wintervolcano / eccentricimr

A Mathematica package for generating gravitational waveforms for nonspinning eccentric binary black hole mergers

EccentricIMR

About

A Mathematica package for generating gravitational waveforms for nonspinning eccentric binary black hole mergers.

EccentricIMR was originally written by Ian Hinder. This is a Git-forked version modified by Sashwat Tanay.

Copyright (C) Ian Hinder, 2017.

This Mathematica package is based on this paper: Generalized quasi-Keplerian solution for eccentric, non-spinning compact binaries at 4PN order and the associated IMR waveform, 2021.

Installation

You can install EccentricIMR by downloading a zip file.

• Download master.zip,
• Extract the zip file
• There is a directory 'EccentricIMR' in '4PN_IMR_package' (plots the full IMR; does not work for large eccentricities) and also in '4PN_Inspiral_only_package' (uses only the post-Newtonian equations; works for large eccentricities too).
• Move the 'EccentricIMR' directory (from either the '4PN_IMR_package' directory or the '4PN_Inspiral_only_package' directory) into your Mathematica applications directory (~/Library/Mathematica/Applications on Mac OS, ~/.Mathematica/Applications on Linux)
• The file 'How to run the packages.nb' has commands that will run the packages and plot the waveforms. Alternatively, see the Sec. "How to run the packages" below.
• The file 'Lengthy_expressions.nb' and 'Lengthy_expressions.pdf' contains some lengthy expressions which we did not present in the paper for the sake of brevity.

How to run the packages

Once the Mathematica package directory has been moved to the correct location (as explained above), the following codes are to be run to generate the waveforms

For the full IMR package

<<EccentricIMR`;
params=<|"q"->1,"x0"->0.07,"e0"->0.1,"l0"->0,"phi0"->0,"t0"->0|>;
hEcc=EccentricIMRWaveform[params,{0,10000}];
ListLinePlot[Re[hEcc]]

For the Inspiral-only package

<< EccentricIMR`;
finTime1 = 
  10000;                              (*final time; end of simulation*)

params = <|"q" -> 1, "x0" -> 0.07, "e0" -> 0.25, "l0" -> 0, 
   "phi0" -> 0, "t0" -> 0|>;
dt =  1 ;                                 
hEcc = EccentricIMRWaveform[params, {0,   finTime1     , dt}];
ifun = hEcc["h"]  ;     
InterFun = hEcc["h"] ;
iniTime  =    ((InterFun@Domain)[[1]])[[1]]   ;
finTime =      ((InterFun@Domain)[[1]])[[2]]   ;
nDiv = Round[(finTime - iniTime)/dt];                  
timeArr = Array[# &, nDiv + 1, {iniTime, finTime}];     
sigArr = Re[ifun[timeArr]];                       
ListLinePlot[sigArr]

Documentation

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:2110.09608 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.