Parameter estimation of inspiralling compact binaries in ground-based detectors: comparison between Monte Carlo simulations and the Fisher information matrix

Abstract

The Fisher information matrix is employed in the gravitational-wave literature to quantify the statistical errors in estimating the parameters of gravitational-wave sources detectable by ground-based detectors. In particular, it is used to compute the lower bound on the variances of the parameters of the signals emitted by inspiralling compact binaries. However, the Fisher-matrix formalism is known to be valid in the strong-signal approximation only. Hence it is important to quantify the signal-to-noise ratio above which the Fisher information matrix is a reliable estimator, which can be done by performing numerical simulations. In this paper, we perform Monte Carlo simulations for the case of different source configurations of inspiralling compact binaries using 3.5 PN restricted post-Newtonian waveforms. We consider the initial LIGO design sensitivity curve. We found that for a (1.4, 10)M⊙ system, the Fisher information matrix predictions and those from Monte Carlo simulations are in very good agreement above a SNR of 20. We repeat the experiments for equal mass cases, namely a (1.4, 1.4)M⊙ and a (5, 5)M⊙ system. We found a systematic disagreement by a factor of 2 even at large SNRs (errors from the Fisher information matrix being higher). We have shown that by using templates with the symmetric mass ratio η > 0.25, the systematic disagreement vanishes in the regime of SNRs greater than 20.