Efficient asymptotic frame selection for binary black hole spacetimes using asymptotic radiation

TL;DR

This paper introduces an efficient method to estimate the emission direction of binary black hole gravitational waves using asymptotic radiation data, aiding in data analysis and waveform quality assessment.

Contribution

It presents a novel approach utilizing the principal axes of <L_a L_b> at asymptotic infinity to determine source orientations and improve parameter estimation.

Findings

Instantaneous emission directions can be estimated efficiently.

Averaged <L_a L_b> correlates with Fisher matrix components.

Method provides fast, invariant waveform diagnostics.

Abstract

Previous studies have demonstrated that gravitational radiation reliably encodes information about the natural emission direction of the source (e.g., the orbital plane). In this paper, we demonstrate that these orientations can be efficiently estimated by the principal axes of <L_a L_b>, an average of the action of rotation group generators on the Weyl tensor at asymptotic infinity. Evaluating this average at each time provides the instantaneous emission direction. Further averaging across the entire signal yields an average orientation, closely connected to the angular components of the Fisher matrix. The latter direction is well-suited to data analysis and parameter estimation when the instantaneous emission direction evolves significantly. Finally, in the time domain, the average <L_a L_b> provides fast, invariant diagnostics of waveform quality.