Apr 19th, 2020 - CIB Lensing: Statistics of Kappa Shells

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Here, I have the variance, skewness, and kurtosis by [math]\displaystyle{  \ell  }[/math] ([math]\displaystyle{  \Delta \ell = 200  }[/math]) for each [math]\displaystyle{  \kappa  }[/math] (total and field-only) shell covering up to z = 4.0. (There were no CIB pixels at z > 4.2)

Shell # and Corresponding redshifts 'z' (All shells start from z = 0.05)
Shell 2  : z_max = 0.2, z_source = 0.3 (lenses CIB shell from z = 0.2 to 0.4)  
Shell 3  : z_max = 0.4, z_source = 0.5 (lenses CIB shell from z = 0.4 to 0.6) 
... and so on until ... 
Shell 21 : z_max = 4.0, z_source = 4.1 (lenses CIB shell from z = 4.0 to 4.2) 

- As expected, the field dominates each of the shells at low [math]\displaystyle{  \ell  }[/math] for all 3 statistics, but the cut-off seems to be less than [math]\displaystyle{  \ell 
= 1000  }[/math]. 
- All the plots go up to [math]\displaystyle{  \ell_{max}  }[/math], and I have assumed that [math]\displaystyle{  \ell \approx 8000  }[/math] is where n-side effects kick in (dashed lines). For the 2-point and the 4-point, n-side effects seem to be less blatant (perhaps non-existent?), while they are apparent for the 3-point (both field and total) as with the lensing effect. 
- With these plots, it is hard to tell where the scattering effects at [math]\displaystyle{  \ell \gt  2000  }[/math] evident in the lensed vs. unlensed 3-point plots are coming from. It is odd that the field [math]\displaystyle{  \kappa  }[/math], whose 3-point is orders of magnitudes lower than the total [math]\displaystyle{  \kappa  }[/math] is causing these effects. 

 Shell 2  (z_max = 0.2, z_source = 0.3) Order: [math]\displaystyle{  \lt \sigma^2\gt   }[/math], [math]\displaystyle{  \lt \sigma^3\gt   }[/math], [math]\displaystyle{  \lt \sigma^4\gt   }[/math] 

- Total (Field + Halo) -
Var total kappa shell2 200.png Skew total kappa shell2 200.png Kurt total kappa shell2 200.png 

- Field - 
Var field kappa shell2 200.png Skew field kappa shell2 200.png Kurt field kappa shell2 200.png

 Shell 3  (z_max = 0.4, z_source = 0.5) 

- Total (Field + Halo) -
Var total kappa shell3 200.png Skew total kappa shell3 200.png Kurt total kappa shell3 200.png 

- Field - 
Var field kappa shell3 200.png Skew field kappa shell3 200.png Kurt field kappa shell3 200.png

 Shell 4  (z_max = 0.6, z_source = 0.7) 

- Total (Field + Halo) -
Var total kappa shell4 200.png Skew total kappa shell4 200.png Kurt total kappa shell4 200.png 

- Field - 
Var field kappa shell4 200.png Skew field kappa shell4 200.png Kurt field kappa shell4 200.png

 Shell 5  (z_max = 0.8, z_source = 0.9) 

- Total (Field + Halo) -
Var total kappa shell5 200.png Skew total kappa shell5 200.png Kurt total kappa shell5 200.png 

- Field - 
Var field kappa shell5 200.png Skew field kappa shell5 200.png Kurt field kappa shell5 200.png

 Shell 6  (z_max = 1.0, z_source = 1.1) 

- Total (Field + Halo) -
Var total kappa shell6 200.png Skew total kappa shell6 200.png Kurt total kappa shell6 200.png 

- Field - 
Var field kappa shell6 200.png Skew field kappa shell6 200.png Kurt field kappa shell6 200.png

 Shell 7  (z_max = 1.2, z_source = 1.3) 

- Total (Field + Halo) -
Var total kappa shell7 200.png Skew total kappa shell7 200.png Kurt total kappa shell7 200.png 

- Field - 
Var field kappa shell7 200.png Skew field kappa shell7 200.png Kurt field kappa shell7 200.png

 Shell 8  (z_max = 1.4, z_source = 1.5) 

- Total (Field + Halo) -
Var total kappa shell8 200.png Skew total kappa shell8 200.png Kurt total kappa shell8 200.png 

- Field - 
Var field kappa shell8 200.png Skew field kappa shell8 200.png Kurt field kappa shell8 200.png

