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.

See also

Gaussian1D, Moffat1D, Lorentz1D

Notes

Model formula:

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

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

[1]

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, 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.