CoreSersicProfile

class profiles.density.CoreSersicProfile(**kwargs)

Core-Sérsic Surface Density Profile.

Models galaxies with depleted cores and outer Sérsic-like falloff:

\[\Sigma(R) = \Sigma_b \left[1 + \left( \frac{R_b}{R} \right)^\alpha \right]^{\gamma/\alpha} \exp\left( -b_n \left( \left( \frac{R^\alpha + R_b^\alpha}{R_e^\alpha} \right)^{1/(\alpha n)} - \left( \frac{R_b}{R_e} \right)^{1/n} \right) \right)\]

where:

• \(\Sigma_b\) is the surface density at the break radius.

• \(R_b\) is the break radius between core and outer profile.

• \(\gamma\) controls the inner power-law slope.

• \(\alpha\) controls sharpness of transition.

• \(R_e\) is the effective radius of the outer Sérsic portion.

• \(n\) is the Sérsic index.

• \(b_n\) is the usual Sérsic constant.

Parameters

Name	Symbol	Description
Sigma_b	\(\Sigma_b\)	Surface density at break radius
R_b	\(R_b\)	Break radius
R_e	\(R_e\)	Sérsic effective radius
n	\(n\)	Sérsic index
gamma	\(\gamma\)	Inner slope
alpha	\(\alpha\)	Transition sharpness

Example

>>> from pisces.profiles.density import (
...     CoreSersicProfile,
... )
>>> import matplotlib.pyplot as plt
>>> R = np.linspace(0.1, 20, 300)
>>> profile = CoreSersicProfile(
...     Sigma_b=1.0,
...     R_b=2.0,
...     R_e=5.0,
...     n=4.0,
...     gamma=0.5,
...     alpha=5.0,
... )
>>> Sigma = profile(R)
>>> plt.semilogy(R, Sigma)
>>> plt.xlabel("Radius (R)")
>>> plt.ylabel("Surface Density (Sigma)")
>>> plt.title("Core-Sérsic Surface 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.