Automated determination of the end time of junk radiation in binary black hole simulations

TL;DR

This paper introduces an automated algorithm using empirical mode decomposition to accurately identify when junk radiation in binary black hole simulations has decayed, improving the efficiency of waveform analysis.

Contribution

The novel application of EMD-based analysis provides a reliable, automated method to determine junk radiation decay time in large sets of binary black hole simulations.

Findings

Reliable decay time estimates for over 98.6% of simulations

Effective automatic isolation of junk radiation

Applicable to large waveform catalogs

Abstract

When numerically solving Einstein's equations for the evolution of binary black holes, physical imperfections in the initial data manifest as a transient, high-frequency pulse of ''junk radiation.'' This unphysical signal must be removed before the waveform can be used. Improvements in the efficiency of numerical simulations now allow waveform catalogs containing thousands of waveforms to be produced. Thus, an automated procedure for identifying junk radiation is required. To this end, we present a new algorithm based on the empirical mode decomposition (EMD) from the Hilbert-Huang transform. This approach allows us to isolate and measure the high-frequency oscillations present in the measured irreducible masses of the black holes. The decay of these oscillations allows us to estimate the time from which the junk radiation can be ignored. To make this procedure more precise, we propose three distinct threshold criteria that specify how small the contribution of junk radiation has to be before it can be considered negligible. We apply this algorithm to 3403 BBH simulations from the SXS catalog to find appropriate values for the thresholds in the three criteria. We find that this approach yields reliable decay time estimates, i.e., when to consider the simulation physical, for over 98.6% of the simulations studied. This demonstrates the efficacy of the EMD as a suitable tool to automatically isolate and characterize junk radiation in the simulation of binary black hole systems.