BHBH without spin

  1. Introduction
  2. Binary Inspiral and Merger
  3. Gravitational Radiation Waveform
  4. Final Black Hole Parameters


Fig. 1-1 Initial Configuration of Binary
Fig. 1-1 Initial Configuration of Binary
Evolution is performed with the BSSN scheme on an AMR grid with 9 levels of refinement. The outer boundary of our grid is 320M and the mesh spacing ranges from ΔXmax = 8.0 M in the outermost level to ΔXmin = M/32 in the innermost level. In this simulation, the initial coordinate radius of the binary orbit is D0/M = 9.89. Here M is the total initial binary ADM mass. The black hole interiors, bounded by their apparent horizons, are denoted by black spheres. Their motion is shown in the orbital plane. The evolution is performed with "moving puncture" gauge conditions. (Note: The circle in the lower right-hand corner of the above figure is a clock.)

Binary Inspiral and Merger

The binary makes approximately six orbits prior to merging at t ≈ 870 M. As the inital binary merges, we see the development of a common horizon which oscillates until settling down at t ≈ 930 M. The simulation continues until t = 1246 M to demonstrate the stability of the resulting Kerr black hole. The early growth of the apparent horizons is a gauge (coordinate) effect.
Fig. 2-1 Evolution at t/M = 0
Fig. 2-1 Evolution at t/M = 0
Fig. 2-2 Evolution at t/M = 650
Fig. 2-2 Evolution at t/M = 650
Fig. 2-3 Evolution at t/M = 800
Fig. 2-3 Evolution at t/M = 800
Fig. 2-3 Evolution at t/M = 1250
Fig. 2-4 Evolution at t/M = 1250
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Gravitational Radiation Waveform

The gravitational wavetrain from a compact binary system may be separated into three qualitatively different phases: inspiral, merger, and ringdown. During the inspiral phase, which takes up most of the binary's lifetime, gravity wave emission gradually reduces the binary separation as the BHs maintain a quasicircular orbit. Here, we see the gravitational radiation waveform during the late inspiral and merger stages of our binary black hole coalescence simulation. Finally, we see a ringdown as the distorted black hole settles down to Kerr equilibrium. Both polarization modes (h+ and hx) are shown.
Fig. 3-1 h+ both hemispheres
Fig. 3-1 h+ in both hemispheres
Fig. 3-2 h+ one hemisphere
Fig. 3-2 h+ in one hemisphere
Fig. 3-1 h× both hemispheres
Fig. 3-3 h× both hemispheres
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Final Black Hole Parameters

Listed in the table below is the dimensionless spin of the black hole at the end of our simulation. Also shown are the radiated energy and angular momentum from gravitational wave emission. Here, M is the initial binary ADM mass whereas MBH is the final ADM mass of the black hole remnant.
MBH/M 0.962
JBH/MBH2 0.685
ΔE GW/M 0.038
ΔJGW/M2 0.331
δE ≡ (M-MBH-ΔEGW)/M 4 x 10-4
δJ ≡ (J-JBH-ΔJGW)/M 4 x 10-3
Our simulation maintains excellent conservation of energy and momentum, since δE and δJ are on the order of 10-4 and 10-3, respectively.