AHELP for CIAO 4.11 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:

### 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.

### Notes

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 ( [1] ) and GSL ( [2] ).

### References

• [1] HIntLib - High-dimensional Integration Library http://mint.sbg.ac.at/HIntLib/
• [2] 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.