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

TL;DR

This work assesses parameter estimation for inspiraling non-spinning compact binaries using the 3.5PN phasing within a stationary-phase framework, comparing advanced LIGO, initial LIGO, and VIRGO. By constructing the Fisher information matrix from the Fourier-domain waveform and exploring fixed-SNR and fixed-distance scenarios, it demonstrates that advancing from 2PN to 3.5PN phasing improves estimates of the chirp mass $\cal M$ and symmetric mass ratio $\eta$, with the largest gains for BH-BH systems. It also analyzes how detector bandwidth and the number of useful cycles influence accuracy, and it shows that amplitude corrections from the frequency sweep modify the SNR slightly (typically <10%) for some detectors. The study highlights both the practical gains in parameter inference achievable with higher PN orders and the need for more complete waveform models (including amplitude corrections from all harmonics and spins) and more robust error-bounding methods beyond the high-SNR Fisher approach.

Abstract

(Abridged) We revisit the problem of parameter estimation of gravitational-wave chirp signals from inspiralling non-spinning 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 ($\sim v/c$), and examine their convergence. In both initial and advanced detectors the estimation of the chirp mass (${\cal M}$) and symmetric mass ratio ($η$) improve at higher PN orders but oscillate with every half-a-PN order. We compare parameter estimation in different detectors and assess their relative performance in two different ways: at a {\it fixed SNR,} with the aim of understanding how the bandwidth improves parameter estimation, and for a {\it 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. 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.

Figures (3)

• Figure 1: Amplitude spectrum (left panel) of initial LIGO, VIRGO and advanced LIGO together with the luminosity distance (right panel) at which RMS-oriented binaries would produce a SNR of $5.$
• Figure 2: Comparison of errors in the estimation of $t_c$, ${\cal M}$ and $\eta$ for sources with a fixed SNR of 10 (left panels) with those for systems at a fixed distance of 300 Mpc (right panels).
• Figure 3: Left hand panel is the plot of the derivative $dN_{\rm useful}/{d(\ln f)}$ against the frequency (in arbitrary normalization) for the three detectors. Similarly, right panel gives the number of useful cycles as a function of the total mass of the binary for the three detectors.