pygwb.orfs

The relative position and orientation of two detectors is taken into account by the overlap reduction function (ORF) in gravitational-wave background searches. The orfs module combines the different component methods to compute the ORF for a given detector baseline, and polarization. By default, general relativity (GR) polarization is assumed, i.e., tensor. However, the orfs module also supports non-GR polarizations (scalar and vector). For more information about the ORF, see here.

Examples

To illustrate how to compute the ORF, we start by importing the relevant packages:

>>> import numpy as np
>>> from pygwb.orfs import *
>>> import matplotlib.pyplot as plt

For concreteness, we consider the LIGO Hanford-Livingston baseline, and compute the ORF for this baseline. We define empty detectors:

>>> H1 = bilbydet.get_empty_interferometer('H1')
>>> L1 = bilbydet.get_empty_interferometer('L1')

We now compute the ORF for a set of frequencies by using the relevant information contained in the interferometer objects defined above:

>>> freqs = np.arange(10.25, 256.25, 0.25)
>>> orf = calc_orf(freqs, H1.vertex, L1.vertex, H1.x, L1.x, H1.y, L1.y, polarization = "tensor")

Note that the calc_orf method combines the various other methods of the module.

Note that, in practice, these methods are not called by the user, but are called by the baseline module directly. For more information on how the orfs module interacts with the baseline module, see pygwb.baseline.

Functions

Sminus(alpha, beta)	Function used in the computation of the scalar ORF, as given by Eq.
Splus(alpha, beta)	Function used in the computation of the scalar ORF, as given by Eq.
T_right_left(alpha, beta)	param alpha: Given below Eq. (32) of https://arxiv.org/pdf/0903.0528.pdf.
Tminus(alpha, beta)	Function used in the computation of the tensor ORF, as given by Eq.
Tplus(alpha, beta)	Function used in the computation of the tensor ORF, as given by Eq.
Vminus(alpha, beta)	Function used in the computation of the vector ORF, as given by Eq.
Vplus(alpha, beta)	Function used in the computation of the vector ORF, as given by Eq.
calc_orf(frequencies, det1_vertex, ...[, ...])	Calculates the tensor, scalar, and vector overlap reduction functions, following Section IVb of https://arxiv.org/abs/0903.0528.
omega_tangent_bisector(bisector, ...)	Method to compute the angle between bisector and tangent vector.
tangent_vector(vector1, vector2)	Method to compute the tangent vector given two vectors.