May 4th, 2020 - CIB Lensing: Field Contribution to 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) I also show how much the field contributes to the total [math]\displaystyle{  \kappa  }[/math] for each shell. 

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] for the 2-point and less than 500 for the 3 and 4-points. 
- 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) vs. Field -
Var kappa shell2 200 8000.png Skew kappa shell2 200 8000.png Kurt kappa shell2 200 8000.png 

- Field / Total - 
Var kappa ratio shell2 200.png Skew kappa ratio shell2 200.png Kurt kappa ratio shell2 200.png

 Shell 3  (z_max = 0.4, z_source = 0.5) 

- Total (Field + Halo) vs. Field -
Var kappa shell3 200 8000.png Skew kappa shell3 200 8000.png Kurt kappa shell3 200 8000.png 

- Field / Total - 
Var kappa ratio shell3 200.png Skew kappa ratio shell3 200.png Kurt kappa ratio shell3 200.png

 Shell 4  (z_max = 0.6, z_source = 0.7) 

- Total (Field + Halo) vs. Field -
Var kappa shell4 200 8000.png Skew kappa shell4 200 8000.png Kurt kappa shell4 200 8000.png 

- Field / Total - 
Var kappa ratio shell4 200.png Skew kappa ratio shell4 200.png Kurt kappa ratio shell4 200.png

 Shell 5  (z_max = 0.8, z_source = 0.9) 

- Total (Field + Halo) vs. Field -
Var kappa shell5 200 8000.png Skew kappa shell5 200 8000.png Kurt kappa shell5 200 8000.png 

- Field / Total - 
Var kappa ratio shell5 200.png Skew kappa ratio shell5 200.png Kurt kappa ratio shell5 200.png

 Shell 6  (z_max = 1.0, z_source = 1.1) 

- Total (Field + Halo) vs. Field -
Var kappa shell6 200 8000.png Skew kappa shell6 200 8000.png Kurt kappa shell6 200 8000.png 

- Field / Total - 
Var kappa ratio shell6 200.png Skew kappa ratio shell6 200.png Kurt kappa ratio shell6 200.png

 Shell 7  (z_max = 1.2, z_source = 1.3) 

- Total (Field + Halo) vs. Field -
Var kappa shell7 200 8000.png Skew kappa shell7 200 8000.png Kurt kappa shell7 200 8000.png 

- Field / Total - 
Var kappa ratio shell7 200.png Skew kappa ratio shell7 200.png Kurt kappa ratio shell7 200.png

 Shell 8  (z_max = 1.4, z_source = 1.5) 

- Total (Field + Halo) vs. Field -
Var kappa shell8 200 8000.png Skew kappa shell8 200 8000.png Kurt kappa shell8 200 8000.png 

- Field / Total - 
Var kappa ratio shell8 200.png Skew kappa ratio shell8 200.png Kurt kappa ratio shell8 200.png

 Shell 9  (z_max = 1.6, z_source = 1.7) 

- Total (Field + Halo) vs. Field -
Var kappa shell9 200 8000.png Skew kappa shell9 200 8000.png Kurt kappa shell9 200 8000.png 

- Field / Total - 
Var kappa ratio shell9 200.png Skew kappa ratio shell9 200.png Kurt kappa ratio shell9 200.png

 Shell 10  (z_max = 1.8, z_source = 1.9) 

- Total (Field + Halo) vs. Field -
Var kappa shell10 200 8000.png Skew kappa shell10 200 8000.png Kurt kappa shell10 200 8000.png 

- Field / Total - 
Var kappa ratio shell10 200.png Skew kappa ratio shell10 200.png Kurt kappa ratio shell10 200.png

 Shell 11  (z_max = 2.0, z_source = 2.1) 

- Total (Field + Halo) vs. Field -
Var kappa shell11 200 8000.png Skew kappa shell11 200 8000.png Kurt kappa shell11 200 8000.png 

