Sersic2D

class astropy.modeling.functional_models.Sersic2D

Bases: astropy.modeling.Fittable2DModel

Two 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.

x_0 : float, optional

x position of the center.

y_0 : float, optional

y position of the center.

ellip : float, optional

Ellipticity.

theta : float, optional

Rotation angle in radians, counterclockwise from the positive x-axis.

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

Gaussian2D, Moffat2D

Notes

Model formula:

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

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

[R8]	http://ned.ipac.caltech.edu/level5/March05/Graham/Graham2.html

Examples

import numpy as np
from astropy.modeling.models import Sersic2D
import matplotlib.pyplot as plt

x,y = np.meshgrid(np.arange(100), np.arange(100))

mod = Sersic2D(amplitude = 1, r_eff = 25, n=4, x_0=50, y_0=50,
               ellip=.5, theta=-1)
img = mod(x, y)
log_img = np.log10(img)

plt.figure()
plt.imshow(log_img, origin='lower', interpolation='nearest',
           vmin=-1, vmax=2)
plt.xlabel('x')
plt.ylabel('y')
cbar = plt.colorbar()
cbar.set_label('Log Brightness', rotation=270, labelpad=25)
cbar.set_ticks([-1, 0, 1, 2], update_ticks=True)
plt.show()

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

Attributes Summary

amplitude
ellip
n
param_names
r_eff
theta
x_0
y_0

Methods Summary

evaluate(x, y, amplitude, r_eff, n, x_0, ...)

Two dimensional Sersic profile function.

Attributes Documentation

amplitude

ellip

n

param_names = ('amplitude', 'r_eff', 'n', 'x_0', 'y_0', 'ellip', 'theta')

r_eff

theta

x_0

y_0

Methods Documentation

classmethod evaluate(x, y, amplitude, r_eff, n, x_0, y_0, ellip, theta)

Two dimensional Sersic profile function.