gwpopulation.models.spin#

Implemented spin models

Classes#

`GaussianChiEffChiP`	A covariant Gaussian in effective aligned and precessing spins.
`SplineSpinMagnitudeIdentical`	Interpolated spline model for spin magnitudes.
`SplineSpinTiltIdentical`	Interpolated spline model for spin orientations.

Functions#

`iid_spin`(dataset, xi_spin, sigma_spin, amax, ...)	Independently and identically distributed spins.
`iid_spin_magnitude_beta`(dataset[, amax, alpha_chi, ...])	Independent and identically distributed beta distributions for both spin magnitudes.
`independent_spin_magnitude_beta`(dataset, alpha_chi_1, ...)	Independent beta distributions for both spin magnitudes.
`iid_spin_orientation_gaussian_isotropic`(dataset, ...)	A mixture model of spin orientations with isotropic and normally
`independent_spin_orientation_gaussian_isotropic`(...)	A mixture model of spin orientations with isotropic and normally
`gaussian_chi_eff`(dataset, mu_chi_eff, sigma_chi_eff)	A Gaussian in chi effective distribution
`gaussian_chi_p`(dataset, mu_chi_p, sigma_chi_p)	A Gaussian distribution in precessing effective spin (chi p)

Module Contents#

gwpopulation.models.spin.iid_spin(dataset, xi_spin, sigma_spin, amax, alpha_chi, beta_chi)[source]#

Independently and identically distributed spins. The magnitudes are assumed to follow a Beta distribution and the orientations are assumed to follow an isotropic + truncated half Gaussian mixture model.

Parameters:

dataset: dict: Dictionary of numpy arrays containing ‘a_1’ and ‘a_2’.
xi_spin: float: Fraction of black holes in preferentially aligned component.
sigma_spin: float: Width of preferentially aligned component.
alpha_chi, beta_chi: float: Parameters of Beta distribution for both black holes.
amax: float: Maximum black hole spin.

gwpopulation.models.spin.iid_spin_magnitude_beta(dataset, amax=1, alpha_chi=1, beta_chi=1)[source]#

Independent and identically distributed beta distributions for both spin magnitudes.

See Wysocki+ <https://arxiv.org/abs/1805.06442> Eq. (10)

Parameters:

dataset: dict: Dictionary of numpy arrays containing ‘a_1’ and ‘a_2’.
alpha_chi, beta_chi: float: Parameters of Beta distribution for both black holes.
amax: float: Maximum black hole spin.

gwpopulation.models.spin.independent_spin_magnitude_beta(dataset, alpha_chi_1, alpha_chi_2, beta_chi_1, beta_chi_2, amax_1, amax_2)[source]#

Independent beta distributions for both spin magnitudes.

See Wysocki+ <https://arxiv.org/abs/1805.06442> Eq. (10)

Parameters:

dataset: dict: Dictionary of numpy arrays containing ‘a_1’ and ‘a_2’.
alpha_chi_1, beta_chi_1: float: Parameters of Beta distribution for more massive black hole.
alpha_chi_2, beta_chi_2: float: Parameters of Beta distribution for less massive black hole.
amax_1, amax_2: float: Maximum spin of the more/less massive black hole.

gwpopulation.models.spin.iid_spin_orientation_gaussian_isotropic(dataset, xi_spin, sigma_spin)[source]#

A mixture model of spin orientations with isotropic and normally distributed components. The distribution of primary and secondary spin orientations are expected to be identical and independent.

See Talbot and Thrane Eq. (4)

\[p(z_1, z_2 | \xi, \sigma) = \frac{(1 - \xi)^2}{4} + \xi \prod_{i\in\{1, 2\}} \mathcal{N}_{[-1, 1]}(z_i; \mu=1, \sigma=\sigma)\]

Where \(\mathcal{N}_{[a, b]}\) is the truncated normal distribution over \([a, b]\).

Parameters:

dataset: dict: Dictionary of numpy arrays for ‘cos_tilt_1’ and ‘cos_tilt_2’.
xi_spin: float: Fraction of black holes in preferentially aligned component (\(\xi\)).
sigma_spin: float: Width of preferentially aligned component.

gwpopulation.models.spin.independent_spin_orientation_gaussian_isotropic(dataset, xi_spin, sigma_1, sigma_2)[source]#

A mixture model of spin orientations with isotropic and normally distributed components.

See Talbot and Thrane Eq. (4)

\[p(z_1, z_2 | \xi, \sigma) = \frac{(1 - \xi)^2}{4} + \xi \prod_{i\in\{1, 2\}} \mathcal{N}_{[-1, 1]}(z_i; \mu=1, \sigma=\sigma_{i})\]

Where \(\mathcal{N}_{[a, b]}\) is the truncated normal distribution over \([a, b]\).

Parameters:

dataset: dict: Dictionary of numpy arrays for ‘cos_tilt_1’ and ‘cos_tilt_2’.
xi_spin: float: Fraction of black holes in preferentially aligned component (\(\xi\)).
sigma_1: float: Width of preferentially aligned component for the more massive black hole (\(\sigma_1\)).
sigma_2: float: Width of preferentially aligned component for the less massive black hole (\(\sigma_2\)).

gwpopulation.models.spin.gaussian_chi_eff(dataset, mu_chi_eff, sigma_chi_eff)[source]#

A Gaussian in chi effective distribution

\[p(\chi_{\text{eff}} | \mu_\chi, \sigma_\chi) = \mathcal{N}_{[-1, 1]}(\chi_{\text{eff}}; \mu=\mu_\chi, \sigma=\sigma_\chi)\]

Where \(\mathcal{N}_{[a, b]}\) is the truncated normal distribution over \([a, b]\).

