Gravitational waves from inspiraling compact binaries: Parameter estimation using second-post-Newtonian waveforms

The parameters of inspiraling compact binaries can be estimated using matched filtering of gravitational-waveform templates against the output of laser-interferometric gravitational-wave detectors. The estimates are most sensitive to the accuracy with which the phases of the template and signal waveforms match over the many cycles received in the detector frequency bandwidth. Using a recently calculated formula, accurate to second post-Newtonian (2PN) order [order (v/c${)}^{4}$, where v is the orbital velocity], for the frequency sweep (dF/dt) induced by gravitational radiation damping, we study the statistical errors in the determination of such source parameters as the ``chirp mass'' scrM, reduced mass \ensuremath{\mu}, and spin parameters \ensuremath{\beta} and \ensuremath{\sigma} (related to spin-orbit and spin-spin effects, respectively). We find that previous results using template phasing accurate to 1.5PN order actually underestimated the errors in scrM, \ensuremath{\mu}, and \ensuremath{\beta}. Templates with 2PN phasing yield somewhat larger measurement errors because the 2PN corrections act to suppress slightly the importance of spin-orbit contributions to the phase, thereby increasing the measurement error on \ensuremath{\beta}. This, in turn, results in larger measurement errors on scrM and \ensuremath{\mu} because of the strong correlations among the parameters. For two inspiraling neutron stars, the measurement errors increase by less than 16%.