AHELP for CIAO 4.13 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:

Attribute Definition
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.