Equal Mass BHBH Evolution
Introduction
Evolution of
BHBH merger
Evolution of Gravitational
Radiation Profile
Final Black Hole
Parameters
Introduction
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 &Delta
Evolution
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. 2-2 Evolution at t/M = 770 |
Fig. 2-3 Evolution at t/M = 845 | Fig. 2-4 Evolution at t/M = 1246 |
Evolution of
Gravitational Radiation Profile
The gravitational wavetrain from a compact binary system may be separated into three qualitatively different phases: the 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. Figures 3-3 and 3-7 show the gravitational radiation profile 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 (Figures 3-4 and 3-8). Both polarization modes (h+ and hx) are shown.
h+
Fig. 3-1 Color code for radiation profile |
Fig. 3-2 Evolution at t/M = 0 |
Fig. 3-3 Evolution at t/M = 725 | Fig. 3-4 Evolution at t/M = 945 |
hx
Fig. 3-5 Color code for radiation profile |
Fig. 3-6 Evolution at t/M = 0 |
Fig. 3-7 Evolution at t/M = 725 | Fig. 3-8 Evolution at t/M = 945 |
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 ADM mass whereas MBH is the final ADM mass of the black hole.
MBH/M | 0.962 |
JBH/M2 BH | 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.