wcosmo.astropy.WCosmoMixin#

class wcosmo.astropy.WCosmoMixin[source]#

Bases: object

Mixin to provide access to the wcosmo functionality to astropy cosmology objects.

We clobber all units to ensure consistent behavior across backends.

Notes

The following methods are not compatible with non-numpy backends:

kpc_comoving_per_arcmin
kpc_proper_per_arcmin
nu_relative_density

These methods internally coerce the input to numpy arrays if the backend supports implicit conversion. Additionally, we don’t overwrite the various integrands, protected methods, and other utility methods, e.g., clone.

We include the following methods that are not present in astropy:

dLdH - derivative of the luminosity distance w.r.t. the Hubble distance
dDLdz - Jacobian for the conversion of luminosity distance to redshift, see dDLdz()
detector_to_source_frame - convert masses and luminosity distance from the detector frame to the source frame, also returns the jacobian, see detector_to_source_frame()
source_to_detector_frame - convert masses and redshift from the source frame to the detector frame, see source_to_detector_frame()

__init__(*args, **kwargs)#

Methods

`H`(z)	Compute the Hubble parameter \(H(z)\) for a flat wCDM cosmology.
`__init__`(args, *kwargs)
`absorption_distance`(z)	Compute the absorption distance using an analytic integral of the Pade approximation.
`age`(z[, zmax])	Compute the age of the universe at redshift z.
`comoving_distance`(z)	Compute the comoving distance using an analytic integral of the Pade approximation.
`comoving_transverse_distance`(z)	Compute the comoving distance using an analytic integral of the Pade approximation.
`comoving_volume`(z)	Compute the comoving volume out to redshift z.
`dDLdz`(z)	The Jacobian for the conversion of redshift to luminosity distance.
`dLdH`(z)	Derivative of the luminosity distance w.r.t.
`de_density_scale`(z)	Dark energy density at redshift z.
`detector_to_source_frame`(m1z, m2z, dL[, ...])	Convert masses and luminosity distance from the detector frame to source frame masses and redshift.
`differential_comoving_volume`(z)	Compute the differential comoving volume element.
`distmod`(z)	Compute the distance modulus at redshift z.
`efunc`(z)	Compute the \(E(z)\) function for a flat wCDM cosmology.
`inv_efunc`(z)	Compute the inverse of the E(z) function for a flat wCDM cosmology.
`lookback_time`(z)	Compute the lookback time using an analytic integral of the Pade approximation.
`luminosity_distance`(z)	Compute the luminosity distance using an analytic integral of the Pade approximation.
`source_to_detector_frame`(m1, m2, z)	Convert masses and redshift from the source frame to the detector frame.

Attributes

`H0`
`hubble_distance`	Compute the Hubble distance \(D_H = c H_0^{-1}\) in Mpc.
`hubble_time`	Compute the Hubble time \(t_H = H_0^{-1}\) in Gyr.

H(z)[source]#

Compute the Hubble parameter \(H(z)\) for a flat wCDM cosmology.

\[H(z; H_0, \Omega_{m,0}, w_0) = \frac{d_H(H_0)}{E(z; \Omega_{m,0}, w_0)}\]

Parameters:

z: array_like: Redshift

Returns:

H(z): array_like: The Hubble parameter

absorption_distance(z)[source]#

Compute the absorption distance using an analytic integral of the Pade approximation.

\[d_{A} = \int_{0}^{z} \frac{dz' (1 + z')^2}{E(z'; \Omega_{m,0}, w_0)}\]

Parameters:

z: array_like: Redshift

Returns:

absorption_distance: array_like: The absorption distance in Mpc

age(z, zmax=100000.0)[source]#

Compute the age of the universe at redshift z.

Parameters:

z: array_like
Redshift
zmax: float, optional: The maximum redshift to consider, default is 1e5

Returns:

age: array_like: The age of the universe in Gyr

comoving_distance(z)[source]#

Compute the comoving distance using an analytic integral of the Pade approximation.

\[d_{C} = d_{H} \int_{0}^{z} \frac{dz'}{E(z'; \Omega_{m,0}, w_0)}\]

Parameters:

z: array_like: Redshift

Returns:

comoving_distance: array_like: The comoving distance in Mpc

comoving_transverse_distance(z)#

Compute the comoving distance using an analytic integral of the Pade approximation.

\[d_{C} = d_{H} \int_{0}^{z} \frac{dz'}{E(z'; \Omega_{m,0}, w_0)}\]

Parameters:

z: array_like: Redshift

Returns:

comoving_distance: array_like: The comoving distance in Mpc

comoving_volume(z)[source]#

Compute the comoving volume out to redshift z.

\[V_C = \frac{4\pi}{3} d^3_C(z; H_0, \Omega_{m,0}, w_0)\]

Parameters:

z: array_like: Redshift

Returns:

Vc: array_like: The comoving volume in \(\rm{Gpc}^3\)

dDLdz(z)[source]#

The Jacobian for the conversion of redshift to luminosity distance.

\[\frac{dd_{L}}{z} = d_C(z; H_0, \Omega_{m,0}, w_0) + (1 + z) d_{H} E(z; \Omega_{m, 0}, w0)\]

Here \(d_{C}\) is comoving distance and \(d_{H}\) is the Hubble distance.

