July 29th, 2019 - CIB Lensing: Finding the Bias Factor (for Power Spectra): Theory/Halo (All Shells)
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In this post, I am attaching plots that show the ratio of the theory kappa power spectrum to the halo power spectrum for each kappa shell as a function of [math]\displaystyle{ \ell }[/math].
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)
For the first three (or four) shells, the ratio does not flatten out adequately even at high [math]\displaystyle{ \ell }[/math]'s; the linear prescription [math]\displaystyle{ C_{\ell}^{\text{theory}} \approx C_{\ell}^{\text{field}} + Bias * C_{\ell}^{\text{halo}} }[/math] will not work for these shells. In subsequent shells, the ratio seems to flatten out pretty well. The horizontal line (the value of which is given in the legend) is a fit of the last two ratio values for each shell, so 'error' (calculated by taking the square root of the covariance matrix and dividing by the square root of the number of values) is not very meaningful. However, the values given in the legends should provide an idea of what the ratio flattens out to for each shell.
Shell # Increasing from Left to Right, Top to Bottom (See Distance in Legend)
