July 29th, 2019 - CIB Lensing: Finding the Bias for Theory vs. Field + Bias * Halo (All Shells)

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In this post, I am attaching plots that compare the theory kappa power spectrum to linear prescription [math]\displaystyle{  C_{\ell}^{\text{theory}} \approx C_{\ell}^{\text{field}} + Bias * C_{\ell}^{\text{halo}}  }[/math] halo power spectrum for each kappa shell as a function of [math]\displaystyle{  \ell  }[/math] taking the bias factors as the ratios C_{\ell}^{\text{theory}} \approx C_{\ell}^{\text{halo}} (at high <\ell>) calculated in the previous post. 

Shell # and Corresponding Comoving Distances for Kappa 
Shell 1 : 0 ~ 400 Mpcs (Source at 600)      Shell 2 : 0 ~ 800 Mpcs (Source at 1000)      Shell 3 : 0 ~ 1200 Mpcs (Source at 1400)    Shell 4 : 0 ~ 1600 Mpcs (Source at 1800)      
Shell 5 : 0 ~ 2000 Mpcs (Source at 2200)    Shell 6 : 0 ~ 2400 Mpcs (Source at 2600)     Shell 7 : 0 ~ 2800 Mpcs (Source at 3000)    Shell 8 : 0 ~ 3200 Mpcs (Source at 3400)    
Shell 9 : 0 ~ 3600 Mpcs (Source at 3800)    Shell 10 : 0 ~ 4000 Mpcs (Source at 4200)    Shell 11 : 0 ~ 4400 Mpcs (Source at 4600)   Shell 12 : 0 ~ 4800 Mpcs (Source at 5000)   
Shell 13 : 0 ~ 5200 Mpcs (Source at 5400)   Shell 14 : 0 ~ 5600 Mpcs (Source at 5800)    Shell 15 : 0 ~ 6000 Mpcs (Source at 6200)   Shell 16 : 0 ~ 6400 Mpcs (Source at 6600)
Shell 17 : 0 ~ 6800 Mpcs (Source at 7000)   Shell 18 : 0 ~ 7200 Mpcs (Source at 7400)

As mentioned in the previous post (https://mocks.cita.utoronto.ca/index.php/July_29th,_2019_-_CIB_Lensing:_Finding_the_Bias_Factor_(for_Power_Spectra):_Theory/Halo_(All_Shells)), the two curves in the first four shells do not match. For Shell 5 ~ Shell 13, the two curves match very well at low to mid- [math]\displaystyle{  \ell  }[/math], deviating by 10 ~ 20 % at [math]\displaystyle{  \ell \lt  100  }[/math], [math]\displaystyle{  \ell \gt  3000  }[/math]. In shells that cover the most redshifts (comoving distances), the this deviation becomes larger (up to 50%) and the two curves show some discrepancy (around 10%) at [math]\displaystyle{  100 \lt  \ell \lt  3000  }[/math] as well. The bias factors for Shell 14 ~ 18 could be calculated more accurately by extrapolating the ratio (from the previous post) to higher [math]\displaystyle{  \ell  }[/math] (presumably).

Shell # Increasing from Left to Right, Top to Bottom (See Distance in Legend)

Theory vs bias fit0600 Mpc.png Theory vs bias fit1000 Mpc.png Theory vs bias fit1400 Mpc.png

Theory vs bias fit1800 Mpc.png Theory vs bias fit2200 Mpc.png Theory vs bias fit2600 Mpc.png

Theory vs bias fit3000 Mpc.png Theory vs bias fit3400 Mpc.png Theory vs bias fit3800 Mpc.png

Theory vs bias fit4200 Mpc.png Theory vs bias fit4600 Mpc.png Theory vs bias fit5000 Mpc.png

Theory vs bias fit5400 Mpc.png Theory vs bias fit5800 Mpc.png Theory vs bias fit6200 Mpc.png

Theory vs bias fit6600 Mpc.png Theory vs bias fit7000 Mpc.png Theory vs bias fit7400 Mpc.png

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