July 18th, 2019 - CIB Lensing: Shell By Shell Analysis (All Shells)

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In this post, I am attaching the plots that show the difference induced by lensing on the power spectrum and reduced bispectrum of each of the shells (all shells that are lensed, so from shell #2). 

Shell # and Corresponding Comoving Distances
Shell 0 : 0 ~ 100 Mpcs         Shell 1 : 100 ~ 400 Mpcs       Shell 2 : 400 ~ 800 Mpcs       Shell 3 : 800 ~ 1200 Mpcs      Shell 4 : 1200 ~ 1600 Mpcs
Shell 5 : 1600 ~ 2000 Mpcs     Shell 6 : 2000 ~ 2400 Mpcs     Shell 7 : 2400 ~ 2800 Mpcs     Shell 8 : 2800 ~ 3200 Mpcs     Shell 9 : 3200 ~ 3600 Mpcs
Shell 10 : 3600 ~ 4000 Mpcs    Shell 11 : 4000 ~ 4400 Mpcs    Shell 12 : 4400 ~ 4800 Mpcs    Shell 13 : 4800 ~ 5200 Mpcs    Shell 14 : 5200 ~ 5600 Mpcs
Shell 15 : 5600 ~ 6000 Mpcs    Shell 16 : 6000 ~ 6400 Mpcs    Shell 17 : 6400 ~ 6800 Mpcs    Shell 18 : 6800 ~ 7200 Mpcs    Shell 19 : 7200 ~ 7600 Mpcs

The effect of lensing on the [math]\displaystyle{ C_{\ell} }[/math] is smaller than the effect on [math]\displaystyle{ b_{\ell} }[/math] for each of the shells. The [math]\displaystyle{ b_{\ell} }[/math] fractional difference at very high [math]\displaystyle{ \ell }[/math] decreases (away from zero) as the comoving distances to the shells increase. This effect is not seen for [math]\displaystyle{ C_{\ell} }[/math] however.

Also, there must be significant amounts of correlations between the shells for [math]\displaystyle{ b_{\ell} }[/math] as the fractional difference between the total lensed and unlensed maps are right at zero at high [math]\displaystyle{ \ell }[/math]. 

 Shell 2  (400 ~ 800 Mpcs, z = 0.0993 to 0.2029 )

- [math]\displaystyle{ C_{\ell} }[/math], [math]\displaystyle{ b_{\ell} }[/math] Comparison, [math]\displaystyle{ C_{\ell} }[/math] and [math]\displaystyle{ b_{\ell} }[/math] Fractional Difference Comparison

Cl shell 2-1.png Bl shell 2-1 log.png Cl fd binned shell 2-1.png Bl fd shell 2-1.png 

 Shell 3  (800 ~ 1200 Mpcs, z = 0.2029 to 0.3117 )

- [math]\displaystyle{ C_{\ell} }[/math], [math]\displaystyle{ b_{\ell} }[/math] Comparison, [math]\displaystyle{ C_{\ell} }[/math] and [math]\displaystyle{ b_{\ell} }[/math] Fractional Difference Comparison

Cl shell 3-1.png Bl shell 3-1 log.png Cl fd binned shell 3-1.png Bl fd shell 3-1.png 

 Shell 4  (1200 ~ 1600 Mpcs, z = 0.3117 to 0.4266 )

- [math]\displaystyle{ C_{\ell} }[/math], [math]\displaystyle{ b_{\ell} }[/math] Comparison, [math]\displaystyle{ C_{\ell} }[/math] and [math]\displaystyle{ b_{\ell} }[/math] Fractional Difference Comparison

Cl shell 4-1.png Bl shell 4-1 log.png Cl fd binned shell 4-1.png Bl fd shell 4-1.png 

 Shell 5  (1600 ~ 2000 Mpcs, z = 0.4266 to 0.5487 )

- [math]\displaystyle{ C_{\ell} }[/math], [math]\displaystyle{ b_{\ell} }[/math] Comparison, [math]\displaystyle{ C_{\ell} }[/math] and [math]\displaystyle{ b_{\ell} }[/math] Fractional Difference Comparison

Cl shell 5-1.png Bl shell 5-1 log.png Cl fd binned shell 5-1.png Bl fd shell 5-1.png 

 Shell 6  (2000 ~ 2400 Mpcs, z = 0.5487 to 0.6794 )

- [math]\displaystyle{ C_{\ell} }[/math], [math]\displaystyle{ b_{\ell} }[/math] Comparison, [math]\displaystyle{ C_{\ell} }[/math] and [math]\displaystyle{ b_{\ell} }[/math] Fractional Difference Comparison

Cl shell 6-1.png Bl shell 6-1 log.png Cl fd binned shell 6-1.png Bl fd shell 6-1.png 

