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:
amplitudefloat

Surface brightness at r_eff.

r_efffloat

Effective (half-light) radius.

nfloat

Sersic index controlling the shape of the profile. Particular values of n are equivalent to the following profiles:

  • n=4 : de Vaucouleurs \(r^{1/4}\) profile

  • n=1 : Exponential profile

  • n=0.5 : Gaussian profile

Other Parameters:
fixeddict, 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.

tieddict, 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.

boundsdict, 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.

eqconslist, optional

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

ineqconslist, optional

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

Notes

The r and r_eff inputs must have compatible units or be unitless numbers.

Model formula:

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

where \(I_{e}\) is the amplitude and \(r_{e}\) is reff.

The constant \(b_{n}\) is defined such that \(r_{e}\) contains half the total luminosity. It can be solved for numerically from the following equation:

\[\Gamma(2n) = 2\gamma (2n, b_{n})\]

where \(\Gamma(a)\) is the gamma function and \(\gamma(a, x)\) is the lower incomplete gamma function.

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, 0.01)

for n in range(1, 10):
     s1.n = n
     plt.plot(r, s1(r))

plt.axis([1e-1, 30, 1e-2, 1e3])
plt.xlabel('log Radius')
plt.ylabel('log Surface Brightness')
plt.text(0.25, 1.5, 'n=1')
plt.text(0.25, 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.