Sphere2D

class gammapy.image.models.Sphere2D(amplitude, x_0, y_0, r_0, normed=True, **constraints)

Bases: astropy.modeling.Fittable2DModel

Projected homogeneous radiating sphere model.

This model can be used for a simple PWN source morphology.

Parameters:

amplitude : float

Value of the integral of the sphere function

x_0 : float

x position center of the sphere

y_0 : float

y position center of the sphere

r_0 : float

Radius of the sphere

normed : bool (True)

If set the amplitude parameter corresponds to the integral of the function. If not set the ‘amplitude’ parameter corresponds to the peak value of the function (value at $r = 0$).

See also

Shell2D, Delta2D, astropy.modeling.models.Gaussian2D

Notes

Model formula with integral normalization:

$$\begin{split}f(r) = A \frac{3}{4 \pi r_0^3} \cdot \left \{ \begin{array}{ll} \sqrt{r_0^2 - r^2} & : r \leq r_0 \\ 0 & : r > r_0 \end{array} \right.\end{split}$$

Model formula with peak normalization:

$$\begin{split}f(r) = A \frac{1}{r_0} \cdot \left \{ \begin{array}{ll} \sqrt{r_0^2 - r^2} & : r \leq r_0 \\ 0 & : r > r_0 \end{array} \right.\end{split}$$

Examples

import numpy as np
import matplotlib.pyplot as plt
from gammapy.image.models import Sphere2D

sphere = Sphere2D(amplitude=100, x_0=25, y_0=25, r_0=20)
y, x = np.mgrid[0:50, 0:50]
plt.imshow(sphere(x, y), origin='lower', interpolation='none')
plt.xlabel('x (pix)')
plt.ylabel('y (pix)')
plt.colorbar(label='Brightness (A.U.)')
plt.grid(False)
plt.show()

(Source code, png, hires.png, pdf)

Attributes Summary

amplitude
param_names
r_0
x_0
y_0

Methods Summary

evaluate(x, y, amplitude, x_0, y_0, r_0)	Two dimensional Sphere model function normed to integral
evaluate_peak_norm(x, y, amplitude, x_0, ...)	Two dimensional Sphere model function normed to peak value

Attributes Documentation

amplitude

param_names = ('amplitude', 'x_0', 'y_0', 'r_0')

r_0

x_0

y_0

Methods Documentation

static evaluate(x, y, amplitude, x_0, y_0, r_0)

Two dimensional Sphere model function normed to integral

static evaluate_peak_norm(x, y, amplitude, x_0, y_0, r_0)

Two dimensional Sphere model function normed to peak value