Sersic1D

class astropy.modeling.functional_models.Sersic1D

Bases: astropy.modeling.Fittable1DModel

One dimensional Sersic surface brightness profile.

Parameters:

amplitude : float

Central surface brightness, within r_eff.

r_eff : float

Effective (half-light) radius

n : float

Sersic Index.

Other Parameters:  

fixed : a dict

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.

tied : dict

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.

bounds : dict

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

eqcons : list

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

ineqcons : list

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:

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

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

[R7]	http://ned.ipac.caltech.edu/level5/March05/Graham/Graham2.html

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()

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

Attributes Summary

amplitude
n
param_names
r_eff

Methods Summary

evaluate(r, amplitude, r_eff, n)

One dimensional Sersic profile function.

Attributes Documentation

amplitude

n

param_names = ('amplitude', 'r_eff', 'n')

r_eff

Methods Documentation

classmethod evaluate(r, amplitude, r_eff, n)

One dimensional Sersic profile function.