### Abstract

One promising source of gravitational waves for future ground-based interferometric detectors is the last several minutes of inspiral of a compact binary. Observations of the gravitational radiation from such a source can be used to obtain astrophysically interesting information, such as the masses of the binary components and the distance to the binary. Accurate theoretical models of the wave-form are needed to construct the matched filters that will be used to extract the information. We investigate the applicability of post-Newtonian methods for this purpose. We consider the particular case of a compact object (e.g., either a neutron star or a stellar mass black hole) in a circular orbit about a much more massive Schwarzschild black hole. In this limit, the gravitational radiation luminosity can be calculated by integrating the Teukolsky equation. Numerical integration is used to obtain accurate estimates of the luminosity dEdt as a function of the orbital radius r0. These estimates are fitted to a post-Newtonian expansion of the form dEdt=(dEdt)N kakxk, where (dEdt)N is the standard quadrupole-formula expression and x(Mr0)12. From our fits we obtain values for the expansion coefficients ak up through order x6. While our results are in excellent agreement with low-order post-Newtonian calculations, we find that the post-Newtonian expansion converges slowly. Corrections beyond x6 may be needed to achieve the desired accuracy for the construction of the template waveforms.

Original language | English (US) |
---|---|

Pages (from-to) | 1511-1518 |

Number of pages | 8 |

Journal | Physical Review D |

Volume | 47 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 1993 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D*,

*47*(4), 1511-1518. https://doi.org/10.1103/PhysRevD.47.1511

}

*Physical Review D*, vol. 47, no. 4, pp. 1511-1518. https://doi.org/10.1103/PhysRevD.47.1511

**Gravitational radiation from a particle in circular orbit around a black hole. II. Numerical results for the nonrotating case.** / Cutler, Curt; Finn, Lee S.; Poisson, Eric; Sussman, Gerald Jay.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Gravitational radiation from a particle in circular orbit around a black hole. II. Numerical results for the nonrotating case

AU - Cutler, Curt

AU - Finn, Lee S.

AU - Poisson, Eric

AU - Sussman, Gerald Jay

PY - 1993/1/1

Y1 - 1993/1/1

N2 - One promising source of gravitational waves for future ground-based interferometric detectors is the last several minutes of inspiral of a compact binary. Observations of the gravitational radiation from such a source can be used to obtain astrophysically interesting information, such as the masses of the binary components and the distance to the binary. Accurate theoretical models of the wave-form are needed to construct the matched filters that will be used to extract the information. We investigate the applicability of post-Newtonian methods for this purpose. We consider the particular case of a compact object (e.g., either a neutron star or a stellar mass black hole) in a circular orbit about a much more massive Schwarzschild black hole. In this limit, the gravitational radiation luminosity can be calculated by integrating the Teukolsky equation. Numerical integration is used to obtain accurate estimates of the luminosity dEdt as a function of the orbital radius r0. These estimates are fitted to a post-Newtonian expansion of the form dEdt=(dEdt)N kakxk, where (dEdt)N is the standard quadrupole-formula expression and x(Mr0)12. From our fits we obtain values for the expansion coefficients ak up through order x6. While our results are in excellent agreement with low-order post-Newtonian calculations, we find that the post-Newtonian expansion converges slowly. Corrections beyond x6 may be needed to achieve the desired accuracy for the construction of the template waveforms.

AB - One promising source of gravitational waves for future ground-based interferometric detectors is the last several minutes of inspiral of a compact binary. Observations of the gravitational radiation from such a source can be used to obtain astrophysically interesting information, such as the masses of the binary components and the distance to the binary. Accurate theoretical models of the wave-form are needed to construct the matched filters that will be used to extract the information. We investigate the applicability of post-Newtonian methods for this purpose. We consider the particular case of a compact object (e.g., either a neutron star or a stellar mass black hole) in a circular orbit about a much more massive Schwarzschild black hole. In this limit, the gravitational radiation luminosity can be calculated by integrating the Teukolsky equation. Numerical integration is used to obtain accurate estimates of the luminosity dEdt as a function of the orbital radius r0. These estimates are fitted to a post-Newtonian expansion of the form dEdt=(dEdt)N kakxk, where (dEdt)N is the standard quadrupole-formula expression and x(Mr0)12. From our fits we obtain values for the expansion coefficients ak up through order x6. While our results are in excellent agreement with low-order post-Newtonian calculations, we find that the post-Newtonian expansion converges slowly. Corrections beyond x6 may be needed to achieve the desired accuracy for the construction of the template waveforms.

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U2 - 10.1103/PhysRevD.47.1511

DO - 10.1103/PhysRevD.47.1511

M3 - Article

AN - SCOPUS:0000996163

VL - 47

SP - 1511

EP - 1518

JO - Physical Review D

JF - Physical Review D

SN - 0556-2821

IS - 4

ER -