Eccentricity estimation from initial data for Numerical Relativity Simulations

Abstract

We describe and study an instantaneous definition of eccentricity to be applied at the initial moment of full numerical simulations of binary black holes. The method consists of evaluating the eccentricity at the moment of maximum separation of the binary. We estimate it using up to third post-Newtonian (3PN) order, and compare these results with those of evolving (conservative) 3PN equations of motion for a full orbit and compute the eccentricity $e_r$ from the radial turning points, finding excellent agreement. We next include terms with spins up to 3.5PN, and then compare this method with the corresponding estimates of the eccentricity $e_r^{NR}$ during full numerical evolutions of spinning binary black holes, characterized invariantly by a fractional factor $0\le f\le 1$ of the initial tangential momenta. It is found that our initial instantaneous definition is a very useful tool to predict and characterize even highly eccentric full numerical simulations.

7 pages, 7 figures, 1 Table

References in corpus (6)

• GW190521: A Binary Black Hole Merger with a Total Mass of $150M_{\odot }$
• Properties and astrophysical implications of the 150 Msun binary black hole merger GW190521
• How to move a black hole without excision: gauge conditions for the numerical evolution of a moving puncture
• Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling
• Eccentric Binary Black Holes with Spin via the Direct Integration of the Post-Newtonian Equations of Motion
• Ancestral Black Holes of Binary Merger GW190521