GaussianRingProfile

class profiles.density.GaussianRingProfile(**kwargs)

Gaussian Ring Surface Density Profile.

Models an annular structure with a peak surface density at a characteristic radius, declining in both inward and outward directions as a Gaussian:

\[\Sigma(R) = \Sigma_0 \, \exp\left( -\frac{(R - R_0)^2}{2 \sigma^2} \right)\]

This profile is useful for representing ring galaxies, star-forming rings, or resonance features.

Parameters

Name	Symbol	Description
Sigma_0	\(\Sigma_0\)	Peak surface density at \(R = R_0\)
R_0	\(R_0\)	Radius of the peak surface density
sigma	\(\sigma\)	Width of the ring

Example

>>> from pisces.profiles.density import (
...     GaussianRingProfile,
... )
>>> import matplotlib.pyplot as plt
>>> R = np.linspace(0, 10, 200)
>>> profile = GaussianRingProfile(
...     Sigma_0=1.0, R_0=5.0, sigma=0.5
... )
>>> Sigma = profile(R)
>>> plt.plot(R, Sigma)
>>> plt.xlabel("Radius (R)")
>>> plt.ylabel("Surface Density (Sigma)")
>>> plt.title("Gaussian Ring Profile")
>>> plt.grid(True)
>>> plt.show()

(Source code, png, hires.png, pdf)

Methods

__init__(**kwargs)	Initialize a profile instance with specific parameter values.
from_dict(data)	Reconstruct a profile instance from a dictionary.
from_hdf5(h5obj[, name])	Reconstruct a profile from HDF5 attributes.
from_json(filepath)	Reconstruct a profile from a JSON file.
from_yaml(filepath)	Reconstruct a profile from a YAML file.
get_derived_profile(profile_name, **kwargs)	Access and instantiate a derived profile by name.
get_expression_latex([substitute])	Return the LaTeX representation of the profile's symbolic expression.
get_output_units(*argu)	Determine the output units of the operation given some set of input units.
get_parameters_latex()	Return a LaTeX table of the profile parameters.
lambdify_expression(expression)	Convert a symbolic expression into a callable function.
list_derived_profiles()	List all available derived profiles for this instance.
substitute_expression(expression)	Replace symbolic parameters with numerical values in an expression.
to_dict()	Serialize this profile to a minimal dictionary representation.
to_hdf5(h5obj[, name])	Store profile metadata into an HDF5 object as attributes.
to_json(filepath, **kwargs)	Serialize the profile to a JSON file.
to_yaml(filepath, **kwargs)	Serialize the profile to a YAML file.

Attributes

derived_profile_classes	Get the available derived profile classes for this instance.
parameter_symbols	Get the symbolic representations of the coordinate system parameters.
parameters	The parameters of this coordinate system.
variable_symbols	The symbols representing each of the coordinate axes in this coordinate system.
variables	The axes names present in this coordinate system.