Spin expansion for binary black hole mergers: New predictions and future directions

In a recent paper [L. Boyle, M. Kesden, and S. Nissanke, Phys. Rev. Lett. 100, 151101 (2008)], we introduced a spin expansion that provides a simple yet powerful way to understand aspects of binary black hole merger. This approach relies on the symmetry properties of initial and final quantities like the black hole mass m, kick velocity k, and spin vector 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.