High accuracy simulations of black hole binaries: Spins anti-aligned with the orbital angular momentum

Abstract

High-accuracy binary black hole simulations are presented for black holes with spins anti-aligned with the orbital angular momentum. The particular case studied represents an equal-mass binary with spins of equal magnitude S/m^2=0.437 57±0.000 01. The system has initial orbital eccentricity ∼4×10^(-5), and is evolved through 10.6 orbits plus merger and ringdown. The remnant mass and spin are M_f=(0.961 109±0.000 003)M and S_f/M_f^2=0.547 81±0.000 01, respectively, where M is the mass during early inspiral. The gravitational waveforms have accumulated numerical phase errors of ≲0.1 radians without any time or phase shifts, and ≲0.01 radians when the waveforms are aligned with suitable time and phase shifts. The waveform is extrapolated to infinity using a procedure accurate to ≲0.01 radians in phase, and the extrapolated waveform differs by up to 0.13 radians in phase and about 1% in amplitude from the waveform extracted at finite radius r=350M. The simulations employ different choices for the constraint damping parameters in the wave zone; this greatly reduces the effects of junk radiation, allowing the extraction of a clean gravitational wave signal even very early in the simulation.