The spin expansion for binary black hole merger: new predictions and future directions
arXiv:0712.2819 · doi:10.1103/PhysRevD.78.024017
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.
32 pages, 8 figures, matches Phys. Rev. D version. Added new appendix: "Minimum-variance estimators for the spin coefficients"
References in corpus (14)
- Supermassive recoil velocities for binary black-hole mergers with antialigned spins
- Recoil velocities from equal-mass binary black-hole mergers: a systematic investigation of spin-orbit aligned configurations
- High-spin binary black hole mergers
- Black Hole Mergers and Unstable Circular Orbits
- Anatomy of the binary black hole recoil: A multipolar analysis
- Observable Signatures of a Black Hole Ejected by Gravitational Radiation Recoil in a Galaxy Merger
- Modeling kicks from the merger of non-precessing black-hole binaries
- Binary black hole mergers: large kicks for generic spin orientations
- Binary Black Holes: Spin Dynamics and Gravitational Recoil
- Circularization and Final Spin in Eccentric Binary Black Hole Inspirals
- Binary black hole merger: symmetry and the spin expansion
- Approximate Killing Vectors on S^2
- Final spin of a coalescing black-hole binary: an Effective-One-Body approach
- Measuring eccentricity in binary black-hole initial data