 Shell 9  (z_max = 1.6, z_source = 1.7) 

- Total (Field + Halo) -
Var total kappa shell9 200.png Skew total kappa shell9 200.png Kurt total kappa shell9 200.png 

- Field - 
Var field kappa shell9 200.png Skew field kappa shell9 200.png Kurt field kappa shell9 200.png

 Shell 10  (z_max = 1.8, z_source = 1.9) 

- Total (Field + Halo) -
Var total kappa shell10 200.png Skew total kappa shell10 200.png Kurt total kappa shell10 200.png 

- Field - 
Var field kappa shell10 200.png Skew field kappa shell10 200.png Kurt field kappa shell10 200.png

 Shell 11  (z_max = 2.0, z_source = 2.1) 

- Total (Field + Halo) -
Var total kappa shell11 200.png Skew total kappa shell11 200.png Kurt total kappa shell11 200.png 

- Field - 
Var field kappa shell11 200.png Skew field kappa shell11 200.png Kurt field kappa shell11 200.png

 Shell 12  (z_max = 2.2, z_source = 2.3) 

- Total (Field + Halo) -
Var total kappa shell12 200.png Skew total kappa shell12 200.png Kurt total kappa shell12 200.png 

- Field - 
Var field kappa shell12 200.png Skew field kappa shell12 200.png Kurt field kappa shell12 200.png

 Shell 13  (z_max = 2.4, z_source = 2.5) 

- Total (Field + Halo) -
Var total kappa shell13 200.png Skew total kappa shell13 200.png Kurt total kappa shell13 200.png 

- Field - 
Var field kappa shell13 200.png Skew field kappa shell13 200.png Kurt field kappa shell13 200.png

 Shell 14  (z_max = 2.6, z_source = 2.7) 

- Total (Field + Halo) -
Var total kappa shell14 200.png Skew total kappa shell14 200.png Kurt total kappa shell14 200.png 

- Field - 
Var field kappa shell14 200.png Skew field kappa shell14 200.png Kurt field kappa shell14 200.png

 Shell 15  (z_max = 2.8, z_source = 2.9) 

- Total (Field + Halo) -
Var total kappa shell15 200.png Skew total kappa shell15 200.png Kurt total kappa shell15 200.png 

- Field - 
Var field kappa shell15 200.png Skew field kappa shell15 200.png Kurt field kappa shell15 200.png

 Shell 16  (z_max = 3.0, z_source = 3.1) 

- Total (Field + Halo) -
Var total kappa shell16 200.png Skew total kappa shell16 200.png Kurt total kappa shell16 200.png 

- Field - 
Var field kappa shell16 200.png Skew field kappa shell16 200.png Kurt field kappa shell16 200.png

 Shell 17  (z_max = 3.2, z_source = 3.3) 

- Total (Field + Halo) -
Var total kappa shell17 200.png Skew total kappa shell17 200.png Kurt total kappa shell17 200.png 

- Field - 
Var field kappa shell17 200.png Skew field kappa shell17 200.png Kurt field kappa shell17 200.png

 Shell 18  (z_max = 3.4, z_source = 3.5) 

- Total (Field + Halo) -
Var total kappa shell18 200.png Skew total kappa shell18 200.png Kurt total kappa shell18 200.png 

- Field - 
Var field kappa shell18 200.png Skew field kappa shell18 200.png Kurt field kappa shell18 200.png

 Shell 19  (z_max = 3.6, z_source = 3.7) 

- Total (Field + Halo) -
Var total kappa shell19 200.png Skew total kappa shell19 200.png Kurt total kappa shell19 200.png 

- Field - 
Var field kappa shell19 200.png Skew field kappa shell19 200.png Kurt field kappa shell19 200.png

 Shell 20  (z_max = 3.8, z_source = 3.9) 

- Total (Field + Halo) -
Var total kappa shell20 200.png Skew total kappa shell20 200.png Kurt total kappa shell20 200.png 

- Field - 
Var field kappa shell20 200.png Skew field kappa shell20 200.png Kurt field kappa shell20 200.png

 Shell 21  (z_max = 4.0, z_source = 4.1) 

- Total (Field + Halo) -
Var total kappa shell21 200.png Skew total kappa shell21 200.png Kurt total kappa shell21 200.png 

- Field - 
Var field kappa shell21 200.png Skew field kappa shell21 200.png Kurt field kappa shell21 200.png
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