Duffy08¶

class hmf.core.concentration.Duffy08(*, definition: Literal['200c', 'vir', '200m'] = '200c', sample: Literal['full', 'relaxed'] = 'full', redshifts: Literal['0-2', '0'] = '0-2')[source]¶

The NFW concentration-mass relation of Duffy et al. (2008).

\[c = A\left(\frac{M}{2\times10^{12}\,h^{-1}M_\odot}\right)^B (1+z)^C,\]

with (A, B, C) from their Table 1 (DUFFY08_PARAMETERS), for the chosen mass definition, sample and redshift range. M and c are in definition. It was fitted to haloes of \(10^{11}\)-\(10^{15}\) M☉/h, at z = 0-2 (or z = 0), in the WMAP5 cosmology. The full sample, the default, is the median of all haloes, which is what a mass function counts; the relaxed sample’s concentrations are about 10% higher.

Parameters:

definition (Literal['200c', 'vir', '200m'], default '200c') – The mass definition of the parameter set: ‘200c’ (200 times the critical density), ‘vir’ (Bryan & Norman 1998) or ‘200m’ (200 times the mean).
sample (Literal['full', 'relaxed'], default 'full') – The halo sample: ‘full’ (all haloes) or ‘relaxed’.
redshifts (Literal['0-2', '0'], default '0-2') – The redshift range the set was fitted to: ‘0-2’, or ‘0’ (with C = 0).

Attributes

definition: Literal['200c', 'vir', '200m']¶

sample: Literal['full', 'relaxed']¶

redshifts: Literal['0-2', '0']¶

alias: ClassVar[str | None] = 'Duffy08'¶: The short name the model is registered under, if any. Set by the alias class keyword; never inherited.

calibration¶: 1e11-1e15 Msun/h (in definition), and z = 0-2 (or z = 0).

calibration_domain: ClassVar[Domain | None] = Domain(bounds=(('m', Interval(lower=100000000000.0, upper=1000000000000000.0, unit=Unit("solMass / littleh"), lower_open=False, upper_open=False)), ('z', Interval(lower=0.0, upper=2.0, unit=None, lower_open=False, upper_open=False))), source="Duffy et al. 2008 (arXiv:0804.2486 v4): haloes of 1e11-1e15 Msun/h (abstract; Sec. 3), in the relation's own mass definition; z = 0-2 (Table 1). One cosmology (WMAP5: Omega_m = 0.258, sigma_8 = 0.796; Sec. 2).")¶

ask an instance for calibration, that of its set.

Type:: The calibration domain of the default set (z = 0-2)

m_pivot: ClassVar[float] = 2000000000000.0¶: The pivot mass, in Msun/h.

mass_definition¶: SOCritical(200), SOVirial() or SOMean(200), from definition.

parameter_source: ClassVar[str] = 'Duffy et al. 2008 (arXiv:0804.2486 v4), Table 1, NFW.'¶: The exact source (paper, version, table or equation) of the parameter defaults, e.g. “Tinker et al. 2008, ApJ 688, 709 (published), Table 2”.

parameters¶: The parameters (A, B, C) of the chosen set.

references: ClassVar[tuple[str, ...]] = ('Duffy, A. R., Schaye, J., Kay, S. T., Dalla Vecchia, C., 2008. MNRAS 390, L64. https://doi.org/10.1111/j.1745-3933.2008.00537.x',)¶: References to cite when the model is used, each a formatted citation.

valid_domain: ClassVar[Domain] = Domain(bounds=(('m', Interval(lower=0.0, upper=inf, unit=Unit("solMass / littleh"), lower_open=True, upper_open=True)), ('z', Interval(lower=0.0, upper=inf, unit=None, lower_open=False, upper_open=True))), source='m > 0, z >= 0.')¶

ln_concentration_and_slope_kernel() raises a DomainError outside it.

Type:: Where the relation can be evaluated

Methods

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

concentration(*, m: Any, z: ArrayLike) → ndarray[tuple[Any, ...], dtype[float64]]¶

The median concentration c(M, z), in mass_definition.

Parameters:

m (Quantity) – Masses in Msun/h, in mass_definition.
z (float or array_like) – Redshifts, broadcast with m.

Returns:

Dimensionless, with the broadcast shape.

Return type:

numpy.float64 or numpy.ndarray

Raises:

DomainError – Outside valid_domain.

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

in_calibration_domain_kernel(*, m: ArrayLike, z: ArrayLike) → ndarray[tuple[Any, ...], dtype[bool]]¶

Whether (m, z) is inside calibration, at kernel level.

Parameters:

m – Masses in Msun/h, in mass_definition.
z – Redshifts, broadcast with m.

Returns:

With the broadcast shape; True everywhere without a calibration domain.

Return type:

numpy.ndarray of bool

Raises:

DomainError – If a mass or redshift is outside valid_domain (from their extent).

ln_concentration_and_slope_kernel(*, m: ArrayLike, z: ArrayLike) → tuple[ndarray[tuple[Any, ...], dtype[float64]], ndarray[tuple[Any, ...], dtype[float64]]]¶

Ln c(M, z) and its slope \(d\ln c/d\ln M\), at kernel level.

Parameters:

m – Masses in Msun/h, in mass_definition: a plain array.
z – Redshifts, broadcast with m.

Returns:

ln_c, dln_c_dln_m – Dimensionless, with the broadcast shape.

Return type:

numpy.ndarray

Raises:

DomainError – If a mass or redshift is outside valid_domain (from their extent).

classmethod qualified_name() → str¶: Return this class’s qualified name, package.module:Class.