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

TL;DR

This paper analyzes how higher post-Newtonian orders affect parameter estimation of non-spinning inspiralling compact binaries in gravitational wave signals, highlighting improvements and oscillations in accuracy at different PN orders.

Contribution

It provides a detailed study of the impact of extending the PN phasing formula up to 3.5PN on parameter estimation accuracy for non-spinning binaries.

Findings

Higher PN orders improve mass parameter estimates but oscillate with each half-PN step.

Advanced LIGO achieves lower errors for fixed sources due to greater sensitivity.

Parameter estimation errors are smaller for VIRGO at fixed SNR.

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 ($\eta$) 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.