Gravitational waves from merging compact binaries: How accurately can one extract the binary’s parameters from the inspiral waveform?

The most promising source of gravitational waves for the planned kilometer-size laser-interferometer detectors LIGO and VIRGO are merging compact binaries, i.e., neutron-star–neutron-star (NS-NS), neutron-star–black-hole (NS-BH), and black-hole–black-hole (BH-BH) binaries. We investigate how accurately the distance to the source and the masses and spins of the two bodies will be measured from the inspiral gravitational wave signals by the three-detector LIGO-VIRGO network using ‘‘advanced detectors’’ (those present a few years after initial operation). The large number of cycles in the observable waveform increases our sensitivity to those parameters that affect the inspiral rate, and thereby the evolution of the waveform’s phase. These parameters are thus measured much more accurately than parameters which affect the waveform’s polarization or amplitude. To lowest order in a post-Newtonian expansion, the evolution of the waveform’s phase depends only on the combination scrM≡(${\mathit{M}}_1$ ${\mathit{M}}_2$ ${)}^{3/5}$(${\mathit{M}}_1$+${\mathit{M}}_2$ ${)}^{\mathrm{-}1/5}$ of the masses ${\mathit{M}}_1$ and ${\mathit{M}}_2$ of the two bodies, which is known as the ‘‘chirp mass.’’ To post-1-Newtonian order, the waveform’s phase also depends sensitively on the binary’s reduced mass μ≡${\mathit{M}}_1$ ${\mathit{M}}_2$/(${\mathit{M}}_1$+${\mathit{M}}_2$) allowing, in principle, a measurement of both ${\mathit{M}}_1$ and ${\mathit{M}}_2$ with high accuracy.