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

Abstract

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)3/5 (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 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 DELTAM/M almost-equal-to 0.1%-1%. Although this is a remarkably small error bar, it is approximately 10 times larger than previous estimates of 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). Measurements of the masses and spins are strongly correlated; there is a combination of mu and the spin angular momenta that is measured to within approximately 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 M2(2), respectively), then mu could be determined to within approximately 1%. Finally, building on earlier work of Markovic, we derive an approximate, 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 the signal-to-noise ratio. We also show that, contrary to previous expectations, contributions to DELTAD/D that are nonlinear in 1/rho are significant, and we develop an approximation scheme for including the dominant of these nonlinear effects. Using a Monte Carlo simulation we estimate that distance measurement accuracies will be less-than-or-equal-to 15% for approximately 8% of the detected signals, and less-than-or-equal-to 30% for approximately 60% of the signals, for the LIGO-VIRGO three-detector network.