On Estimation of the Post-Newtonian Parameters in the Gravitational-Wave Emission of a Coalescing Binary
Andrzej Królak, Kostas D. Kokkotas, Gerhard Schäfer
TL;DR
This work analyzes how second-order post-Newtonian corrections affect gravitational-wave parameter estimation for coalescing binaries, using a restricted PN waveform and maximum-likelihood inference with Fisher information bounds. It finds that while the chirp mass and coalescence time are robustly measured, individual component masses become poorly constrained as PN terms and spin parameters increase, though the chirp mass remains the dominant mass-related observable. The study compares Newtonian and post-Newtonian search templates, showing that PN templates improve parameter accuracy, while the Newtonian filter can serve as a fast online detector and yields an effective mass parameter that informs the broader inference. It also explores how gravitational theories beyond GR, such as Jordan-Fierz-Brans-Dicke and Damour-Esposito-Farèse, could be constrained by gravitational-wave observations through shifts in the mass-parameterization of the waveform. Overall, the results guide practical data-analysis strategies for future detectors by combining simple online scans with more precise PN templates and by enabling tests of alternative gravity theories with GW signals.
Abstract
The effect of the recently obtained 2nd post-Newtonian corrections on the accuracy of estimation of parameters of the gravitational-wave signal from a coalescing binary is investigated. It is shown that addition of this correction degrades considerably the accuracy of determination of individual masses of the members of the binary. However the chirp mass and the time parameter in the signal is still determined to a very good accuracy. The possibility of estimation of effects of other theories of gravity is investigated. The performance of the Newtonian filter is investigated and it is compared with performance of post-Newtonian search templates introduced recently. It is shown that both search templates can extract accurately useful information about the binary.