No abstract

Gravitational-wave interferometers are expected to monitor the last three minutes of inspiral and final coalescence of neutron star and black hole binaries at distances approaching cosmological, where the event rate may be many per year. Because the binary's accumulated orbital phase can be measured to a fractional accuracy <^C 10~3 and relativistic effects are large, the wave forms will be far more complex and carry more information than has been expected. Improved wave form modeling is needed as a foundation for extracting the waves' information, but is not necessary for wave detection.

One promising source of gravitational waves for future ground-based interferometric detectors is the last severd minutes of inspird 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 waveform 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 dE/dt as a function of the orbital radius ro. These estimates are fitted to a post-Newtonian expansion of the form dE/dt = ( d E / d t )~ xk akxk, where ( d E / d t )~ is the standard quadrupole-formula expression and x r (~l r o ) " ' . F'rorn our fits we obtain values for the expansion coefficients ar, up through order z6. 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. PACS number(s): 04.30.+x, 04.80.+z, 97.60. Jd, 97.60.Lf

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