Interpolation in waveform space: enhancing the accuracy of gravitational waveform families using numerical relativity

TL;DR

This paper introduces a method that uses singular value decomposition and interpolation to improve the accuracy of gravitational waveform models by calibrating phenomenological templates against numerical relativity simulations.

Contribution

It presents a novel approach combining SVD and interpolation to enhance phenomenological waveform models with better accuracy and faithfulness.

Findings

Improved waveform accuracy over original models

Reduced bias in phenomenological templates

Enhanced representation of numerical relativity signals

Abstract

Matched-filtering for the identification of compact object mergers in gravitational-wave antenna data involves the comparison of the data stream to a bank of template gravitational waveforms. Typically the template bank is constructed from phenomenological waveform models since these can be evaluated for an arbitrary choice of physical parameters. Recently it has been proposed that singular value decomposition (SVD) can be used to reduce the number of templates required for detection. As we show here, another benefit of SVD is its removal of biases from the phenomenological templates along with a corresponding improvement in their ability to represent waveform signals obtained from numerical relativity (NR) simulations. Using these ideas, we present a method that calibrates a reduced SVD basis of phenomenological waveforms against NR waveforms in order to construct a new waveform approximant with improved accuracy and faithfulness compared to the original phenomenological model. The new waveform family is given numerically through the interpolation of the projection coefficients of NR waveforms expanded onto the reduced basis and provides a generalized scheme for enhancing phenomenological models.