Statistical and systematic errors for gravitational-wave inspiral signals: A principal component analysis

TL;DR

This paper uses principal component analysis within an adapted coordinate system to efficiently analyze statistical and systematic errors in gravitational-wave inspiral signals, focusing on parameter measurement accuracy and waveform modeling.

Contribution

It introduces a linear Fisher-matrix approach combined with PCA to identify key parameter combinations and assess waveform systematic errors efficiently.

Findings

Chirp mass is the most effectively measured parameter.

Spin and mass ratio combinations significantly influence parameter estimation.

Including spin-orbit corrections up to next-to-leading order improves waveform accuracy.

Abstract

Identifying the source parameters from a gravitational-wave measurement alone is limited by our ability to discriminate signals from different sources and the accuracy of the waveform family employed in the search. Here we address both issues in the framework of an adapted coordinate system that allows for linear Fisher-matrix type calculations of waveform differences that are both accurate and computationally very efficient. We investigate statistical errors by using principal component analysis of the post-Newtonian (PN) expansion coefficients, which is well conditioned despite the Fisher matrix becoming ill conditioned for larger numbers of parameters. We identify which combinations of physical parameters are most effectively measured by gravitational-wave detectors for systems of neutron stars and black holes with aligned spin. We confirm the expectation that the dominant parameter of the inspiral waveform is the chirp mass. The next dominant parameter depends on a combination of the spin and the symmetric mass ratio. In addition, we can study the systematic effect of various spin contributions to the PN phasing within the same parametrization, showing that the inclusion of spin-orbit corrections up to next-to-leading order, but not necessarily of spin-spin contributions, is crucial for an accurate inspiral waveform model. This understanding of the waveform structure throughout the parameter space is important to set up an efficient search strategy and correctly interpret future gravitational-wave observations.