GaussianRing

class dysmalpy.models.GaussianRing(baryon_type='gas+stars', **kwargs)

Bases: MassModel, _LightMassModel

Mass distribution following an infinitely thin Gaussian ring profile.

Parameters:

• total_mass (float) – Log10 of the total mass in solar units

• R_peak (float) – Peak of gaussian (radius) in kpc

• FWHM (float) – FWHM of gaussian, in kpc

• baryon_type (string) – What type of baryons are included. Used for dlnrhogas/dlnr. Options: {‘gas+stars’, ‘stars’, ‘gas’}

Notes

Model formula:

\[ \begin{align}\begin{aligned}M(r)&=M_0\exp\left(\frac{(r-r_{\rm peak})^2}{2\sigma_R^2}\right)\\\sigma_R &= \mathrm{FWHM}/(2\sqrt{2\ln 2})\end{aligned}\end{align} \]

Attributes Summary

FWHM
R_peak
mass_to_light
param_names	Names of the parameters that describe models of this type.
total_mass
tracer

Methods Summary

circular_velocity(r)	Circular velocity as a function of radius
dlnrhogas_dlnr(r)	Sersic asymmetric drift term
enclosed_mass(r)	Sersic enclosed mass
evaluate(r, total_mass, R_peak, FWHM, ...)	Gaussian ring mass surface density
light_profile(r)	Conversion from mass to light as a function of radius
potential_gradient(r)	Method to evaluate the gradient of the potential, \(\Delta\Phi(r)/\Delta r\).
projected_enclosed_mass(r)	Same as enclosed mass as this is infinitely thin gaussian ring
r_eff()
rhogas(r)	Mass density as a function of radius (if noord_flat; otherwise surface density)
ring_invh()
ring_reff()
sigma_R()
surface_density(r)	Gaussian ring mass surface density
vcirc_sq(r)	Square of circular velocity as a function of radius

Attributes Documentation

FWHM = DysmalParameter('FWHM', value=1.0, bounds=(0, 50), prior=<dysmalpy.parameters.UniformPrior object>)

R_peak = DysmalParameter('R_peak', value=1.0, bounds=(0, 50), prior=<dysmalpy.parameters.UniformPrior object>)

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

param_names = ('total_mass', 'R_peak', 'FWHM', 'mass_to_light')

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.

total_mass = DysmalParameter('total_mass', value=1.0, bounds=(5, 14), prior=<dysmalpy.parameters.UniformPrior object>)

tracer = 'mass'

Methods Documentation

circular_velocity(r)

Circular velocity as a function of radius

Parameters:

r (float or array) – Radii at which to calculate the enclosed mass

Returns:

vcirc – Circular velocity in km/s

Return type:

float or array

dlnrhogas_dlnr(r)

Sersic asymmetric drift term

Parameters:

r (float or array) – Radius in kpc

Returns:

log_drhodr – Log surface density derivative as a function or radius

Return type:

float or array

enclosed_mass(r)

Sersic enclosed mass

Parameters:

r (float or array) – Radii at which to calculate the enclosed mass

Returns:

menc – Enclosed mass profile

Return type:

float or array

static evaluate(r, total_mass, R_peak, FWHM, mass_to_light)

Gaussian ring mass surface density

light_profile(r)

Conversion from mass to light as a function of radius

Parameters:

r (float or array) – Radii at which to calculate the enclosed mass

Returns:

light – Relative line flux as a function of radius

Return type:

float or array

potential_gradient(r)

Method to evaluate the gradient of the potential, \(\Delta\Phi(r)/\Delta r\).

Parameters:

r (float or array) – Radius or radii at which to calculate circular velocity in kpc

Returns:

dPhidr – Gradient of the potential at r

Return type:

float or array

projected_enclosed_mass(r)

Same as enclosed mass as this is infinitely thin gaussian ring

r_eff()

rhogas(r)

Mass density as a function of radius (if noord_flat; otherwise surface density)

Parameters:

r (float or array) – Radii at which to calculate the enclosed mass

Returns:

dens – Mass density at r in units of Msun/kpc^3 (if noord_flat; otherwise surface density)

Return type:

float or array

ring_invh()

ring_reff()

sigma_R()

surface_density(r)

Gaussian ring mass surface density

vcirc_sq(r)

Square of circular velocity as a function of radius

Parameters:

r (float or array) – Radii at which to calculate the enclosed mass

Returns:

vcirc_sq – Square of circular velocity in km^2/s^2

Return type:

float or array

Notes

Calculated as \(v_{\mathrm{circ}}^2(R) = R * \partial \Phi / \partial R\) from the gradient of the potential, as the potential gradient has negative values.