Disk on sphere

[3]:

# Parameters
func_name = "Disk_on_sphere"

Description

[5]:

func.display()

description: A bidimensional disk/tophat function on a sphere (in spherical coordinates)
formula: $$ f(\vec{x}) = \left(\frac{180}{\pi}\right)^2 \frac{1}{\pi~({\rm radius})^2} ~\left\{\begin{matrix} 1 & {\rm if}& {\rm | \vec{x} - \vec{x}_0| \le {\rm radius}} \\ 0 & {\rm if}& {\rm | \vec{x} - \vec{x}_0| > {\rm radius}} \end{matrix}\right. $$
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
- radius:
  - value: 15.0
  - desc: Radius of the disk
  - min_value: 0.0
  - max_value: 20.0
  - unit:
  - is_normalization: False
  - delta: 1.5
  - 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)