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:
- amplitude
float
Surface brightness at
r_eff
.- r_eff
float
Effective (half-light) radius.
- n
float
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
- amplitude
- Other Parameters:
- fixed
dict
, optional A dictionary
{parameter_name: boolean}
of parameters to not be varied during fitting. True means the parameter is held fixed. Alternatively thefixed
property of a parameter may be used.- tied
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 thetied
property of a parameter may be used.- bounds
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, themin
andmax
properties of a parameter may be used.- eqcons
list
, optional A list of functions of length
n
such thateqcons[j](x0,*args) == 0.0
in a successfully optimized problem.- ineqcons
list
, optional A list of functions of length
n
such thatieqcons[j](x0,*args) >= 0.0
is a successfully optimized problem.
- fixed
See also
Notes
The
r
andr_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 \(r_{e}\) isreff
.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()
Attributes Summary
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).Names of the parameters that describe models of this type.
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