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 (Formula presented) is (Formula presented) 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 (Formula presented) 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 (Formula presented) with the distance to Earth chosen to be (Formula presented) These (Formula presented) 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 (Formula presented) parameter space, for which (Formula presented) at (Formula presented) during the last year of inspiral. The hole’s spin a has a factor of (Formula presented) influence on the range of M (at fixed μ) for which (Formula presented) and the presence or absence of a white-dwarf–binary background has a factor of (Formula presented) 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)|
|Number of pages||1|
|Journal||Physical Review D - Particles, Fields, Gravitation and Cosmology|
|State||Published - 2000|
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)