SersicProfile

class profiles.density.SersicProfile(**kwargs)

Sérsic Surface Density Profile.

Describes the surface brightness or surface mass density distribution of galaxies, particularly elliptical galaxies and bulges. The profile is defined as:

\[\Sigma(R) = \Sigma_0 \, \exp\left( -b_n \left[ \left( \frac{R}{R_e} \right)^{1/n} - 1 \right] \right)\]

where:

• \(\Sigma_0\) is the central surface density.

• \(R_e\) is the effective radius enclosing half the total projected mass.

• \(n\) is the Sérsic index controlling the shape (with \(n=1\) being exponential, and \(n=4\) the de Vaucouleurs profile).

• \(b_n\) is a normalization constant dependent on \(n\).

Note

The constant \(b_n\) is approximately given by:

\[b_n \approx 2n - \frac{1}{3} + \frac{4}{405n} + \frac{46}{25515n^2}\]

which ensures that \(R_e\) encloses half the total projected mass.

Parameters

Name	Symbol	Description
Sigma_0	\(\Sigma_0\)	Central surface density
R_e	\(R_e\)	Effective (half-light) radius
n	\(n\)	Sérsic index (controls profile shape)

Example

>>> from pisces.profiles.density import SersicProfile
>>> import matplotlib.pyplot as plt
>>> R = np.linspace(0.01, 10, 200)
>>> profile = SersicProfile(
...     Sigma_0=1.0, R_e=2.0, n=4.0
... )
>>> Sigma = profile(R)
>>> plt.semilogy(R, Sigma)
>>> plt.xlabel("Radius (R)")
>>> plt.ylabel("Surface Density (Sigma)")
>>> plt.title("Sérsic Surface Profile (n=4)")
>>> plt.grid(True)
>>> plt.show()

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

See also

BaseProfile, ExponentialDiskDensityProfile

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.