The following table lists some binary-black-hole (BBH)
cases that we have evolved with the SXS collaboration's
Spectral Einstein Code (SpEC), grouped into non-spinning,
non-precessing and generic configurations. For the initial
spin
parameters
S1/
M12
and
S2/
M22,
the
z direction is parallel to the orbital angular
momentum. In the "Merger" column, "Yes" means the
simulation has evolved until the merged hole settles into
its final state; otherwise the simulation has stopped
about one orbit before merger. Click on the numbers in the "References" column to view the corresponding arXiv eprints.
| Case |
M2/M1 |
S1/M12 |
S2/M22 |
Norbits |
Merger? | References |
Comments |
| N1 | 1 |
0 | 0 |
16 | Yes |
1,
2,
3,
4,
5
|
a |
| N2 | 2 |
0 | 0 |
15 | Yes |
4,
5 |
a, b |
| N3 | 3 |
0 | 0 |
15 | - |
4,
5 |
a, b |
| N4 | 4 |
0 | 0 |
15 | - |
5 |
a |
| N5 | 6 |
0 | 0 |
8 | Yes |
5 |
a |
| N6 | 1 |
0 | 0 |
17 | - |
|
|
| S1 | 1 |
0 | 0.5ez |
15 | - |
|
c |
| S2 | 3 |
0 | 0.5ez |
14 | - |
|
c |
| S3 | 1 |
-0.4ez | -0.4ez |
11 | Yes |
5,
6 |
a |
| S4 | 1 |
0.4ez | 0.4ez |
15 | Yes |
5 |
a |
| S5 | 1 |
0.1ez | 0.1ez |
18 | - |
|
|
| S6 | 1 |
0.2ez | 0.2ez |
19 | - |
|
|
| S7 | 1 |
0.3ez | 0.3ez |
19 | - |
|
|
| S8 | 1 |
0.5ez | 0 |
15 | - |
|
|
| G1 | 1 |
-0.5ex | -0.5ez |
6.5 | - |
|
precessing |
| G2 | 2 |
0.2(ez-ex)/√2 |
-0.4(ez+ey)/√2 |
8.5 | Yes |
5, See below |
generic |
| G3 | 5 |
0.24ex-0.19ey-0.148ez | 0 |
6 | - |
|
generic, d |
| G4 | 2.9622 |
0.24ex-0.19ey-0.148ez | -0.158ex+0.370ey-0.045ez |
6.25 | - |
|
generic, d |
| G5 | 2 |
-0.349ex-0.446ey+0.565ez | 0 |
3 | - |
|
generic, |S1/M12|=0.8, d |
Comments
-
We and collaborators are currently using this simulation’s
numerical-relativity waveform to underpin
the effective-one-body
parametrized analytical fit (Buonanno et. al.) and also the phenomenological
parametrized analytical fit (Chen, Hannam, Husa, Parmeswaran) for future LIGO
data analysis.
-
An earlier 8-orbit version of this run has been used for calibrating EOB waveforms to numerical-relativity waveforms in Buonanno et al [Phys. Rev. D 79, 124028 (2009), arXiv:0902.0790].
-
These ongoing runs are expected to proceed
through about 15 orbits before merger.
-
These simulations are being used as test cases for automating the process of
generating initial data, interpolating onto the evolution grid, and evolving
through inspiral, merger, and ringdown.
Selected figures for Case G2
| M2/M1 |
S1/M12 |
S2/M22 |
Norbits |
| 2 |
0.2 (ez - ex)/√2 | -0.4 (ez + ey)/√2 |
8.25 |
The following plots illustrate some of the features of case G2, which is
an evolution of generic binary-black-hole initial data. The initial
masses and spins for this simulation are summarized in the above table.
The total number of orbits for this simulation is also shown.
Horizon trajectories during inspiral
The trajectories of hole 1 (blue) and hole 2 (red). Specifically,
the centers of the apparent horizons in the asymptotically
inertial coordinates of the simulation. The
z=0 plane is shaded
translucent gray; portions of the trajectories below
z=0 then
appear darker than portions of the curves that are above
z=0.
Spin precession during inspiral
The evolution of the spin directions for hole 1 (blue) and hole 2 (red).
The tips of unit vectors (in the asymptotically inertial coordinates used
in the simulation) trace out paths on the unit sphere (translucent gray).
Horizon masses and spins during inspiral
The mass ratio and dimensionless spins are nearly constant
throughout the 8.25 orbits of the inspiral shown here
(with the merger occurring shortly thereafter). The axes are normalized by the total
Arnowitt–Deser–Misner (ADM) mass of the system.
Proper separation of the two holes' apparent horizons during inspiral
The separation of the holes decreases by about a factor of two
throughout the simulation.
Individual and common horizons
The individual and common apparent horizons are shown just after the common horizon forms. The wireframe mesh is colored by the value of the lapse.
