### Abstract

Results are presented from high-precision computations of the orbital evolution and emitted gravitational waves for a stellar-mass object spiraling into a massive black hole in a slowly shrinking, circular, equatorial orbit. The focus of these computations is inspiral near the innermost stable circular orbit (isco) - more particularly, on orbits for which the angular velocity Ω is 0.03≲Ω/Ω_{isco}≤1.0. The computations are based on the Teuksolsky-Sasaki-Nakamura formalism, and the results are tabulated in a set of functions that are of order unity and represent relativistic corrections to low-orbital-velocity formulas. These tables can form a foundation for future design studies for the LISA space-based gravitational-wave mission. A first survey of applications to LISA is presented: Signal to noise ratios S/N are computed and graphed as functions of the time-evolving gravitational-wave frequency for the lowest three harmonics of the orbital period, and for various representative values of the hole's mass M and spin a and the inspiraling object's mass μ, with the distance to Earth chosen to be r_{0}=1 Gpc. These S/N's show a very strong dependence on the black-hole spin, as well as on M and μ. Graphs are presented showing the range of the {M,a,μ} parameter space, for which S/N>10 at r_{0} =1 Gpc during the last year of inspiral. The hole's spin a has a factor of ∼10 influence on the range of M (at fixed μ) for which S/N>10, and the presence or absence of a white-dwarf-binary background has a factor of ∼3 influence. A comparison with predicted event rates shows strong promise for detecting these waves, but not beyond about 1 Gpc if the inspiraling object is a white dwarf or neutron star. This argues for a modest lowering of LISA's noise floor. A brief discussion is given of the prospects for extracting information from the observed waves.

Original language | English (US) |
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Article number | 124021 |

Pages (from-to) | 1-20 |

Number of pages | 20 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 62 |

Issue number | 12 |

Publication status | Published - Dec 15 2000 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*62*(12), 1-20. [124021].