A Mathematica package for generating gravitational waveforms for nonspinning eccentric binary black hole mergers.
Requirements: Mathematica v10 (Jul 2014) or later
EccentricIMR was written by Ian Hinder and is distributed under the terms of the GNU General Public Licence (GPL) version 2.
Copyright (C) Ian Hinder, 2017.
See Hinder, Kidder and Pfeiffer - An eccentric binary black hole inspiral-merger-ringdown gravitational waveform model from numerical relativity and post-Newtonian theory, 2017 for details of the construction of the waveform.
You can install EccentricIMR either using Git (recommended) or by downloading a zip file.
Change into your Mathematica applications directory.
For Mac OS,
cd ~/Library/Mathematica/Applications
For Linux,
cd ~/.Mathematica/Applications
Clone the repository
git clone https://github.com/ianhinder/EccentricIMR.git
- Download master.zip,
- Extract the zip file
- Rename the extracted directory EccentricIMR-master as EccentricIMR
- Move the directory into your Mathematica applications directory (~/Library/Mathematica/Applications on Mac OS, ~/.Mathematica/Applications on Linux)
Open a new Mathematica notebook and enter the following:
<< EccentricIMR`;
params = <|"q" -> 1, "x0" -> 0.07, "e0" -> 0.1,
"l0" -> 0, "phi0" -> 0, "t0" -> 0|>;
hEcc = EccentricIMRWaveform[params, {0, 10000}];
ListLinePlot[Re[hEcc]]
Generate an eccentric inspiral-merger-ringdown waveform with the parameters given in the time range {t1,t2}.
parameters is an Association with the following entries:
| Parameter | Meaning |
|---|---|
| q | Mass ratio of the binary (q=m1/m2) |
| t0 | Reference time at which the remaining parameters are quoted |
| x0 | Dimensionless frequency parameter (x = (M om_orb)^(2/3)) evaluated at the reference time |
| e0 | Eccentricity at the reference time |
| l0 | Mean anomaly at the reference time |
| phi0 | Orbital phase at the reference time |
See arXiv:0806.1037 for full details about the meaning of the parameters.
The returned waveform is expressed as a list of {t, h22} pairs, where t is the retarted time coordinate and h22 is the l=2, m=2 spin-weighted spherical harmonic coefficient of the waveform.
Example:
In[1]:= hEcc = EccentricIMRWaveform[<|"q" -> 1, "x0" -> 0.07,
"e0" -> 0.1, "l0" -> 0, "phi0" -> 0, "t0" -> 0|>,
{0, 10000}];
In[2]:= Take[hEcc, 10]
Out[2]:= {{0., -0.127741 + 0.000381028 I}, {1., -0.127596 +
0.00619006 I}, {2., -0.127182 + 0.0119862 I}, {3., -0.126498 +
0.0177567 I}, {4., -0.125546 + 0.0234884 I}, {5., -0.12433 +
0.0291683 I}, {6., -0.122851 + 0.0347835 I}, {7., -0.121113 +
0.0403215 I}, {8., -0.119122 + 0.0457697 I}, {9., -0.11688 +
0.051116 I}}
Open the notebook EccentricIMRTests.nb from the package directory and evaluate it. The will run tests of several internal functions, as well as EccentricIMRWaveform.