- Field / Total - 
Var kappa ratio shell11 200.png Skew kappa ratio shell11 200.png Kurt kappa ratio shell11 200.png

 Shell 12  (z_max = 2.2, z_source = 2.3) 

- Total (Field + Halo) vs. Field -
Var kappa shell12 200 8000.png Skew kappa shell12 200 8000.png Kurt kappa shell12 200 8000.png 

- Field / Total - 
Var kappa ratio shell12 200.png Skew kappa ratio shell12 200.png Kurt kappa ratio shell12 200.png

 Shell 13  (z_max = 2.4, z_source = 2.5) 

- Total (Field + Halo) vs. Field -
Var kappa shell13 200 8000.png Skew kappa shell13 200 8000.png Kurt kappa shell13 200 8000.png 

- Field / Total - 
Var kappa ratio shell13 200.png Skew kappa ratio shell13 200.png Kurt kappa ratio shell13 200.png

 Shell 14  (z_max = 2.6, z_source = 2.7) 

- Total (Field + Halo) vs. Field -
Var kappa shell14 200 8000.png Skew kappa shell14 200 8000.png Kurt kappa shell14 200 8000.png 

- Field / Total - 
Var kappa ratio shell14 200.png Skew kappa ratio shell14 200.png Kurt kappa ratio shell14 200.png

 Shell 15  (z_max = 2.8, z_source = 2.9) 

- Total (Field + Halo) vs. Field -
Var kappa shell15 200 8000.png Skew kappa shell15 200 8000.png Kurt kappa shell15 200 8000.png 

- Field / Total - 
Var kappa ratio shell15 200.png Skew kappa ratio shell15 200.png Kurt kappa ratio shell15 200.png

 Shell 16  (z_max = 3.0, z_source = 3.1) 

- Total (Field + Halo) vs. Field -
Var kappa shell16 200 8000.png Skew kappa shell16 200 8000.png Kurt kappa shell16 200 8000.png 

- Field / Total - 
Var kappa ratio shell16 200.png Skew kappa ratio shell16 200.png Kurt kappa ratio shell16 200.png

 Shell 17  (z_max = 3.2, z_source = 3.3) 

- Total (Field + Halo) vs. Field -
Var kappa shell17 200 8000.png Skew kappa shell17 200 8000.png Kurt kappa shell17 200 8000.png 

- Field / Total - 
Var kappa ratio shell17 200.png Skew kappa ratio shell17 200.png Kurt kappa ratio shell17 200.png

 Shell 18  (z_max = 3.4, z_source = 3.5) 

- Total (Field + Halo) vs. Field -
Var kappa shell18 200 8000.png Skew kappa shell18 200 8000.png Kurt kappa shell18 200 8000.png 

- Field / Total - 
Var kappa ratio shell18 200.png Skew kappa ratio shell18 200.png Kurt kappa ratio shell18 200.png

 Shell 19  (z_max = 3.6, z_source = 3.7) 

- Total (Field + Halo) vs. Field -
Var kappa shell19 200 8000.png Skew kappa shell19 200 8000.png Kurt kappa shell19 200 8000.png 

- Field / Total - 
Var kappa ratio shell19 200.png Skew kappa ratio shell19 200.png Kurt kappa ratio shell19 200.png

 Shell 20  (z_max = 3.8, z_source = 3.9) 

- Total (Field + Halo) vs. Field -
Var kappa shell20 200 8000.png Skew kappa shell20 200 8000.png Kurt kappa shell20 200 8000.png 

- Field / Total - 
Var kappa ratio shell20 200.png Skew kappa ratio shell20 200.png Kurt kappa ratio shell20 200.png

 Shell 21  (z_max = 4.0, z_source = 4.1) 

- Total (Field + Halo) vs. Field -
Var kappa shell21 200 8000.png Skew kappa shell21 200 8000.png Kurt kappa shell21 200 8000.png 

- Field / Total - 
Var kappa ratio shell21 200.png Skew kappa ratio shell21 200.png Kurt kappa ratio shell21 200.png
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