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Published December 15, 2000 | public
Journal Article Open

Gravitational waves from a compact star in a circular, inspiral orbit, in the equatorial plane of a massive, spinning black hole, as observed by LISA


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/Ωisco<~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 ro=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 r0=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.

Additional Information

©2000 The American Physical Society Received 7 April 2000; revised 1 August 2000; published 28 November 2000 For helpful discussions we thank Fintan Ryan and Eric Poisson. For information and advice about the LISA noise curve we thank John Armstrong, Peter Bender, Curt Cutler, Frank Estabrook, Robin (Tuck) Stebbins, and Massimo Tinto, and we thank Bender and Stebbins for providing us with a table of the noise curve from Ref. [39]. For information and advice about white-dwarf–binary background noise, we thank Peter Bender, Sterl Phinney and Tuck Stebbins. This paper was supported in part by NASA grants NAGW-4274, NAG5-6840 and their predecessors, and in view of its future applications to LIGO, by NSF grants PHY-9800111, PHY-9996213, AST-9731698 and their predecessors.


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