BBKS¶

class hmf.density_field.transfer_models.BBKS(cosmo, **model_parameters)[source]¶

BBKS (1986) transfer function.

Parameters:

cosmo (astropy.cosmology.FLRW instance) – The cosmology used in the calculation
**model_parameters (unpack-dict) – Parameters specific to this model. In this case, available parameters are the following: a, b, c, d, e. To see their default values, check the _defaults class attribute.

Notes

The fit is given as

\[T(k) = \frac{\ln(1+aq)}{aq} \left(1 + bq + (cq)^2 + (dq)^3 + (eq)^4\right)^{-1/4},\]

where

\[q = \frac{k}{\Gamma}\]

and \(\Gamma = \Omega_{m,0} h\). Note that here k is in units of h/Mpc, which accounts for the extra h in the equations in BBKS.

These equations are taken from BBKS 1986, Eq. G3.

Further modifications can be made in the presence of baryons. Sugiyama 1995, Eq. 3.9 gives

\[\Gamma \rightarrow \Gamma \exp\left(-\Omega_{b,0}(1 + 1/\Omega_{m,0})\right)\]

and Liddle and Lythe (2000) Eq. 5.14 give a slight extra:

\[\Gamma \rightarrow \Gamma \exp\left(-\Omega_{b,0}(1 + \sqrt{2h}/\Omega_{m,0})\right).\]

Methods

classmethod get_models() → dict[str, type]: Get a dictionary of all implemented models for this component.

lnt(lnk)[source]

Natural log of the transfer function.