GRAVITATIONAL-WAVES FROM MERGING COMPACT BINARIES - HOW ACCURATELY CAN ONE EXTRACT THE BINARYS PARAMETERS FROM THE INSPIRAL WAVE-FORM

The most promising source of gravitational waves for the planned kilom eter-size laser-interferometer detectors LIGO and VIRGO are merging co mpact binaries, i.e., neutron-star-neutron-star (NS-NS), neutron-star- black-hole (NS-BH), and black-hole-black-hole (BH-BH) binaries. We inv estigate how accurately the distance to the source and the masses and spins of the two bodies will be measured from the inspiral gravitation al wave signals by the three-detector LIGO-VIRGO network using ''advan ced detectors'' (those present a few years after initial operation). T he large number of cycles in the observable waveform increases our sen sitivity to those parameters that affect the inspiral rate, and thereb y the evolution of the waveform's phase. These parameters are thus mea sured much more accurately than parameters which affect the waveform's polarization or amplitude. To lowest order in a post-Newtonian expans ion, the evolution of the waveform's phase depends only on the combina tion M = (M1M2)3/5 (M1+M2)-1/5 of the masses M1 and M2 of the two bodi es, which is known as the ''chirp mass.'' To post-1-Newtonian order, t he waveform's phase also depends sensitively on the binary's reduced m ass mu = M1M2/(M1 + M2), allowing, in principle, a measurement of both M1 and M2 with high accuracy. We show that the principal obstruction to measuring M1 and M2 is the post-1.5-Newtonian effect of the bodies' spins on the waveform's phase, which can mimic the effects that allow mu to be determined. The chirp mass is measurable with an accuracy DE LTAM/M almost-equal-to 0.1%-1%. Although this is a remarkably small er ror bar, it is approximately 10 times larger than previous estimates o f DELTAM/M which neglected post-Newtonian effects. The reduced mass is measurable to approximately 10%-15% for NS-NS and NS-BH binaries, and approximately 50% for BH-BH binaries (assuming 10M. BH's). Measuremen ts of the masses and spins are strongly correlated; there is a combina tion of mu and the spin angular momenta that is measured to within app roximately 1%. Moreover, if both spins were somehow known to be small (less than or similar to 0.01 M1(2) and less than or similar to 0.01 M 2(2), respectively), then mu could be determined to within approximate ly 1%. Finally, building on earlier work of Markovic, we derive an app roximate, analytic expression for the accuracy DELTAD of measurements of the distance D to the binary, for an arbitrary network of detectors . This expression is accurate to linear order in 1/rho, where rho is t he signal-to-noise ratio. We also show that, contrary to previous expe ctations, contributions to DELTAD/D that are nonlinear in 1/rho are si gnificant, and we develop an approximation scheme for including the do minant of these nonlinear effects. Using a Monte Carlo simulation we e stimate that distance measurement accuracies will be less-than-or-equa l-to 15% for approximately 8% of the detected signals, and less-than-o r-equal-to 30% for approximately 60% of the signals, for the LIGO-VIRG O three-detector network.