Sersic2D

class astropy.modeling.functional_models.Sersic2D(amplitude=1, r_eff=1, n=4, x_0=0, y_0=0, ellip=0, theta=0.0, **kwargs)

Bases: Fittable2DModel

Two dimensional Sersic surface brightness profile.

Parameters:

amplitudepython:float

Surface brightness at r_eff.

r_effpython:float

Effective (half-light) radius

npython:float

Sersic Index.

x_0python:float, optional

x position of the center.

y_0python:float, optional

y position of the center.

ellippython:float, optional

Ellipticity.

thetapython:float or Quantity, optional

The rotation angle as an angular quantity (Quantity or Angle) or a value in radians (as a float). The rotation angle increases counterclockwise from the positive x axis.

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

Gaussian2D, Moffat2D

Notes

Model formula:

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

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

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

References

[1]

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()

(png, svg, pdf)

Attributes Summary

amplitude
ellip
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
theta
x_0
y_0

Methods Summary

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

Two dimensional Sersic profile function.

Attributes Documentation

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

ellip = Parameter('ellip', value=0.0)

input_units

n = Parameter('n', value=4.0)

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

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)

theta = Parameter('theta', value=0.0)

x_0 = Parameter('x_0', value=0.0)

y_0 = Parameter('y_0', value=0.0)

Methods Documentation

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

Two dimensional Sersic profile function.