Power law on sphere

[3]:
# Parameters
func_name = "Power_law_on_sphere"

Description

[5]:
func.display()
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  • 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)


index
0.0 180.0 -180.0 180.0
../_images/notebooks_Power_law_on_sphere_8_2.png