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 M ≡ (M1M2)(M1 +M2)−1/5 of the masses M1 and M2 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 ≡ M1M2/(M1+M2), allowing, in principle, a measurement of both M1 and M2 with high accuracy. We show that the principal obstruction to measuringM1 andM2 is the post-1.5-Newtonian effect of the bodies’ spins on the waveform’s phase, which can mimic the effects that allow μ to be determined. The chirp mass is measurable with an accuracy ∆M/M ≈ 0.1% − 1%.