Sersic1D

class astropy.modeling.functional_models.Sersic1D(amplitude=1, r_eff=1, n=4, **kwargs)[source]

Bases: Fittable1DModel

One dimensional Sersic surface brightness profile.

Parameters:
amplitudepython:float

Surface brightness at r_eff.

r_effpython:float

Effective (half-light) radius

npython:float

Sersic Index.

Other Parameters:
fixeda python:dict, optional

A dictionary {parameter_name: boolean} of parameters to not be varied during fitting. True means the parameter is held fixed. Alternatively the fixed property of a parameter may be used.

tiedpython:dict, optional

A dictionary {parameter_name: callable} of parameters which are linked to some other parameter. The dictionary values are callables providing the linking relationship. Alternatively the tied property of a parameter may be used.

boundspython:dict, optional

A dictionary {parameter_name: value} of lower and upper bounds of parameters. Keys are parameter names. Values are a list or a tuple of length 2 giving the desired range for the parameter. Alternatively, the min and max properties of a parameter may be used.

eqconspython:list, optional

A list of functions of length n such that eqcons[j](x0,*args) == 0.0 in a successfully optimized problem.

ineqconspython:list, optional

A list of functions of length n such that ieqcons[j](x0,*args) >= 0.0 is a successfully optimized problem.

See also

Gaussian1D, Moffat1D, Lorentz1D

Notes

Model formula:

\[I(r)=I_e\exp\left\{-b_n\left[\left(\frac{r}{r_{e}}\right)^{(1/n)}-1\right]\right\}\]

The constant \(b_n\) is defined such that \(r_e\) contains half the total luminosity, and can be solved for numerically.

\[\Gamma(2n) = 2\gamma (b_n,2n)\]

References

Examples

import numpy as np
from astropy.modeling.models import Sersic1D
import matplotlib.pyplot as plt

plt.figure()
plt.subplot(111, xscale='log', yscale='log')
s1 = Sersic1D(amplitude=1, r_eff=5)
r=np.arange(0, 100, .01)

for n in range(1, 10):
     s1.n = n
     plt.plot(r, s1(r), color=str(float(n) / 15))

plt.axis([1e-1, 30, 1e-2, 1e3])
plt.xlabel('log Radius')
plt.ylabel('log Surface Brightness')
plt.text(.25, 1.5, 'n=1')
plt.text(.25, 300, 'n=10')
plt.xticks([])
plt.yticks([])
plt.show()

(png, svg, pdf)

../_images/astropy-modeling-functional_models-Sersic1D-1.png

Attributes Summary

amplitude

input_units

This property is used to indicate what units or sets of units the evaluate method expects, and returns a dictionary mapping inputs to units (or None if any units are accepted).

n

param_names

Names of the parameters that describe models of this type.

r_eff

Methods Summary

evaluate(r, amplitude, r_eff, n)

One dimensional Sersic profile function.

Attributes Documentation

amplitude = Parameter('amplitude', value=1.0)
input_units
n = Parameter('n', value=4.0)
param_names = ('amplitude', 'r_eff', 'n')

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.

r_eff = Parameter('r_eff', value=1.0)

Methods Documentation

classmethod evaluate(r, amplitude, r_eff, n)[source]

One dimensional Sersic profile function.