Hierarchical data-driven approach to fitting numerical relativity data for nonprecessing binary black holes with an application to final spin and radiated energy

TL;DR

This paper introduces a hierarchical data-driven fitting method for numerical relativity data of nonprecessing binary black holes, improving accuracy in predicting final spin and radiated energy, especially near extremal and unequal-spin configurations.

Contribution

It presents a novel hierarchical fitting approach that incorporates extreme-mass-ratio and unequal-spin effects, enhancing the modeling of binary black hole merger outcomes.

Findings

Achieved improved fit accuracy over previous models.

Effectively incorporated extreme-mass-ratio limits.

Highlighted importance of data quality and error analysis.

Abstract

Numerical relativity is an essential tool in studying the coalescence of binary black holes (BBHs). It is still computationally prohibitive to cover the BBH parameter space exhaustively, making phenomenological fitting formulas for BBH waveforms and final-state properties important for practical applications. We describe a general hierarchical bottom-up fitting methodology to design and calibrate fits to numerical relativity simulations for the three-dimensional parameter space of quasicircular nonprecessing merging BBHs, spanned by mass ratio and by the individual spin components orthogonal to the orbital plane. Particular attention is paid to incorporating the extreme-mass-ratio limit and to the subdominant unequal-spin effects. As an illustration of the method, we provide two applications, to the final spin and final mass (or equivalently: radiated energy) of the remnant black hole. Fitting to 427 numerical relativity simulations, we obtain results broadly consistent with previously published fits, but improving in overall accuracy and particularly in the approach to extremal limits and for unequal-spin configurations. We also discuss the importance of data quality studies when combining simulations from diverse sources, how detailed error budgets will be necessary for further improvements of these already highly accurate fits, and how this first detailed study of unequal-spin effects helps in choosing the most informative parameters for future numerical relativity runs.