# 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

## 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)