BBKS

class hmf.core.transfer_models.BBKS(*, a=2.34, b=3.89, c=16.1, d=5.46, e=6.71, baryons: Literal['sugiyama95', 'sugiyama95_preprint', 'none'] = 'sugiyama95')[source]

The Bardeen et al. (1986) fit, with a baryon correction to the shape parameter.

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

with k in h/Mpc and \(\Gamma = \Omega_{m,0} h\) (BBKS Eq. G3). The baryon correction multiplies \(\Gamma\) by

  • "sugiyama95" (the default): \(\exp(-\Omega_b(1 + \sqrt{2h}/\Omega_m))\), the published form of Sugiyama (1995), as quoted by Meiksin, White & Peacock (1999, Eq. 4) and Liddle & Lyth (2000, Eq. 5.14);

  • "sugiyama95_preprint": \(\exp(-\Omega_b(1 + 1/\Omega_m))\), the form of the preprint (astro-ph/9412025, Eq. 3.9);

  • "none": 1.

The two Sugiyama forms agree at h = 0.5. (In hmf v3 these were the use_liddle_baryons and use_sugiyama_baryons flags.)

Parameters:

  • a (float, default 2.34) – Coefficient a of Eq. G3.

  • b (float, default 3.89) – Coefficient b of Eq. G3.

  • c (float, default 16.1) – Coefficient c of Eq. G3.

  • d (float, default 5.46) – Coefficient d of Eq. G3.

  • e (float, default 6.71) – Coefficient e of Eq. G3.

  • baryons (Literal['sugiyama95', 'sugiyama95_preprint', 'none'], default 'sugiyama95') – The baryon correction to the shape parameter (see above).

Attributes

a: float
b: float
c: float
d: float
e: float
baryons: Literal['sugiyama95', 'sugiyama95_preprint', 'none']
alias: ClassVar[str | None] = 'BBKS'

The short name the model is registered under, if any. Set by the alias class keyword; never inherited.

backend: ClassVar[str | None] = None

The Boltzmann code that computes the model ("camb" or "class"), if any.

calibration_domain: ClassVar[Domain | None] = None

Where the model was calibrated, if that is stated by its source.

parameter_source: ClassVar[str] = 'Bardeen et al. 1986, ApJ 304, 15, Eq. G3'

The exact source (paper, version, table or equation) of the parameter defaults, e.g. “Tinker et al. 2008, ApJ 688, 709 (published), Table 2”.

references: ClassVar[tuple[str, ...]] = ('Bardeen, J. M., Bond, J. R., Kaiser, N., Szalay, A. S., 1986. ApJ 304, 15. https://doi.org/10.1086/164143', 'Sugiyama, N., 1995. ApJS 100, 281. https://doi.org/10.1086/192220')

References to cite when the model is used, each a formatted citation.

valid_domain: ClassVar[Domain] = Domain(bounds=(('k', Interval(lower=0.0, upper=inf, unit=Unit("littleh / Mpc"), lower_open=True, upper_open=True)),), source='T(k) is defined for k > 0.')

any k > 0. The Transfer stage checks k against the model’s class’s domain, so a model can narrow it.

Type:

Where the model can be evaluated

Methods

check_cosmology(cosmology: FLRW) → None

Raise if the model does not apply to cosmology (by default it does).

Raises:

ValueError – If it does not apply: a model that does not apply to a cosmology is a configuration error.

classmethod coerce(value: object) → Self

Convert a value to a model of this kind: the converter of a model field.

Parameters:

value – An instance of cls, which is returned as it is; or a name, import path or class that get() accepts, which is looked up and instantiated with its default parameters.

Returns:

An instance of cls.

Return type:

Model

Raises:

  • ModelNotFoundError – If value is a name that no model of this kind is known by.

  • TypeError – If value is of any other type, or names a class that is not a concrete subclass of cls.

Examples

>>> from hmf.core.filters import Filter, TopHat
>>> Filter.coerce("TopHat") == TopHat()
True
classmethod fields_info() → tuple[FieldInfo, ...]

Describe this class’s fields, without creating an instance.

Returns:

The name, type, default and documentation of each field.

Return type:

tuple of FieldInfo

classmethod get(name: str | type[Model]) → type[Self]

Look up a model of this kind.

Parameters:

name – An alias ("Tinker08"), a qualified name ("hmf.core.fits:Tinker08"), an import path to a class not yet imported ("pkg.mod:Cls" or "pkg.mod.Cls"), or a class.

Returns:

The model class (not an instance). It is always a subclass of cls.

Return type:

type

Raises:

  • ModelNotFoundError – If no model of this kind is known by name, even after loading the hmf.models entry points and trying name as an import path.

  • TypeError – If name resolves to something that is not a concrete subclass of cls.

classmethod get_aliases() → Mapping[str, str]

Return a read-only mapping from alias to qualified name, for this kind.

classmethod get_models() → Mapping[str, type[Self]]

Return the registered models of this kind, by qualified name.

Plugins advertised in the hmf.models entry-point group are loaded first.

Returns:

A read-only mapping from qualified name to class. Called on a kind, it is a live view of the registry. Called on a non-kind subclass, it holds only the models that subclass it.

Return type:

Mapping

classmethod qualified_name() → str

Return this class’s qualified name, package.module:Class.

shape_parameter(cosmology: FLRW) → Any[source]

The shape parameter Gamma, including the baryon correction.

Parameters:

cosmology – The cosmology.

Returns:

\(\Gamma\), a scalar Quantity in h/Mpc.

Return type:

astropy.units.Quantity

solve(cosmology: FLRW, k_accuracy: KAccuracy, *, disk_cache: DiskCache | None = None) → TransferSolution[source]

Compute the transfer function (see TransferModel.solve()).