AHELP for CIAO 4.11 Sherpa v1

# sersic2d

Context: models

## Synopsis

Two-dimensional Sersic model.

## Syntax

`sersic2d`

## Description

This is a generalization of the DeVaucouleurs2D model, in which the exponent n can vary (  ,  , and  ).

## Example

```>>> create_model_component("sersic2d", "mdl")
>>> print(mdl)```

Create a component of the sersic2d model and display its default parameters. The output is:

```mdl
Param        Type          Value          Min          Max      Units
-----        ----          -----          ---          ---      -----
mdl.r0       thawed           10            0  3.40282e+38
mdl.xpos     thawed            0 -3.40282e+38  3.40282e+38
mdl.ypos     thawed            0 -3.40282e+38  3.40282e+38
mdl.ellip    thawed            0            0        0.999
mdl.theta    thawed            0     -6.28319      6.28319    radians
mdl.ampl     thawed            1 -3.40282e+38  3.40282e+38
mdl.n        frozen            1          0.1           10           ```

### ATTRIBUTES

The attributes for this object are:

The core radius.

### xpos

The center of the model on the x0 axis.

### ypos

The center of the model on the x1 axis.

### ellip

The ellipticity of the model.

### theta

The angle of the major axis. It is in radians, measured counter-clockwise from the X0 axis (i.e. the line X1=0).

### ampl

The amplitude refers to the maximum peak of the model.

### n

The Sersic index (n=4 replicates the DeVaucouleurs2D model).

The functional form of the model for points is can be expressed as the following:

```f(x0,x1) = ampl * exp(-b(n) * (r(x0,x1)^(1/n) - 1))

b(n) = 2 * n - 1 / 3 + 4 / (405 * n) + 46 / (25515 * n^2)

r(x0,x1)^2 = xoff(x0,x1)^2 * (1-ellip)^2 + yoff(x0,x1)^2
-------------------------------------------
r0^2 * (1-ellip)^2

xoff(x0,x1) = (x0 - xpos) * cos(theta) + (x1 - ypos) * sin(theta)

yoff(x0,x1) = (x1 - ypos) * cos(theta) - (x0 - xpos) * sin(theta)```

The grid version is evaluated by adaptive multidimensional integration scheme on hypercubes using cubature rules, based on code from HIntLib (  ) and GSL (  ).

•  http://ned.ipac.caltech.edu/level5/March05/Graham/Graham2.html
•  Graham, A. & Driver, S., 2005, PASA, 22, 118 http://adsabs.harvard.edu/abs/2005PASA...22..118G
•  Ciotti, L. & Bertin, G., A&A, 1999, 352, 447-451 http://adsabs.harvard.edu/abs/1999A%26A...352..447C
•  HIntLib - High-dimensional Integration Library http://mint.sbg.ac.at/HIntLib/
•  GSL - GNU Scientific Library http://www.gnu.org/software/gsl/

## Bugs

See the bugs pages on the Sherpa website for an up-to-date listing of known bugs.

## See Also

models
beta2d, devaucouleurs2d, hubblereynolds, lorentz2d