BHBH Evolution

Introduction
Evolution of BHBH merger
Evolution of Gravitational Radiation Profile
Final Black Hole Parameters


Introduction


Fig. 1-1 Initial Configuration of Binary

In this simulation, the initial orbital radius is D/M = 9.89. The black hole apparent horizons are denoted by black spheres. Their motion is shown in the orbital plane. The evolution is performed with the BSSN scheme utilizing "moving puncture" gauge conditions.


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 = 705

Fig. 2-3 Evolution at t/M = 740

Fig. 2-4 Evolution at t/M = 1246

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Evolution of Gravitational Radiation Profile

The gravitational wavetrain from a compact binary system may be separated into three qualitativly different parts: 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 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 = 705

Fig. 3-4 Evolution at t/M = 940

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hx


Fig. 3-5 Color code for radiation profile

Fig. 3-6 Evolution at t/M = 0

Fig. 3-7 Evolution at t/M = 705

Fig. 3-8 Evolution at t/M = 940

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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.

JBH/M2final0.69
&Delta EGW/Minitial3.8%
&Delta JGW/M2final33.0%

As a check on our integrations we find that the conservation of mass-energy, Minitial = Mfinal + &Delta EGW and the conservation of angular momentum, Jinitial = Jfinal + &Delta JGW are both satisfied within 1%.


last updated 5 December 2014 by aakhan3

Center for Theoretical Astrophysics---University of Illinois at Urbana-Champaign

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