gwNRHME framework#
This framework is developed in https://arxiv.org/abs/2403.15506.
Utilizing publicly available non-spinning eccentric binary black hole (BBH) merger simulations from the SXS collaboration, we presents convincing evidence that the waveform phenomenology in eccentric BBH mergers is significantly simpler than previously thought. We find that the eccentric modulations in the amplitudes, phases, and frequencies in different spherical harmonic modes are all related and can be modeled using a single time series modulation. Using this universal eccentric modulation, we provide a framework named \texttt{gwNRHME} to seamlessly convert a multi-modal (i.e with several spherical harmonic modes) quasi-circular waveform into multi-modal eccentric waveform if the quadrupolar eccentric waveform is known. This reduces the modelling complexity of eccentric BBH mergers drastically as we now have to model only a single eccentric modulation time-series instead of modelling the effect of eccentricity in all modes. When compared with the NR simulations, our framework mismatches are mostly ∼0.001 and are comparable to the numerical errors in the NR simulations. Our method is modular and can be readily added to any quadrupolar non-spinning eccentric waveform model.
import warnings
warnings.filterwarnings("ignore", "Wswiglal-redir-stdio")
import matplotlib.pyplot as plt
import numpy as np
# import gwModels
import sys
PATH_TO_GWMODELS = "/home/tousifislam/Documents/works/git_repos/gwModels/"
sys.path.append(PATH_TO_GWMODELS)
import gwModels
lal.MSUN_SI != Msun
__name__ = gwsurrogate.new.spline_evaluation
__package__= gwsurrogate.new
Loaded NRHybSur3dq8 model
import gwsurrogate
sur = gwsurrogate.LoadSurrogate('NRHybSur3dq8')
Loaded NRHybSur3dq8 model
1. Generate eccentric 22 mode waveform#
We use EccentricIMR model, developed in https://arxiv.org/abs/1709.02007 and is originally hosted in ianhinder/EccentricIMR.
# Set the path to your Wolfram kernel
# you will need Mathematica installed along with wolframclient
wolfram_kernel_path = '/home/tousifislam/Documents/Mathematica/ScriptDir/WolframKernel'
# Set the path to the directory containing the EccentricIMR package
package_directory = PATH_TO_GWMODELS + '/externals/EccentricIMR2017/'
# package_directory = '/home/tousifislam/.Mathematica/Applications/EccentricIMR/'
# instantiate the EccentricIMR class - it may take some time
wf = gwModels.EccentricIMR(wolfram_kernel_path, package_directory)
# Set the binary parameters
params = {"q": 2, # mass ratio
"x0": 0.07, # reference initial dimensionless orbital frequency
"e0": 0.1, # initial eccentricity
"l0": 0, # initial mean anomaly
"phi0": 0, # initial reference phase
"t0": 0} # some initial reference time - not much relevant for us
# generate eccentric 22 mode waveform
tecc, hecc = wf.generate_waveform(params)
Times[1.0, 0] is too small to represent as a normalized machine number; precision may be lost.
Times[1.0, 0] is too small to represent as a normalized machine number; precision may be lost.
Times[1.0, 0] is too small to represent as a normalized machine number; precision may be lost.
Further output of MessageName[General, munfl] will be suppressed during this calculation.
Times[1.0, 0] is too small to represent as a normalized machine number; precision may be lost.
Times[1.0, 0] is too small to represent as a normalized machine number; precision may be lost.
Times[1.0, 0] is too small to represent as a normalized machine number; precision may be lost.
Times[1.0, 0] is too small to represent as a normalized machine number; precision may be lost.
Further output of MessageName[General, munfl] will be suppressed during this calculation.
Times[1.0, 0] is too small to represent as a normalized machine number; precision may be lost.
# plot waveform
plt.figure(figsize=(10,3))
plt.plot(tecc, hecc, '-', lw=2, label='EccentricIMR')
plt.xlabel('$t/M$')
plt.ylabel('$rh_{22}/M$')
plt.tight_layout()
plt.show()
2. Generate multi-modal circular waveform#
We use NRHybSur3dq to generate circular waveform in the non-spinning limit.
gwsur = gwModels.genNRHybSur3dq8()
Loaded NRHybSur3dq8 model
tsur, hsur = gwsur.generate_NRHybSur3dq8(params)
print(hsur.keys())
dict_keys(['h_l2m1', 'h_l2m2', 'h_l3m2', 'h_l4m4', 'h_l3m3', 'h_l3m1', 'h_l4m3', 'h_l4m2', 'h_l5m5'])
# plot waveform
plt.figure(figsize=(10,9))
plt.subplot(411)
plt.plot(tsur, hsur['h_l2m2'], '-', lw=2, label='EccentricIMR')
plt.xlabel('$t/M$')
plt.ylabel('$rh_{22}/M$')
plt.subplot(412)
plt.plot(tsur, hsur['h_l2m1'], '-', lw=2, label='EccentricIMR')
plt.xlabel('$t/M$')
plt.ylabel('$rh_{21}/M$')
plt.subplot(413)
plt.plot(tsur, hsur['h_l3m3'], '-', lw=2, label='EccentricIMR')
plt.xlabel('$t/M$')
plt.ylabel('$rh_{33}/M$')
plt.subplot(414)
plt.plot(tsur, hsur['h_l4m4'], '-', lw=2, label='EccentricIMR')
plt.xlabel('$t/M$')
plt.ylabel('$rh_{44}/M$')
plt.tight_layout()
plt.show()
3. Combine them to obtain multi-modal eccentric waveforms#
gwnrhme = gwModels.NRHME(t_ecc = tecc,
h_ecc_dict = {'h_l2m2': hecc},
t_cir = tsur,
h_cir_dict = hsur)
tNRE = gwnrhme.t_common
hNRE = gwnrhme.hNRE
print(hNRE.keys())
dict_keys(['h_l2m2', 'h_l2m1', 'h_l3m2', 'h_l4m4', 'h_l3m3', 'h_l3m1', 'h_l4m3', 'h_l4m2', 'h_l5m5'])
# plot waveform
plt.figure(figsize=(10,9))
plt.subplot(411)
plt.plot(tNRE, hNRE['h_l2m2'], '-', lw=2, label='EccentricIMR')
plt.xlabel('$t/M$')
plt.ylabel('$rh_{22}/M$')
plt.subplot(412)
plt.plot(tNRE, hNRE['h_l2m1'], '-', lw=2, label='EccentricIMR')
plt.xlabel('$t/M$')
plt.ylabel('$rh_{21}/M$')
plt.subplot(413)
plt.plot(tNRE, hNRE['h_l3m3'], '-', lw=2, label='EccentricIMR')
plt.xlabel('$t/M$')
plt.ylabel('$rh_{33}/M$')
plt.subplot(414)
plt.plot(tNRE, hNRE['h_l4m4'], '-', lw=2, label='EccentricIMR')
plt.xlabel('$t/M$')
plt.ylabel('$rh_{44}/M$')
plt.tight_layout()
plt.show()
