Bayesian comparison of Post-Newtonian approximations of gravitational wave chirp signals

TL;DR

This study uses Bayesian model selection to compare different Post-Newtonian waveform approximations for gravitational wave signals, assessing detection probabilities and parameter estimation accuracy in simulated interferometer data.

Contribution

It introduces a Bayesian framework employing reversible jump MCMC to compare PN waveform models and evaluate their effectiveness in gravitational wave detection and parameter estimation.

Findings

Detection probabilities remain stable despite model simplifications.

Parameter estimation accuracy decreases with simplified waveform models.

Bayesian comparison effectively distinguishes between different PN orders.

Abstract

We estimate the probability of detecting a gravitational wave signal from coalescing compact binaries in simulated data from a ground-based interferometer detector of gravitational radiation using Bayesian model selection. The simulated waveform of the chirp signal is assumed to be a spin-less Post-Newtonian (PN) waveform of a given expansion order, while the searching template is assumed to be either of the same Post-Newtonian family as the simulated signal or one level below its Post-Newtonian expansion order. Within the Bayesian framework, and by applying a reversible jump Markov chain Monte Carlo simulation algorithm, we compare PN1.5 vs. PN2.0 and PN3.0 vs. PN3.5 wave forms by deriving the detection probabilities, the statistical uncertainties due to noise as a function of the SNR, and the posterior distributions of the parameters. Our analysis indicates that the detection probabilities are not compromised when simplified models are used for the comparison, while the accuracies in the determination of the parameters characterizing these signals can be significantly worsened, no matter what the considered Post-Newtonian order expansion comparison is.