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

When numerically solving Einstein's equations for the evolution of binary black holes (BBHs), physical imperfections in the initial data manifest as a transient, high-frequency pulse of "junk radiation." This unphysical signal must be removed before accurate templates for gravitational wave analyses can be produced. 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 time series data for the areal mass of the black holes, thereby estimating the decay time of the junk radiation. To make this procedure precise, we propose threshold criteria that specify how small the contribution of junk radiation has to be before it can be considered negligible. We apply this method to 3714 BBH waveforms from the SXS catalog and identify five groups of simulations, each characterized by specific values of the criteria. The algorithm applies the most appropriate values of the thresholds to each simulation. We find that this approach yields reliable decay time estimates, i.e., when to consider the simulation physical, for >98.6% of the simulations studied. This demonstrates the efficacy of EMD as a suitable tool to isolate and characterize junk radiation in the simulation of BBH systems.