# 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 $$h Mpc^{-1}$$ Pk – the linear power spectrum evaluated at k in units of $$h^{-3} \mathrm{Mpc}^3$$ float, array_like
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.

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 $$\mathrm{Mpc/h}$$