# 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)