""" Utilities for introducing nonlinear tidal effects into waveform approximants
"""
import pycbc.conversions
import numpy
import lal
[docs]def nltides_fourier_phase_difference(f, delta_f, f0, amplitude, n, m1, m2):
"""Calculate the change to the Fourier phase change due
to non-linear tides. Note that the Fourier phase Psi(f)
is not the same as the gravitational-wave phase phi(f) and
is computed by
Delta Psi(f) = 2 \pi f Delta t(f) - Delta phi(f)
Parameters
----------
f: numpy.array
Array of frequency values to calculate the fourier phase difference
delta_f: float
Frequency resolution of f array
f0: float
Frequency that NL effects switch on
amplitude: float
Amplitude of effect
n: float
Growth dependence of effect
m1: float
Mass of component 1
m2: float
Mass of component 2
Returns
-------
delta_psi: numpy.array
Fourier phase as a function of frequency
"""
kmin = int(f0/delta_f)
kmax = len(f)
f_ref, t_of_f_factor, phi_of_f_factor = \
pycbc.conversions.nltides_coefs(amplitude, n, m1, m2)
# Fourier phase shift below f0 from \Delta \phi(f)
delta_psi_f_le_f0 = numpy.ones(kmin)
delta_psi_f_le_f0 *= - phi_of_f_factor * (f0/f_ref)**(n-3.)
# Fourier phase shift above f0 from \Delta \phi(f)
delta_psi_f_gt_f0 = - phi_of_f_factor * (f[kmin:kmax]/f_ref)**(n-3.)
# Fourier phase shift below f0 from 2 pi f \Delta t(f)
delta_psi_f_le_f0 += 2.0 * lal.lal.PI * f[0:kmin] * t_of_f_factor * \
(f0/f_ref)**(n-4.)
# Fourier phase shift above f0 from 2 pi f \Delta t(f)
delta_psi_f_gt_f0 += 2.0 * lal.lal.PI * f[kmin:kmax] * t_of_f_factor * \
(f[kmin:kmax]/f_ref)**(n-4.)
# Return the shift to the Fourier phase
return numpy.concatenate((delta_psi_f_le_f0, delta_psi_f_gt_f0), axis=0)
[docs]def nonlinear_tidal_spa(**kwds):
"""Generates a frequency-domain waveform that implements the
TaylorF2+NL tide model described in https://arxiv.org/abs/1808.07013
"""
from pycbc import waveform
from pycbc.types import Array
# We start with the standard TaylorF2 based waveform
kwds.pop('approximant')
hp, hc = waveform.get_fd_waveform(approximant="TaylorF2", **kwds)
# Add the phasing difference from the nonlinear tides
f = numpy.arange(len(hp)) * hp.delta_f
pd = Array(numpy.exp(-1.0j * nltides_fourier_phase_difference(f,
hp.delta_f,
kwds['f0'], kwds['amplitude'], kwds['n'],
kwds['mass1'], kwds['mass2'])),
dtype=hp.dtype)
hp *= pd
hc *= pd
return hp, hc