beta1d

Context: models

Synopsis

One-dimensional beta model function.

Syntax

beta1d

Description

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

Example

>>> create_model_component("beta1d", "mdl")
>>> print(mdl)

Create a component of the beta1d model and display its default parameters. The output is:

mdl
   Param        Type          Value          Min          Max      Units
   -----        ----          -----          ---          ---      -----
   mdl.r0       thawed            1  1.17549e-38  3.40282e+38           
   mdl.beta     thawed            1        1e-05           10           
   mdl.xpos     frozen            0            0  3.40282e+38           
   mdl.ampl     thawed            1            0  3.40282e+38

ATTRIBUTES

The attributes for this object are:

Attribute	Definition
r0	The core radius.
beta	This parameter controls the slope of the profile at large radii.
xpos	The reference point of the profile. This is frozen by default.
ampl	The amplitude refers to the maximum value of the model, at x = xpos.

Notes

The functional form of the model for points is:

f(x) = ampl * (1 + ((x - xpos) / r0)^2)^(0.5 - 3 * beta)

The grid version is evaluated by numerically intgerating the function over each bin using a non-adaptive Gauss-Kronrod scheme suited for smooth functions [1] , falling over to a simple trapezoid scheme if this fails.

References

[1] https://www.gnu.org/software/gsl/manual/html_node/QNG-non_002dadaptive-Gauss_002dKronrod-integration.html

Bugs

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