Parameter estimation of inspiralling compact binaries using 3.5 post-Newtonian gravitational wave phasing: The nonspinning case

We revisit the problem of parameter estimation of gravitational-wave chirp signals from inspiralling nonspinning compact binaries in the light of the recent extension of the post-Newtonian (PN) phasing formula to order (v/c)(7) beyond the leading Newtonian order. We study in detail the implications of higher post-Newtonian orders from 1PN up to 3.5PN in steps of 0.5PN (similar to v/c), and examine their convergence. In both initial and advanced detectors the estimation of the chirp mass (M) and symmetric mass ratio (eta) improve at higher PN orders but oscillate with every half-a-PN order. In initial LIGO, for a 10M-10M binary at a signal-to-noise ratio (SNR) of 10, the improvement in the estimation of M (eta) at 3.5PN relative to 2PN is similar to 19% (52%). We compare parameter estimation in different detectors and assess their relative performance in two different ways: at a fixed SNR, with the aim of understanding how the bandwidth improves parameter estimation, and for a fixed source, to gauge the importance of sensitivity. Errors in parameter estimation at a fixed SNR are smaller for VIRGO than for both initial and advanced LIGO. This is because of the larger bandwidth over which it observes the signals. However, for sources at a fixed distance it is advanced LIGO that achieves the lowest errors owing to its greater sensitivity. Finally, we compute the amplitude corrections due to the "frequency-sweep" in the Fourier domain representation of the waveform within the stationary phase approximation and discuss its implication on parameter estimation. We find that the amplitude corrections change the errors in M and eta by less than 10% for initial LIGO at a signal-to-noise ratio of 10. Our analysis makes explicit the significance of higher PN order modeling of the inspiralling compact binary on parameter estimation.