Power law on sphere

[3]:

# Parameters
func_name = "Power_law_on_sphere"

Description

[5]:

func.display()

description: A power law function on a sphere (in spherical coordinates)
formula: $$ f(\vec{x}) = \left(\frac{180}{\pi}\right)^{-1.*index} \left\{\begin{matrix} 0.05^{index} & {\rm if} & ||\vec{x}-\vec{x}_0|| \le 0.05\\ ||\vec{x}-\vec{x}_0||^{index} & {\rm if} & 0.05 < ||\vec{x}-\vec{x}_0|| \le maxr \\ 0 & {\rm if} & ||\vec{x}-\vec{x}_0||>maxr\end{matrix}\right. $$
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
- index:
  - value: -2.0
  - desc: power law index
  - min_value: -5.0
  - max_value: -1.0
  - unit:
  - is_normalization: False
  - delta: 0.2
  - free: True
- maxr:
  - value: 20.0
  - desc: max radius
  - min_value: None
  - max_value: None
  - unit:
  - is_normalization: False
  - delta: 2.0
  - free: False
- minr:
  - value: 0.05
  - desc: radius below which the PL is approximated as a constant
  - min_value: None
  - max_value: None
  - unit:
  - is_normalization: False
  - delta: 0.005000000000000001
  - free: False

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)