AHELP for CIAO 4.13 Sherpa v1

# beta2d

Context: models

## Synopsis

Two-dimensional beta model function.

`beta2d`

## Description

The beta model is a Lorentz model with a varying power law.

## Example

```>>> create_model_component("beta2d", "mdl")
>>> print(mdl)```

Create a component of the beta2d model and display its default parameters. The output is:

```mdl
Param        Type          Value          Min          Max      Units
-----        ----          -----          ---          ---      -----
mdl.r0       thawed           10  1.17549e-38  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    frozen            0            0        0.999
mdl.theta    frozen            0     -6.28319      6.28319    radians
mdl.ampl     thawed            1 -3.40282e+38  3.40282e+38
mdl.alpha    thawed            1          -10           10           ```

### ATTRIBUTES

The attributes for this object are:

Attribute Definition
r0 The core radius.
xpos X0 axis coordinate of the model center (position of the peak).
ypos X1 axis coordinate of the model center (position of the peak).
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 model value at the peak position (xpos, ypos).
alpha The power-law slope of the profile at large radii.

The functional form of the model for points is:

```f(x0,x1) = ampl * (1 + r(x0,x1)^2)^(-alpha)

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 (  ).

•  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
beta1d, devaucouleurs2d, hubblereynolds, sersic2d