Creating data

The events dictionary

The WF4Py functions take as input dictionaries containing the parameters of the events to analyse. As an example, the dictionary can be structured as

events
Type

dict(numpy.ndarray, numpy.ndarray, …)

events = {'Mc':np.array([…]), 'eta':np.array([…]), 'dL':np.array([…]), 'iota':np.array([…]), 'Phicoal':np.array([…]), 'chi1x':np.array([…]), 'chi2x':np.array([…]), 'chi1y':np.array([…]), 'chi2y':np.array([…]), 'chi1z':np.array([…]), 'chi2z':np.array([…]), 'LambdaTilde':np.array([…]), 'deltaLambda':np.array([…]), 'ecc':np.array([…])}

Note

The arrays in the events dictionary have to be 1-D and all of the same size.

Parameters names and conventions

Here we report the naming conventions used in WF4Py, as well as the units of the parameters and their physical range

Parameter symbol

Parameter name

Parameter description

Units in WF4Py

Physical range

\({\cal M}_c\)

'Mc'

chirp mass

\(\rm M_{\odot}\)

\((0,\,+\infty)\)

\(\eta\)

'eta'

symmetric mass ratio

–

\((0,\,0.25]\)

\(d_L\)

'dL'

luminosity distance

\(\rm Gpc\)

\((0,\,+\infty)\)

\(\iota\)

'iota'

inclination angle with respect to orbital angular momentum

\(\rm rad\)

\([0,\,\pi]\)

\(\theta_{JN}\)

'thetaJN'

inclination angle with respect to total angular momentum

\(\rm rad\)

\([0,\,\pi]\)

\(\Phi_c\)

'Phicoal'

phase at coalescence

\(\rm rad\)

\([0,\,2\pi]\)

\(\chi_{1,x}\)

'chi1x'

spin of object 1 along the axis \(x\)

–

\([-1,\,1]\)

\(\chi_{2,x}\)

'chi2x'

spin of object 2 along the axis \(x\)

–

\([-1,\,1]\)

\(\chi_{1,y}\)

'chi1y'

spin of object 1 along the axis \(y\)

–

\([-1,\,1]\)

\(\chi_{2,y}\)

'chi2y'

spin of object 2 along the axis \(y\)

–

\([-1,\,1]\)

\(\chi_{1,z}\)

'chi1z'

spin of object 1 along the axis \(z\)

–

\([-1,\,1]\)

\(\chi_{2,z}\)

'chi2z'

spin of object 2 along the axis \(z\)

–

\([-1,\,1]\)

\(\chi_s\)

'chiS'

symmetric spin component

–

\([-1,\,1]\)

\(\chi_a\)

'chiA'

asymmetric spin component

–

\([-1,\,1]\)

\(\chi_1\)

'chi1'

spin magnitude of object 1

–

\([0,\,1]\)

\(\chi_2\)

'chi2'

spin magnitude of object 2

–

\([0,\,1]\)

\(\theta_{s,1}\)

'tilt1'

spin tilt of object 1

\(\rm rad\)

\([0,\,\pi]\)

\(\theta_{s,2}\)

'tilt2'

spin tilt of object 2

\(\rm rad\)

\([0,\,\pi]\)

\(\phi_{JL}\)

'phiJL'

azimuthal angle of orbital angular momentum relative to total angular momentum

\(\rm rad\)

\([0,\,2\pi]\)

\(\phi_{1,2}\)

'phi12'

difference in azimuthal angle between spin vectors

\(\rm rad\)

\([0,\,2\pi]\)

\(\Lambda_1\)

'Lambda1'

adimensional tidal deformability of object 1

–

\([0,\,+\infty)\)

\(\Lambda_2\)

'Lambda2'

adimensional tidal deformability of object 2

–

\([0,\,+\infty)\)

\(\tilde{\Lambda}\)

'LambdaTilde'

adimensional tidal deformability of combination \(\tilde{\Lambda}\)

–

\([0,\,+\infty)\)

\(\delta\tilde{\Lambda}\)

'deltaLambda'

adimensional tidal deformability of combination \(\delta\tilde{\Lambda}\)

–

\((-\infty,\,+\infty)\)

\(e_0\)

'ecc'

orbital eccentricity at reference frequency \(f_{e_{0}}\)

–

\([0,\,1)\)

Warning

The spin components are defined on a sphere, i.e. they have to satisfy \(\chi_{1,x}^2 + \chi_{1,y}^2 + \chi_{1,z}^2\leq 1\) and \(\chi_{2,x}^2 + \chi_{2,y}^2 + \chi_{2,z}^2\leq 1\).

Note

The symmetric and asymmetric spin components are defined as

\begin{eqnarray} \chi_s & = & \frac{1}{2} (\chi_{1,z} + \chi_{2,z}) \\ \chi_a & = & \frac{1}{2} (\chi_{1,z} - \chi_{2,z}) \end{eqnarray}

Note

The adimensional tidal deformability combinations \(\tilde{\Lambda}\) and \(\delta\tilde{\Lambda}\) are defined as (see arXiv:1402.5156).

\begin{eqnarray} \tilde{\Lambda} & = & \dfrac{8}{13} \left[(1+7\eta-31\eta^2)(\Lambda_1 + \Lambda_2) + \sqrt{1-4\eta}(1+9\eta-11\eta^2)(\Lambda_1 - \Lambda_2)\right] \\ \delta\tilde{\Lambda} & = & \dfrac{1}{2} \left[\sqrt{1-4\eta} \left(1-\dfrac{13272}{1319}\eta + \dfrac{8944}{1319}\eta^2\right)(\Lambda_1 + \Lambda_2) + \right. \\ & & \ \ + \left. \left(1 - \dfrac{15910}{1319}\eta + \dfrac{32850}{1319}\eta^2 + \dfrac{3380}{1319}\eta^3\right)(\Lambda_1 - \Lambda_2)\right] \end{eqnarray}