Ellipse on sphere

[3]:

# Parameters
func_name = "Ellipse_on_sphere"

Description

[5]:

func.display()

description: An ellipse function on a sphere (in spherical coordinates)
formula: $$ f(\vec{x}) = \left(\frac{180}{\pi}\right)^2 \frac{1}{\pi~ a b} ~\left\{\begin{matrix} 1 & {\rm if}& {\rm | \vec{x} - \vec{x}_{f1}| + | \vec{x} - \vec{x}_{f2}| \le {\rm 2a}} \\ 0 & {\rm if}& {\rm | \vec{x} - \vec{x}_{f1}| + | \vec{x} - \vec{x}_{f2}| > {\rm 2a}} \end{matrix}\right. $$
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
- a:
  - value: 15.0
  - desc: semimajor axis of the ellipse
  - min_value: 0.0
  - max_value: 20.0
  - unit:
  - is_normalization: False
  - delta: 1.5
  - free: True
- e:
  - value: 0.9
  - desc: eccentricity of ellipse
  - min_value: 0.0
  - max_value: 1.0
  - unit:
  - is_normalization: False
  - delta: 0.09000000000000001
  - free: True
- theta:
  - value: 0.0
  - desc: inclination of semimajoraxis to a line of constant latitude
  - min_value: -90.0
  - max_value: 90.0
  - unit:
  - is_normalization: False
  - delta: 0.1
  - free: True

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)