SechSquaredDiskDensityProfile

class profiles.density.SechSquaredDiskDensityProfile(**kwargs)

Sech² Vertical Disk Density Profile.

Models a disk with exponential radial falloff and hyperbolic secant squared vertical structure:

\[\rho(r, z) = \rho_0 \, \exp\left( -\frac{r}{r_s} \right) \, \mathrm{sech}^2 \left( \frac{z}{z_s} \right)\]

Widely used for isothermal, self-gravitating stellar disks.

Parameters

Name	Symbol	Description
rho_0	\(\rho_0\)	Central density
r_s	\(r_s\)	Radial scale length
z_s	\(z_s\)	Vertical scale height

Example

>>> from pisces.profiles.density import (
...     SechSquaredDiskDensityProfile,
... )
>>> r, z = np.meshgrid(
...     np.linspace(0, 10, 100),
...     np.linspace(-2, 2, 100),
... )
>>> profile = SechSquaredDiskDensityProfile(
...     rho_0=1.0, r_s=3.0, z_s=0.3
... )
>>> rho = profile(r, z)

(Source code)

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.