Case E
Case E
Introduction
Evolution of
Density Profile
Evolution of Density
Profile with Velocity Field
Evolution of
Gravitational Radiation Profile
Final
Black Hole Parameters
Introduction
Fig. 1-1 Initial Configuration
of Binary
Evolution is
performed on an AMR (Adaptive Mesh Refinement) grid. The outermost grid
is 435 M x 435 M, the innermost refinement level for
the BH is 1.47 M x 1.47 M and the innermost
refinement level for the NS is 6.8 M x 6.8 M. Here
M is the total (ADM) mass of the initial system. The innermost
resolution is ΔXmin/M = 1/58.8. In this
simulation, the initial binary coordinate separation is D0/M = 8.61, the initial
angular momentum of the system is J/M2 = 0.938, the mass
ratio is MBH:MNS = 1:1,
and the black hole spin parameter is JBH/MBH2 = 0
.00. (Note: The open circle in the lower right-hand corner of the
above figure is a clock.)
Evolution of the Density Profile
In the clip from the equatorial plane, the rest-mass density of the neutron star is plotted on a logarithmic scale normalized to the initial central density. The gravitational field is evolved via the BSSN scheme using "moving puncture" gauge conditions. The relativistic hydrodynamic equations are solved using a high-resolution shock-capturing (HRSC) method.
Because of the low mass ratio in Case E, tidal disruption occurs at a
farther binary separation. After tidal disruption, the NS matter curls
around the BH forming a hot, low-density spiral that winds around the AH
and smashes into the tidal tail, generating a large amount of shock
heating. A fraction of the heated NS matter in the tail loses angular
momentum and falls into the BH. The rest (2.3% of the rest mass) deforms into an inhomogeneous
disk before settling into a quasistationary state. At the end of the
simulation, the NS matter in the disk settles into a high density, low temperature
torus of matter surrounding the BH.
 Fig. 2-1 Color code for density profile |  Fig. 2-2 Density Profile at t/M = 250 |
 Fig. 2-3 Density Profile at t/M = 350 |  Fig. 2-4 Density Profile at t/M = 572 |
Evolution of Density Profile with Velocity Field
 Fig. 3-1 Density Profile at t = 0 |
 Fig. 3-2 Density Profile at t = 250 |
 Fig. 3-3 Density Profile t/M = 350 |  Fig. 3-4 Density Profile at t/M = 572 |
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. The merger phase of the gravitational wavetrain is characterized by tidal disruption of the neutron star. Finally, ringdown radiation is emitted as the distorted black hole settles down to Kerr-like equilibrium (Note: Only in the case of a vacuum spacetime does the spinning BH obey the Kerr solution. The BHs formed here are surrounded by gaseous disks with small, but nonnegligible, rest mass). Both polarization modes (h+ and hx) are shown. Total energy conservation is obeyed to within 0.01%. Total angular momentum conservation is obeyed to within 0.9%.
 Fig. 4-1 h+ Profile |
 Fig. 4-2 hx Profile |
Fig. 4-3 h+ in orbital plane
Final Black Hole Parameters
Listed in the table below is the dimensionless spin of the Kerr-like black hole at the end of our simulation. Also shown are the radiated energy, angular momentum, and linear recoil velocity resulting from gravitational wave emission. Additional parameters for the disk are given in the film clip.
| JBH/M2BH | 0.851 |
| &Delta JGW/J | 7.2% |
| &Delta EGW/M | 0.35% |
| Recoil velocity | 17 km/s |