[Paper Review] Detection of gravitational waves from inspiraling compact binaries using non-restricted post-Newtonian approximations

A. M. Sintes, A. Vecchio|ArXiv.org|May 16, 2000

Pulsars and Gravitational Waves Research3 citations

TL;DR

This paper investigates the impact of including post-Newtonian (PN) corrections in the amplitude of gravitational wave templates for compact binary inspirals, beyond the standard restricted PN approximation that only includes PN corrections in the phase. It shows that incorporating 0.5PN amplitude corrections improves mass parameter estimation by a factor of ~2 in signal-to-noise ratio (SNR) = 10, reduces parameter correlations, and introduces measurable information about inclination and polarization, though signal-to-noise degradation remains minimal for detection.

ABSTRACT

The set up of matched filters for the detection of gravitational waves from in-spiraling compact binaries is usually carried out using the restricted post-Newtonian approximation: the filter phase is modelled including post-Newtonian corrections, whereas the amplitude is retained at the Newtonian order. Here we investigate the effects of the introduction of post-Newtonian corrections also to the amplitude and we discuss some of the implications for signal detection and parameter estimation.

Motivation & Objective

• To assess the impact of including post-Newtonian corrections in the amplitude of gravitational wave templates for compact binary inspirals.
• To evaluate whether amplitude corrections beyond the restricted PN approximation affect detection performance and parameter estimation accuracy.
• To investigate the information content in the 0.5PN amplitude corrections, particularly regarding source inclination and polarization.
• To quantify the improvement in parameter estimation errors and correlations when using non-restricted PN waveforms.

Proposed method

• The authors derive a non-restricted post-Newtonian waveform model that includes 0.5PN corrections to the amplitude while retaining the 2PN phase evolution.
• They compute the Fourier transform of the full waveform using the stationary phase approximation, resulting in a signal model with a complex envelope factor Λ that depends on inclination and symmetric mass ratio.
• The signal is cross-correlated with template banks using the match metric and fitting factor to assess detection performance.
• Parameter estimation is performed via the Fisher information matrix, comparing restricted PN and non-restricted PN waveforms under identical SNR conditions.
• The match between true signals and templates is evaluated using the fitting factor and the match in the restricted PN plane.
• Correlation coefficients between parameters are computed to assess degeneracy reduction in the non-restricted case.

Experimental results

Research questions

• RQ1 Does including 0.5PN corrections in the amplitude of gravitational wave templates significantly affect detection performance for compact binary inspirals?
• RQ2 To what extent do amplitude corrections improve the accuracy of mass and source parameter estimation compared to the restricted PN approximation?
• RQ3 How do the new parameters introduced by amplitude corrections—specifically $ F_{\times}/F_{+} $ and $ \cos\iota $—affect parameter degeneracies and measurement errors?
• RQ4 What is the quantitative improvement in fitting factor and match when using non-restricted PN waveforms?
• RQ5 How do the correlation coefficients between parameters change when amplitude corrections are included?

Key findings

• The fitting factor between the true signal and templates improves significantly when 0.5PN amplitude corrections are included, especially at high inclination angles and low symmetric mass ratios.
• For SNR = 10, the error in chirp mass estimation is reduced by a factor of approximately 2 when using non-restricted PN waveforms compared to the restricted PN case.
• The measurement error for $ \cos\iota $ is reduced to 0.4291, and for $ F_{\times}/F_{+} $ to 0.9435, indicating measurable information about polarization and inclination.
• The correlation coefficients between parameters are reduced in the non-restricted case, particularly between amplitude and other parameters, which were uncorrelated in the restricted approximation.
• The amplitude is now correlated with other parameters in the non-restricted case, but the overall correlation structure is less degenerate than in the restricted PN framework.
• The match between signal and template is well approximated by the product of the fitting factor and the match in the restricted PN plane, validating the use of this decomposition for performance estimation.