See Miller+ and Callister+.

Parameters:

dataset: dict: Input data, must contain chi_eff (\(\chi_{\text{eff}}\))
mu_chi_eff: float: Mean of the distribution (\(\mu_\chi\))
sigma_chi_eff: float: Standard deviation of the distribution (\(\sigma_\chi\))

Returns:

array-like: The probability

gwpopulation.models.spin.gaussian_chi_p(dataset, mu_chi_p, sigma_chi_p)[source]#

A Gaussian distribution in precessing effective spin (chi p)

\[p(\chi_p) = \mathcal{N}_{[0, 1]}(\chi_p; \mu=\mu_\chi, \sigma=\sigma_\chi)\]

Where \(\mathcal{N}_{[a, b]}\) is the truncated normal distribution over \([a, b]\).

See Miller+ and Callister+.

Parameters:

dataset: dict: Input data, must contain chi_eff (\(\chi_p\))
mu_chi_p: float: Mean of the distribution (\(\mu_\chi\))
sigma_chi_p: float: Standard deviation of the distribution (\(\sigma_\chi\))

Returns:

array-like: The probability

class gwpopulation.models.spin.GaussianChiEffChiP[source]#

Bases: object

A covariant Gaussian in effective aligned and precessing spins.

\[p(\chi_{\rm eff}, \chi_p | \Lambda) = \mathcal{N}_{[-1, 1], [0, 1]}(\chi_{\rm eff}, \chi_p; [\mu_{\rm eff}, \mu_{p}], \Sigma)\]

Where \(\mathcal{N}_{[a, b], [c, d]}\) is the two-dimensional truncated normal distribution over \([a, b]\) and \([c, d]\).

The covariance matrix is given by:

\[\begin{split}\Sigma = \begin{bmatrix} \sigma^2_{\text{eff}} & \rho \sigma_{\text{eff}} \sigma_{p} \\ \rho \sigma_{\text{eff}} \sigma_{p} & \sigma^2_{p} \end{bmatrix}\end{split}\]

See Miller+ and Callister+.

Parameters:

dataset: dict: Dictionary of numpy arrays for chi_eff and chi_p.
mu_chi_eff: float: Mean of the chi effective distribution (\(\mu_{\text{eff}}\))
mu_chi_p: float: Mean of the chi p distribution (\(\mu_{p}\))
sigma_chi_eff: float: Standard deviation of the chi effective distribution (\(\sigma_{\text{eff}}\))
sigma_chi_p: float: Standard deviation of the chi p distribution (\(\sigma_{p}\))
spin_covariance: float: Covariance between the two parameters (\(\rho\))

chi_eff[source]#

chi_p[source]#

__call__(dataset, mu_chi_eff, sigma_chi_eff, mu_chi_p, sigma_chi_p, spin_covariance)[source]#

_normalization(mu_chi_eff, sigma_chi_eff, mu_chi_p, sigma_chi_p, spin_covariance)[source]#

Numerically calculate the normalization over a two-dimensional grid with trapezoidal integration

Parameters:

mu_chi_eff: float: Mean of the chi effective distribution (\(\mu_{\text{eff}}\))
mu_chi_p: float: Mean of the chi p distribution (\(\mu_{p}\))
sigma_chi_eff: float: Standard deviation of the chi effective distribution (\(\sigma_{\text{eff}}\))
sigma_chi_p: float: Standard deviation of the chi p distribution (\(\sigma_{p}\))
spin_covariance: float: Covariance between the two parameters (\(\rho\))

Returns:

float: The normalizing constant

class gwpopulation.models.spin.SplineSpinMagnitudeIdentical(minimum=0, maximum=1, nodes=5, kind='cubic', regularize=False)[source]#

Bases: gwpopulation.models.interped.InterpolatedNoBaseModelIdentical

Interpolated spline model for spin magnitudes.

See Golomb and Talbot

Parameters:

minimum: float: Minimum value to normalize the spline over, default=0.
maximum: float: Maximum value to normalize the spline over, default=1.
nodes: int: Number of nodes to use in the spline, default=5.
kind: str: The interpolation order of the spline, default=”cubic”.
regularize: bool: Whether to regularize the spline node values to have root-mean-square value rms{name}, default=False.

class gwpopulation.models.spin.SplineSpinTiltIdentical(minimum=-1, maximum=1, nodes=5, kind='cubic', regularize=False)[source]#

Bases: gwpopulation.models.interped.InterpolatedNoBaseModelIdentical

Interpolated spline model for spin orientations.

See Golomb and Talbot

Parameters:

minimum: float: Minimum value to normalize the spline over, default=-1.
maximum: float: Maximum value to normalize the spline over, default=1.
nodes: int: Number of nodes to use in the spline, default=5.
kind: str: The interpolation order of the spline, default=”cubic”.
regularize: bool: Whether to regularize the spline node values to have root-mean-square value rms{name}, default=False.