hmf.mass_function.fitting_functions.Watson

class hmf.mass_function.fitting_functions.Watson

Watson mass function fit.

For details on attributes, see documentation for FittingFunction.

Parameters

• nu2 (array_like) – A vector of peak-heights, \(\delta_c^2/\sigma^2\) corresponding to m

• m (array_like, optional) – A vector of halo masses [units M_sun/h]. Only necessary if req_mass is True. Typically provides limits of applicability. Must correspond to nu2.

• z (float, optional) – The redshift. Only required if req_z is True, in which case the default is 0.

• n_eff (array_like, optional) – The effective spectral index at m. Only required if req_neff is True.

• mass_definition (hmf.halos.mass_definitions.MassDefinition instance, optional) – A halo mass definition. Only required for fits which explicitly include a parameterization for halo definition.

• cosmo (astropy.cosmology.FLRW instance, optional) – A cosmology. Default is Planck15. Either omegam_z or cosmo is required if req_omz is True. If both are passed, omegam_z takes precedence.

• **model_parameters (unpacked-dictionary) – These parameters are model-specific. For any model, list the available parameters (and their defaults) using <model>._defaults

Notes

The Watson [1] form is:

\[f_{\rm WatS}(\sigma) = \Gamma A \left((\frac{\beta}{\sigma}^\alpha+1\right)\exp(-\gamma/\sigma^2)\]

References

1

Watson, W. A., et al., MNRAS, 2013. http://adsabs.harvard.edu/abs/2013MNRAS.433.1230W

Methods

__init__(nu2[, m, z, n_eff, …])	Initialize self.
gamma()	Calculate \(\Gamma\) for the Watson fit.
get_measured_mdef()
get_models()	Get a dictionary of all implemented models for this component.

Attributes

cutmask	A logical mask array specifying which elements of fsigma are within the fitted range.
fsigma	The function \(f(\sigma)\equiv\nu f(\nu)\).
lnsigma	Negative log of sigma.
nu	The peak height, sigma/delta_c.
omegam_z	Normalised matter density at current redshift.
req_cosmo
req_dhalo
req_mass	Whether m is required for this subclass
req_neff	Whether n_eff is required for this subclass
req_omz
sigma	The sqrt of mass variance as a function of mass.
sim_definition	Details of the defining simulation, subclass of SimDetails