The spin expansion for binary black hole merger: new predictions and future directions

TL;DR

The paper refines a spin expansion method for binary black hole mergers, validating predictions with simulations, and proposes future directions including calibration techniques and extensions to eccentric orbits.

Contribution

It advances the spin expansion approach by testing its predictions, proposing calibration methods with minimal simulations, and discussing extensions to more general orbital configurations.

Findings

Some predictions confirmed by simulations

Calibration requires only a small number of simulations

Extension to eccentric orbits proposed

Abstract

In a recent paper arXiv:0709.0299, we introduced a spin expansion that provides a simple yet powerful way to understand aspects of binary black hole (BBH) merger. This approach relies on the symmetry properties of initial and final quantities like the black hole mass m, kick velocity {\bf k}, and spin vector {\bf s}, rather than a detailed understanding of the merger dynamics. In this paper, we expand on this proposal, examine how well its predictions agree with current simulations, and discuss several future directions that would make it an even more valuable tool. The spin expansion yields many new predictions, including several exact results that may be useful for testing numerical codes. Some of these predictions have already been confirmed, while others await future simulations. We explain how a relatively small number of simulations -- 10 equal-mass simulations, and 16 unequal-mass simulations -- may be used to calibrate all of the coefficients in the spin expansion up to second order at the minimum computational cost. For a more general set of simulations of given covariance, we derive the minimum-variance unbiased estimators for the spin expansion coefficients. We discuss how this calibration would be interesting and fruitful for general relativity and astrophysics. Finally, we sketch the extension to eccentric orbits.