Application of the effective Fisher matrix to the frequency domain inspiral waveforms

Abstract

The Fisher matrix (FM) has been generally used to predict the accuracy of the gravitational wave parameter estimation. Although the limitation of the FM has been well known, it is still mainly used due to its very low computational cost compared to the Monte Carlo simulations. Recently, Rodriguez et al (2013 Phys. Rev. D 88 084013) performed Markov chain Monte Carlo (MCMC) simulations using a frequency domain inspiral waveform model (TaylorF2) for nonspinning binary systems with total masses , and they found systematic differences between the predictions from FM and MCMC for . On the other hand, an effective Fisher matrix (eFM) was recently introduced by Cho et al (2013 Phys. Rev. D 87 24004). The eFM is a semi-analytic approach to the standard FM, in which the derivative is taken of a quadratic function fitted to the local overlap surface. In this work, we apply the eFM method to the TaylorF2 waveform for nonspinning binary systems with a moderately high signal-to-noise ratio () and find that the eFM can reproduce the MCMC error bounds in Rodriguez et al well, even for high masses. By comparing the eFM standard deviation directly with the 1-σ confidence interval of the marginalized overlap that approximates the MCMC posterior distribution, we show that the eFM can be acceptable in all mass regions for the estimation of the MCMC error bounds. We also investigate the dependence on the signal strength.