Sersic2D

class sherpa.astro.models.Sersic2D(name='sersic2d')

Bases: sherpa.models.model.RegriddableModel2D

Two-dimensional Sersic model.

This is a generalization of the DeVaucouleurs2D model, in which the exponent n can vary ([1], [2], and [3]).

r0

The core radius.

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).

See also

Beta2D, DeVaucouleurs2D, HubbleReynolds, Lorentz2D

Notes

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 ([4]) and GSL ([5]).

References

[1]	http://ned.ipac.caltech.edu/level5/March05/Graham/Graham2.html

[2]	Graham, A. & Driver, S., 2005, PASA, 22, 118 http://adsabs.harvard.edu/abs/2005PASA…22..118G

[3]	Ciotti, L. & Bertin, G., A&A, 1999, 352, 447-451 http://adsabs.harvard.edu/abs/1999A%26A…352..447C

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

[5]	GSL - GNU Scientific Library http://www.gnu.org/software/gsl/

Attributes Summary

thawedparhardmaxes
thawedparhardmins
thawedparmaxes
thawedparmins
thawedpars

Methods Summary

apply(outer, *otherargs, **otherkwargs)
calc(*args, **kwargs)	Evaluate the model on a grid.
get_center()
guess(dep, *args, **kwargs)	Set an initial guess for the parameter values.
regrid(*arrays)
reset()
set_center(xpos, ypos, *args, **kwargs)
startup()	Called before a model may be evaluated multiple times.
teardown()	Called after a model may be evaluated multiple times.

Attributes Documentation

thawedparhardmaxes

thawedparhardmins

thawedparmaxes

thawedparmins

thawedpars

Methods Documentation

apply(outer, *otherargs, **otherkwargs)

calc(*args, **kwargs)

Evaluate the model on a grid.

Parameters:

• p (sequence of numbers) – The parameter values to use. The order matches the pars field.
• *args – The model grid. The values can be scalar or arrays, and the number depends on the dimensionality of the model and whether it is being evaluated over an integrated grid or at a point (or points).

get_center()

guess(dep, *args, **kwargs)

Set an initial guess for the parameter values.

Attempt to set the parameter values, and ranges, for the model to match the data values. This is intended as a rough guess, so it is expected that the model is only evaluated a small number of times, if at all.

regrid(*arrays)

reset()

set_center(xpos, ypos, *args, **kwargs)

startup()

Called before a model may be evaluated multiple times.

See also

teardown()

teardown()

Called after a model may be evaluated multiple times.

See also

setup()