Post-merger late-time tail analysis example

• This example is based on the paper “Phenomenology and origin of late-time tails in eccentric binary black hole mergers” by Islam, Faggioli, Khanna, Field, van de Meent and Buonanno.

• Here, we inspect waveforms produced by merging eccentric binary black holes (BBH). These waveforms are all generated using black hole perturbation theory.

• The trajectories are described by the dynamics of the point-particle orbiting the Kerr black hole using effective-one-body formalism: http://arxiv.org/abs/gr-qc/9811091, http://arxiv.org/abs/gr-qc/0001013, http://arxiv.org/abs/2405.19006. These trajectories are then fed into the time-domain Teukolsky solver developed by Gaurav Khanna and collaborators: http://arxiv.org/abs/gr-qc/0703028, http://arxiv.org/abs/0803.0317, http://arxiv.org/abs/0803.0317, http://arxiv.org/abs/1003.0485, http://arxiv.org/abs/1108.1816, http://arxiv.org/abs/arXiv:2010.04760.

import numpy as np
import matplotlib.pyplot as plt

import matplotlib
import matplotlib.pyplot as plt
from matplotlib import cm
import matplotlib.patches as mpatches
matplotlib.rcParams['mathtext.fontset'] ='stix'
matplotlib.rcParams['font.family'] = 'STIXGeneral'
matplotlib.rcParams['axes.linewidth'] = 1 #set the value globally
plt.rcParams["figure.figsize"] = (6,6)
plt.rcParams['font.size'] = '18'
plt.rc('text', usetex=True)

1. Import gwtails

import sys
# provide a path for the gwtails package
PATH_TO_GWTAILS = "/Users/tousifislam/Research/projects/stupid/gwtails/"
sys.path.append(PATH_TO_GWTAILS)
import gwtails
from gwtails import PostMergerAmplitudeFit

cannot import LAL

help(PostMergerAmplitudeFit)

Help on class PostMergerAmplitudeFit in module gwtails.tails:

class PostMergerAmplitudeFit(builtins.object)
 |  PostMergerAmplitudeFit(t=None, f=None, filename=None, qinput=1000, throw_junk_until_indx=None, qnm_fit_window=None, tail_fit_window=None, crossterm_fit_window=None, fit_tail_envelop=False, m1_to_M_scale=True)
 |
 |  Class to fit post-merger late-tile tail data
 |
 |  Methods defined here:
 |
 |  __init__(self, t=None, f=None, filename=None, qinput=1000, throw_junk_until_indx=None, qnm_fit_window=None, tail_fit_window=None, crossterm_fit_window=None, fit_tail_envelop=False, m1_to_M_scale=True)
 |      Parameters:
 |      -----------
 |      t : array-like, optional
 |          Time array. Default is None - in that case you should provide a filename
 |          that contains the strain/psi4.
 |      f : array-like, optional
 |          Function array - it could be strain h_lm or psi4_lm. Default is None -
 |          in that case you should provide a filename that contains the strain/psi4.
 |
 |      filename : str, optional
 |          Name of the waveform data file (Required); should be in .txt or .dat format;
 |          columns should have the following format: time, h_real, h_imag, ..
 |          Default is None - in that case you should provide (time 't' and strain/psi4 'f').
 |      qinput : float, default 1000
 |          Mass ratio values with qinput>=1.
 |
 |      throw_junk_until_indx : int, optional
 |          Last index until which data should be discarded before applying qnm or tail fits;
 |          Default is None.
 |      tail_fit_window : list, optional
 |          Provide a window for fitting tail coefficients only; e.g. [200,800] (in M);
 |          Default is None (in that case no tail fit is performed).
 |      qnm_fit_window : list, optional
 |          Provide a window for fitting qnm coefficients only; e.g. [200,800] (in M);
 |          Default is None (in that case no qnm fit is performed).
 |      crossterm_fit_window : list, optional
 |          Provide a window for fitting cross-term coefficients only; e.g. [100,200] (in M);
 |          Default is None (in that case no cross-term fit is performed).
 |      fit_tail_envelop : bool, default False
 |          Whether the data has oscillatory tail behaviour - in which case, we fit the tail envelop.
 |
 |      m1_to_M_scale : bool, default True
 |          Whether a mass-scale transformation from m1 (mass of the primary) to total mass M is needed.
 |
 |  freq(time, h, s=0.1)
 |      Calculate frequency from phase derivative.
 |
 |  plot_interpolated_amplitude(self)
 |      Plots interpolated amplitudes after time shift or junk removal.
 |
 |  plot_raw_amplitude(self)
 |      Plots raw amplitudes without time shift or junk removal.
 |
 |  qnm_and_tail_fit_func(self, t, phi_tail, omega)
 |      Combined QNM + tail + cross-terms fitting function.
 |
 |  qnm_fit_func(self, t, Aqnm, tau)
 |      QNM exponential decay function.
 |
 |  tail_fit_func(self, t, Atail, c, n)
 |      Tail power-law decay function.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  __weakref__
 |      list of weak references to the object

2. Analyze post-merger waveforms

# import data file
# this is for a merging binary with
# mass ratio q=1000, eccentricity e=0.9 and spin a=0.0
file = 'hm02_ecc_p09_e09_a00_q_1000.dat'

# pass it too gwtails without doing anything
# we will check the raw data first
rd = PostMergerAmplitudeFit(filename=file)

.......... Data read. Shape: (11, 11500)
..... time and strain/psi4 data is loaded
..... waveform mass-scale changed from m1 to M
..... strain/psi4 is cast onto a common time grid

rd.plot_raw_amplitude()

# plot the waveform amplitude after making sure that the peak at t=0
# and interpolating on a new time grid
rd.plot_interpolated_amplitude()

# make sure to throw the initial orbits for the post-merger fits
rd = PostMergerAmplitudeFit(filename=file,
                                throw_junk_until_indx=1200)
# and we are done
rd.plot_interpolated_amplitude()

.......... Data read. Shape: (11, 11500)
..... time and strain/psi4 data is loaded
..... waveform mass-scale changed from m1 to M
..... junk data is removed from the start
..... strain/psi4 is cast onto a common time grid

# now pass it again to gwtails with fit options
rd = PostMergerAmplitudeFit(filename=file,
                            throw_junk_until_indx=1100, # initial indices to remove before analyzing post-merger data
                            qnm_fit_window=[20,70], # time window to fit qnm
                            tail_fit_window=[200,1000],  # time window to fit tails
                            crossterm_fit_window=[30,400]) # time window to fit the crossterms

.......... Data read. Shape: (11, 11500)
..... time and strain/psi4 data is loaded
..... waveform mass-scale changed from m1 to M
..... junk data is removed from the start
..... strain/psi4 is cast onto a common time grid
..... fitting the tails with a decaying power law
..... fitting QNM with the 220 mode
..... fitting oscillatory intermediate part

rd._plot_qnm_fit()

rd._plot_tail_fits()

rd._plot_all_fits()

# print interesting fit params
rd._print_all_fits()

Atail : 3.616772819e+05
c     : 2.816224671e+02
n     : 3.671228711e+00
Aqnm  : 5.773862018
tau   : 12.037748089
phi_tail : 7.762114539
omega    : 0.752691895