beta2d

Context: models

Synopsis

Two-dimensional beta model function.

Syntax

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.

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.