Parameters:

z: array_like: Redshift

Returns:

dDLdz: array_like: The derivative of the luminosity distance with respect to redshift in Mpc

Notes

This function does not have a direct analog in the astropy cosmology objects, but is needed for accounting for expressing distributions of redshift as distributions over luminosity distance.

dLdH(z)[source]#

Derivative of the luminosity distance w.r.t. the Hubble distance.

\[\frac{dd_L}{dd_H} = \frac{d_L}{d_H}\]

Parameters:

z: array_like
Redshift

Returns:

array_like:: The derivative of the luminosity distance w.r.t., the Hubble distance

de_density_scale(z)[source]#

Dark energy density at redshift z.

Parameters:

z: array_like
Redshift

Returns:

rho_de: array_like: The dark energy density at redshift z

detector_to_source_frame(m1z, m2z, dL, zmin=0.0001, zmax=100)[source]#

Convert masses and luminosity distance from the detector frame to source frame masses and redshift.

This passes through the arguments to z_at_value to compute the redshift.

Parameters:

m1z: array_like: The primary mass in the detector frame
m2z: array_like: The secondary mass in the detector frame
dL: array_like: The luminosity distance in Mpc
zmin: float: The minimum redshift used in the conversion from distance to redshift, default=1e-4
zmax: float: The maximum redshift used in the conversion from distance to redshift, default=100

Returns:

m1, m2, z: array_like: The primary and secondary masses in the source frame and the redshift

differential_comoving_volume(z)[source]#

Compute the differential comoving volume element.

\[\frac{dV_{C}}{dz} = d_C^2(z; H_0, \Omega_{m,0}, w_0) d_H E(z; \Omega_{m, 0}, w_0)\]

Parameters:

z: array_like: Redshift

Returns:

dVc: array_like: The differential comoving volume element in \(\rm{Gpc}^3\)

distmod(z)[source]#

Compute the distance modulus at redshift z.

Parameters:

z: array_like
Redshift

Returns:

distmod: array_like: The distance modulus (units: mag)

efunc(z)[source]#

Compute the \(E(z)\) function for a flat wCDM cosmology.

\[E(z; \Omega_{m,0}, w_0) = \sqrt{\Omega_{m,0} (1 + z)^3 + (1 - \Omega_{m,0}) (1 + z)^{3(1 + w_0)}}\]

Parameters:

z: array_like: Redshift

Returns:

E(z): array_like: The E(z) function

property hubble_distance#

Compute the Hubble distance \(D_H = c H_0^{-1}\) in Mpc.

Returns:

D_H: float: The Hubble distance in Mpc

property hubble_time#

Compute the Hubble time \(t_H = H_0^{-1}\) in Gyr.

Returns:

t_H: float: The Hubble time in Gyr

inv_efunc(z)[source]#

Compute the inverse of the E(z) function for a flat wCDM cosmology.

Parameters:

z: array_like: Redshift

Returns:

inv_efunc: array_like: The inverse of the E(z) function

lookback_time(z)[source]#

Compute the lookback time using an analytic integral of the Pade approximation.

\[t_{L} = t_{H} \int_{0}^{z} \frac{dz'}{(1 + z')E(z'; \Omega_{m,0}, w_0)}\]

Parameters:

z: array_like: Redshift

Returns:

lookback_time: array_like: The lookback time in km / s / Mpc

luminosity_distance(z)[source]#

Compute the luminosity distance using an analytic integral of the Pade approximation.

\[d_L = (1 + z') d_{H} \int_{0}^{z} \frac{dz'}{E(z'; \Omega_{m,0}, w_0)}\]

Parameters:

z: array_like: Redshift

Returns:

luminosity_distance: array_like: The luminosity distance in Mpc

source_to_detector_frame(m1, m2, z)[source]#

Convert masses and redshift from the source frame to the detector frame.

Parameters:

m1: array_like: The primary mass in the source frame
m2: array_like: The secondary mass in the source frame
z: array_like: Redshift

Returns:

m1z, m2z, dL: array_like: The primary and secondary masses in the detector frame and the luminosity distance