Estimating the parameters of nonspinning binary black holes using ground-based gravitational-wave detectors: Statistical errors

Abstract

We assess the statistical errors in estimating the parameters of nonspinning black hole binaries using ground-based gravitational-wave detectors. While past assessments were based on partial information provided by only the inspiral and/or ring-down pieces of the coalescence signal, the recent progress in analytical and numerical relativity enables us to make more accurate projections using complete inspiral-merger-ring-down waveforms. We employ the Fisher information-matrix formalism to estimate how accurately the source parameters will be measurable using a single interferometric detector as well as a network of interferometers. Those estimates are further vetted by full-fledged Monte Carlo simulations. We find that the parameter accuracies of the complete waveform are, in general, significantly better than those of just the inspiral waveform in the case of binaries with total mass M ≿ 20M☉. In particular, for the case of the Advanced LIGO detector, parameter estimation is the most accurate in the M = 100–200M☉ range. For an M=100M[sun] system, the errors in measuring the total mass and the symmetric mass-ratio are reduced by an order of magnitude or more compared to inspiral waveforms. Furthermore, for binaries located at a fixed luminosity distance d_L, and observed with the Advanced LIGO-Advanced Virgo network, the sky-position error is expected to vary widely across the sky: For M = 100M☉ systems at d_L = 1 Gpc, this variation ranges mostly from about a hundredth of a square degree to about a square degree, with an average value of nearly a tenth of a square degree. This is more than 40 times better than the average sky-position accuracy of inspiral waveforms at this mass range. For the mass parameters as well as the sky position, this improvement in accuracy is due partly to the increased signal-to-noise ratio and partly to the information about these parameters harnessed through the post-inspiral phases of the waveform. The error in estimating d_L is dominated by the error in measuring the wave's polarization and is roughly 43% for low-mass (M ~ 20M☉) binaries and about 23% for high-mass (M ~ 100M☉ ) binaries located at d_L = 1 Gpc.