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

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 $\frac{\mathrm{dE}}{\mathrm{dt}}$ as a function of the orbital radius $r_0$. These estimates are fitted to a post-Newtonian expansion of the form $\frac{\mathrm{dE}}{\mathrm{dt}}={\left(\frac{\mathrm{dE}}{\mathrm{dt}}\right)}_N\Sigma k^{}{a}_k{x}^k$, where ${\left(\frac{\mathrm{dE}}{\mathrm{dt}}\right)}_N$ is the standard quadrupole-formula expression and $x\equiv {\left(\frac{M}{r_0}\right)}^{\frac{1}{2}}$. From our fits we obtain values for the expansion coefficients $a_k$ up through order $x^6$. While our results are in excellent agreement with low-order post-Newtonian calculations, we find that the post-Newtonian expansion converges slowly. Corrections beyond $x^6$ may be needed to achieve the desired accuracy for the construction of the template waveforms.