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

TL;DR

This paper improves parameter estimation accuracy for inspiralling compact binaries by incorporating second post-Newtonian order waveforms, revealing that previous estimates underestimated errors, with only slight increases in measurement errors for neutron star binaries.

Contribution

The study introduces second post-Newtonian order waveforms for more accurate gravitational wave parameter estimation, updating previous error estimates.

Findings

Errors in parameter estimation are slightly higher with 2PN waveforms.

Previous 1.5PN estimates underestimated errors in key parameters.

Measurement errors for neutron star binaries increase by less than 16%.

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 $\mu$, and spin parameters $\beta$ and $\sigma$ (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 $\cal M$, $\mu$, and $\beta$. For two inspiralling neutron stars, the measurement errors increase by less than 16 percent.