGY CONSERVATION; ENERGY TRANSFER; ERRORS; EXCITATION; GRAVITATIONAL WAVE DETECTORS; GRAVITATIONAL WAVES; MAGNETISM; MASS; NET ENERGY; NEUTRON STARS; NONLINEAR PROBLEMS; PHASE SHIFT; SIGNAL-TO-NOISE RATIO; SPIN; SPIN ORIENTATION

Citation Formats

Flanagan, Eanna E, Racine, Etienne, and Theoretical Astrophysics, California Institute of Technology, Pasadena, California, 91125. Gravitomagnetic resonant excitation of Rossby modes in coalescing neutron star binaries. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.044001.
Flanagan, Eanna E, Racine, Etienne, & Theoretical Astrophysics, California Institute of Technology, Pasadena, California, 91125. Gravitomagnetic resonant excitation of Rossby modes in coalescing neutron star binaries. United States. https://doi.org/10.1103/PHYSREVD.75.044001
Flanagan, Eanna E, Racine, Etienne, and Theoretical Astrophysics, California Institute of Technology, Pasadena, California, 91125. 2007. "Gravitomagnetic resonant excitation of Rossby modes in coalescing neutron star binaries". United States. https://doi.org/10.1103/PHYSREVD.75.044001.
@article{osti_21011066,
title = {Gravitomagnetic resonant excitation of Rossby modes in coalescing neutron star binaries},
author = {Flanagan, Eanna E and Racine, Etienne and Theoretical Astrophysics, California Institute of Technology, Pasadena, California, 91125},
abstractNote = {In coalescing neutron star binaries, r-modes in one of the stars can be resonantly excited by the gravitomagnetic tidal field of its companion. This post-Newtonian gravitomagnetic driving of these modes dominates over the Newtonian tidal driving previously computed by Ho and Lai. To leading order in the tidal expansion parameter R/r (where R is the radius of the neutron star and r is the orbital separation), only the l=2, |m|=1, and |m|=2 r-modes are excited. The tidal work done on the star through this driving has an effect on the evolution of the inspiral and on the phasing of the emitted gravitational wave signal. For a neutron star of mass M, radius R, spin frequency f{sub spin}, modeled as a {gamma}=2 polytrope, with a companion also of mass M, the gravitational wave phase shift for the m=2 mode is {approx}0.1 radians (R/10 km){sup 4}(M/1.4M{sub {center_dot}}){sup -10/3}(f{sub spin}/100 Hz){sup 2/3} for optimal spin orientation. For canonical neutron star parameters this phase shift will likely not be detectable by gravitational wave detectors such as LIGO, but if the neutron star radius is larger it may be detectable if the signal-to-noise ratio is moderately large. The energy transfer is large enough to drive the mode into the nonlinear regime if f{sub spin} > or approx. 100 Hz. For neutron star--black hole binaries, the effect is smaller; the phase shift scales as companion mass to the -4/3 power for large companion masses. The net energy transfer from the orbit into the star is negative corresponding to a slowing down of the inspiral. This occurs because the interaction reduces the spin of the star, and occurs only for modes which satisfy the Chandrasekhar-Friedman-Schutz instability criterion. A large portion of the paper is devoted to developing a general formalism to treat mode driving in rotating stars to post-Newtonian order, which may be useful for other applications. We also correct some conceptual errors in the literature on the use of energy conservation to deduce the effect of the mode driving on the gravitational wave signal.},
doi = {10.1103/PHYSREVD.75.044001},
url = {https://www.osti.gov/biblio/21011066}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 4,
volume = 75,
place = {United States},
year = {2007},
month = {2}
}