TwoPowerHalo

class dysmalpy.models.TwoPowerHalo(z=0, cosmo=FlatLambdaCDM(H0=70.0 km / (Mpc s), Om0=0.3, Tcmb0=0.0 K, Neff=3.04, m_nu=None, Ob0=None), **kwargs)

Bases: DarkMatterHalo

Two power law density model for a dark matter halo

Parameters:

• mvirial (float) – Virial mass in logarithmic solar units

• conc (float) – Concentration parameter

• alpha (float) – Power law index at small radii

• beta (float) – Power law index at large radii

• fdm (float) – Dark matter fraction

• z (float) – Redshift

• cosmo (cosmology object) – The cosmology to use for modelling. If this model component will be attached to a Galaxy make sure the respective cosmologies are the same. Default is FlatLambdaCDM with H0=70., and Om0=0.3.

Notes

Model formula:

The mass density follows Equation 2.64 of Binney & Tremaine (2008) [1]:

\[\rho=\frac{\rho_0}{(r/r_s)^\alpha(1 + r/r_s)^{\beta - \alpha}}\]

\(r_s\) is the scale radius and defined as \(r_\mathrm{vir}/c\) where \(r_\mathrm{vir}\) is the virial radius and \(c\) is the concentration parameter. \(\rho_0\) is the normalization parameter.

References

[1]

https://ui.adsabs.harvard.edu/abs/2008gady.book…..B/abstract

Attributes Summary

alpha
beta
conc
fdm
mvirial
param_names	Names of the parameters that describe models of this type.

Methods Summary

calc_alpha_from_fdm(baryons, r_fdm)	Calculate alpha given dark matter fraction and baryonic distribution
calc_rho0([rvirial])	Normalization of the density distribution
enclosed_mass(r)	Enclosed mass as a function of radius
evaluate(r, mvirial, conc, alpha, beta, fdm)	Mass density for the TwoPowerHalo

Attributes Documentation

alpha = DysmalParameter('alpha', value=1.0, prior=<dysmalpy.parameters.UniformPrior object>)

beta = DysmalParameter('beta', value=3.0, prior=<dysmalpy.parameters.UniformPrior object>)

conc = DysmalParameter('conc', value=5.0, bounds=(2, 20), prior=<dysmalpy.parameters.UniformPrior object>)

fdm = DysmalParameter('fdm', value=-99.9, fixed=True, bounds=(0, 1), prior=<dysmalpy.parameters.UniformPrior object>)

mvirial = DysmalParameter('mvirial', value=1.0, bounds=(5, 20), prior=<dysmalpy.parameters.UniformPrior object>)

param_names = ('mvirial', 'fdm', 'conc', 'alpha', 'beta')

Names of the parameters that describe models of this type.

The parameters in this tuple are in the same order they should be passed in when initializing a model of a specific type. Some types of models, such as polynomial models, have a different number of parameters depending on some other property of the model, such as the degree.

When defining a custom model class the value of this attribute is automatically set by the Parameter attributes defined in the class body.

Methods Documentation

calc_alpha_from_fdm(baryons, r_fdm)

Calculate alpha given dark matter fraction and baryonic distribution

Parameters:

• baryons (MassModel or dictionary) – Model component representing the baryons (assumed to be light emitting), or dictionary containing a list of the baryon components (baryons[‘components’]) and a list of whether the baryon components are light emitting or not (baryons[‘light’])

• r_fdm (float) – Radius at which the dark matter fraction is determined

Returns:

alpha – alpha value

Return type:

float

Notes

This uses the current values of fdm, mvirial, and beta together with the input baryon distribution to calculate the necessary value of alpha.

calc_rho0(rvirial=None)

Normalization of the density distribution

Returns:

rho0 – Mass density normalization in \(M_{\odot}/\rm{kpc}^3\)

Return type:

float

enclosed_mass(r)

Enclosed mass as a function of radius

Parameters:

r (float or array) – Radius or radii in kpc

Returns:

menc – Enclosed mass in solar units

Return type:

float or array

evaluate(r, mvirial, conc, alpha, beta, fdm)

Mass density for the TwoPowerHalo