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

TL;DR

This paper addresses how accurately one can estimate the parameters of inspiralling compact binaries from gravitational-wave data when the waveform phasing is known to $2$PN order. It employs a Fisher-information framework with stationary-phase, using a simplified $2f$-dominant waveform to derive $\tilde{h}(f)$ and compute the covariance of parameters $\bigl(\mathcal{M}, \eta, \beta, \sigma\bigr)$ under realistic detector noise, incorporating priors on spins. The main finding is that $2$PN phasing yields larger uncertainties than previously estimated with $1.5$PN phasing, and including the spin-spin parameter $\sigma$ further increases errors; independent analyses even suggest $2$PN templates may be systematically biased and require at least $3$PN phasing to keep systematics below statistical errors. The study highlights the critical role of higher-order phasing, prior information, and modeling assumptions for interpreting LIGO/Virgo measurements, and it underscores the practical need for more accurate templates before precise parameter inference can be trusted.

Abstract

The parameters of inspiralling compact binaries can be estimated using matched filtering of gravitational-waveform templates against the output of laser-interferometric gravitational-wave detectors. 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'' $\cal M$, reduced mass $μ$, and spin parameters $β$ and $σ$ (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 $\cal M$, $μ$, and $β$. For two inspiralling neutron stars, the measurement errors increase by less than 16 percent.