nbodykit.cosmology.power.linear¶

Functions

`EHPower`(cosmo, redshift)
`NoWiggleEHPower`(cosmo, redshift)

Classes

LinearPower(cosmo, redshift[, transfer])

An object to compute the linear power spectrum and related quantities, using a transfer function from the CLASS code or the analytic Eisenstein & Hu approximation.

class nbodykit.cosmology.power.linear.LinearPower(cosmo, redshift, transfer='CLASS')[source]¶

An object to compute the linear power spectrum and related quantities, using a transfer function from the CLASS code or the analytic Eisenstein & Hu approximation.

Parameters

cosmo (Cosmology, astropy.cosmology.FLRW) – the cosmology instance; astropy cosmology objects are automatically converted to the proper type
redshift (float) – the redshift of the power spectrum
transfer (str, optional) – string specifying the transfer function to use; one of ‘CLASS’, ‘EisensteinHu’, ‘NoWiggleEisensteinHu’

cosmo¶

the object giving the cosmological parameters

Type: class:Cosmology

sigma8¶

the z=0 amplitude of matter fluctuations

Type: float

redshift¶

the redshift to compute the power at

Type: float

transfer¶

the type of transfer function used

Type: str

Attributes

attrs: The meta-data dictionary
redshift: The redshift of the power spectrum
sigma8: The present day value of sigma_r(r=8 Mpc/h), used to normalize the power spectrum, which is proportional to the square of this value.

Methods

`__call__`(k)	Return the linear power spectrum in units of \(h^{-3} \mathrm{Mpc}^3\) at the redshift specified by `redshift`.
`sigma_r`(r[, kmin, kmax])	The mass fluctuation within a sphere of radius `r`, in units of \(h^{-1} Mpc\) at `redshift`.
`velocity_dispersion`([kmin, kmax])	The velocity dispersion in units of of \(\mathrm{Mpc/h}\) at `redshift`.

__call__(k)[source]¶

Return the linear power spectrum in units of \(h^{-3} \mathrm{Mpc}^3\) at the redshift specified by redshift.

The transfer function used to evaluate the power spectrum is specified by the transfer attribute.

Parameters: k (float, array_like) – the wavenumber in units of \(h Mpc^{-1}\)
Returns: Pk – the linear power spectrum evaluated at k in units of \(h^{-3} \mathrm{Mpc}^3\)
Return type: float, array_like

property attrs¶: The meta-data dictionary

property redshift¶: The redshift of the power spectrum

property sigma8¶

The present day value of sigma_r(r=8 Mpc/h), used to normalize the power spectrum, which is proportional to the square of this value.

The power spectrum can re-normalized by setting a different value for this parameter

sigma_r(r, kmin=1e-05, kmax=10.0)[source]¶

The mass fluctuation within a sphere of radius r, in units of \(h^{-1} Mpc\) at redshift.

This returns \(\sigma\), where

\[\sigma^2 = \int_0^\infty \frac{k^3 P(k,z)}{2\pi^2} W^2_T(kr) \frac{dk}{k},\]

where \(W_T(x) = 3/x^3 (\mathrm{sin}x - x\mathrm{cos}x)\) is a top-hat filter in Fourier space.

The value of this function with r=8 returns sigma8, within numerical precision.

Parameters

r (float, array_like) – the scale to compute the mass fluctation over, in units of \(h^{-1} Mpc\)
kmin (float, optional) – the lower bound for the integral, in units of \(\mathrm{Mpc/h}\)
kmax (float, optional) – the upper bound for the integral, in units of \(\mathrm{Mpc/h}\)

velocity_dispersion(kmin=1e-05, kmax=10.0, **kwargs)[source]¶

The velocity dispersion in units of of \(\mathrm{Mpc/h}\) at redshift.

This returns \(\sigma_v\), defined as

\[\sigma_v^2 = \frac{1}{3} \int_a^b \frac{d^3 q}{(2\pi)^3} \frac{P(q,z)}{q^2}.\]

Parameters

kmin (float, optional) – the lower bound for the integral, in units of \(\mathrm{Mpc/h}\)
kmax (float, optional) – the upper bound for the integral, in units of \(\mathrm{Mpc/h}\)