waveformtools.CoM

Centre of mass correction for the waveforms.

Functions

X_com_moments(time_axis, Xcom, order)

Compute the nth order temporal moment of the COM coordinates.

boost_waveform(unboosted_waveform, ...)

Boost the waveform given the unboosted waveform and the boost conformal factor.

compute_com_alpha(time_i, time_f, Xcom_0, Xcom_1)

Computes the CoM correction alpha parameter: the mean displacement of the system, of the COM correction as defined in Woodford et al. 2019 (Phys.

compute_com_beta(time_i, time_f, Xcom_0, Xcom_1)

Computes the CoM beta parameter: the mean drift of the system, of the COM correction as defined in Woodford et al. 2019 (Phys.

compute_conformal_k(vec_v, info[, spin_phase])

Compute the conformal factor for the boost transformation

compute_translation_alpha_modes(time_axis, ...)

Compute the translation scalar \(\alpha\) in its spherical harmonic components given the mean motion of the centre of mass.

waveformtools.CoM.X_com_moments(time_axis, Xcom, order)[source]

Compute the nth order temporal moment of the COM coordinates.

Parameters:
time_axis: 1d array

The time axis.

Xcom: list

A list of three 1d arrays, each a 1d array containing the time series of the x, y and z co-ordinates in that order.

order: int

The order of the moment.

Returns:
moments: list

A list containing three real numbers, one each for the moment of x, y and z locations.

waveformtools.CoM.boost_waveform(unboosted_waveform, conformal_factor)[source]

Boost the waveform given the unboosted waveform and the boost conformal factor.

Parameters:
unboosted_waveform: spherical_array

A class instance of spherical array.

conformal_factor: 2d array

The conformal factor for the Lorentz transformation. It may be a single floating point number or an array on a spherical grid. The array will be of dimensions [ntheta, nphi].

gridinfo: class instance

The class instance that contains the properties of the spherical grid.

Returns:
boosted_waveform: sp_array

The class instance sp_array that contains the boosted waveform.

waveformtools.CoM.compute_com_alpha(time_i, time_f, Xcom_0, Xcom_1)[source]

Computes the CoM correction alpha parameter: the mean displacement of the system, of the COM correction as defined in Woodford et al. 2019 (Phys. Rev. D 100, 124010).

Parameters:
time_i: float

initial time

time_f: float

final time

Xcom_0: list

A list containing the zeroth order moments of the COM.

Xcom_1: list

A list containing the first order moments of the COM.

Returns:
com_alpha: list

The list containig the alpha parameter vector

waveformtools.CoM.compute_com_beta(time_i, time_f, Xcom_0, Xcom_1)[source]

Computes the CoM beta parameter: the mean drift of the system, of the COM correction as defined in Woodford et al. 2019 (Phys. Rev. D 100, 124010).

Parameters:
time_i: float

initial time

time_f: float

final time

Xcom_0: list

A list containing the zeroth order moments of the COM.

Xcom_1: list

A list containing the first order moments of the COM.

Returns:
com_beta: list

The list containig the alpha parameter vector

waveformtools.CoM.compute_conformal_k(vec_v, info, spin_phase=0)[source]
Compute the conformal factor for the boost transformation

:math:`k = exp(-2i lambda) gamma^3 (1 - mathbf{v} cdot mathbf{r})^3

waveformtools.CoM.compute_translation_alpha_modes(time_axis, com_alpha, com_beta)[source]

Compute the translation scalar \(\alpha\) in its spherical harmonic components given the mean motion of the centre of mass. These are basically the quantities in Eq. (4-5d) in the reference Woodford et al. 2019.

Parameters:
time_axis: 1d array

The 1D array containing the time axis of the simulation.

alpha: 1d array

The 1D array containing the mean co-ordinate displacement of the COM of the system.

beta: 1d array

The 1D array containing the mean co-ordinate velocity of the COM.

Returns:
alpha_modesmodes_array

A waveforms.modes_array object containing the SH decomposition of the ‘Alpha’ supertranslation variable.