Gaussian on sphere

[3]:
# Parameters
func_name = "Gaussian_on_sphere"

Description

[5]:
func.display()
  • description: A bidimensional Gaussian function on a sphere (in spherical coordinates)
  • formula: $$ f(\vec{x}) = \left(\frac{180^\circ}{\pi}\right)^2 \frac{1}{2\pi \sqrt{\det{\Sigma}}} \, {\rm exp}\left( -\frac{1}{2} (\vec{x}-\vec{x}_0)^\intercal \cdot \Sigma^{-1}\cdot (\vec{x}-\vec{x}_0)\right) \\ \vec{x}_0 = ({\rm RA}_0,{\rm Dec}_0)\\ \Lambda = \left( \begin{array}{cc} \sigma^2 & 0 \\ 0 & \sigma^2 (1-e^2) \end{array}\right) \\ U = \left( \begin{array}{cc} \cos \theta & -\sin \theta \\ \sin \theta & cos \theta \end{array}\right) \\\Sigma = U\Lambda U^\intercal $$
  • parameters:
    • lon0:
      • value: 0.0
      • desc: Longitude of the center of the source
      • min_value: 0.0
      • max_value: 360.0
      • unit:
      • is_normalization: False
      • delta: 0.1
      • free: True
    • lat0:
      • value: 0.0
      • desc: Latitude of the center of the source
      • min_value: -90.0
      • max_value: 90.0
      • unit:
      • is_normalization: False
      • delta: 0.1
      • free: True
    • sigma:
      • value: 10.0
      • desc: Standard deviation of the Gaussian distribution
      • min_value: 0.0
      • max_value: 20.0
      • unit:
      • is_normalization: False
      • delta: 1.0
      • free: True

Shape

The shape of the function on the sky.

[6]:


m=func(ra, dec) hp.mollview(m, title=func_name, cmap="magma") hp.graticule(color="grey", lw=2)


../_images/notebooks_Gaussian_on_sphere_8_0.png