 Shell 7  (2400 ~ 2800 Mpcs, z = 0.6794 to 0.8202 )

- [math]\displaystyle{ C_{\ell} }[/math], [math]\displaystyle{ b_{\ell} }[/math] Comparison, [math]\displaystyle{ C_{\ell} }[/math] and [math]\displaystyle{ b_{\ell} }[/math] Fractional Difference Comparison

Cl shell 7-1.png Bl shell 7-1 log.png Cl fd binned shell 7-1.png Bl fd shell 7-1.png 

 Shell 8  (2800 ~ 3200 Mpcs, z = 0.8202 to 0.9727 )

- [math]\displaystyle{ C_{\ell} }[/math], [math]\displaystyle{ b_{\ell} }[/math] Comparison, [math]\displaystyle{ C_{\ell} }[/math] and [math]\displaystyle{ b_{\ell} }[/math] Fractional Difference Comparison

Cl shell 8-1.png Bl shell 8-1 log.png Cl fd binned shell 8-1.png Bl fd shell 8-1.png 

 Shell 9  (3200 ~ 3600 Mpcs, z = 0.9727 to 1.1390 )

- [math]\displaystyle{ C_{\ell} }[/math], [math]\displaystyle{ b_{\ell} }[/math] Comparison, [math]\displaystyle{ C_{\ell} }[/math] and [math]\displaystyle{ b_{\ell} }[/math] Fractional Difference Comparison

Cl shell 9-1.png Bl shell 9-1 log.png Cl fd binned shell 9-1.png Bl fd shell 9-1.png 

 Shell 10  (3600 ~ 4000 Mpcs, z = 1.1390 to 1.3220 )

- [math]\displaystyle{ C_{\ell} }[/math], [math]\displaystyle{ b_{\ell} }[/math] Comparison, [math]\displaystyle{ C_{\ell} }[/math] and [math]\displaystyle{ b_{\ell} }[/math] Fractional Difference Comparison

Cl shell 10-1.png Bl shell 10-1 log.png Cl fd binned shell 10-1.png Bl fd shell 10-1.png 

 Shell 11  (4000 ~ 4400 Mpcs, z = 1.3220 to 1.5240 )

- [math]\displaystyle{ C_{\ell} }[/math], [math]\displaystyle{ b_{\ell} }[/math] Comparison, [math]\displaystyle{ C_{\ell} }[/math] and [math]\displaystyle{ b_{\ell} }[/math] Fractional Difference Comparison

Cl shell 11-1.png Bl shell 11-1 log.png Cl fd binned shell 11-1.png Bl fd shell 11-1.png 

 Shell 12  (4400 ~ 4800 Mpcs, z = 1.5240 to 1.7487 )

- [math]\displaystyle{ C_{\ell} }[/math], [math]\displaystyle{ b_{\ell} }[/math] Comparison, [math]\displaystyle{ C_{\ell} }[/math] and [math]\displaystyle{ b_{\ell} }[/math] Fractional Difference Comparison

Cl shell 12-1.png Bl shell 12-1 log.png Cl fd binned shell 12-1.png Bl fd shell 12-1.png 

 Shell 13  (4800 ~ 5200 Mpcs, z = 1.7487 to 2.0004 )

- [math]\displaystyle{ C_{\ell} }[/math], [math]\displaystyle{ b_{\ell} }[/math] Comparison, [math]\displaystyle{ C_{\ell} }[/math] and [math]\displaystyle{ b_{\ell} }[/math] Fractional Difference Comparison

Cl shell 13-1.png Bl shell 13-1 log.png Cl fd binned shell 13-1.png Bl fd shell 13-1.png 

 Shell 14  (5200 ~ 5600 Mpcs, z = 2.0004 to 2.2482 )

- [math]\displaystyle{ C_{\ell} }[/math], [math]\displaystyle{ b_{\ell} }[/math] Comparison, [math]\displaystyle{ C_{\ell} }[/math] and [math]\displaystyle{ b_{\ell} }[/math] Fractional Difference Comparison

Cl shell 14-1.png Bl shell 14-1 log.png Cl fd binned shell 14-1.png Bl fd shell 14-1.png 

 Shell 15  (5600 ~ 6000 Mpcs, z = 2.2482 to 2.6065 )

- [math]\displaystyle{ C_{\ell} }[/math], [math]\displaystyle{ b_{\ell} }[/math] Comparison, [math]\displaystyle{ C_{\ell} }[/math] and [math]\displaystyle{ b_{\ell} }[/math] Fractional Difference Comparison

Cl shell 15-1.png Bl shell 15-1 log.png Cl fd binned shell 15-1.png Bl fd shell 15-1.png 

 Shell 16  (6000 ~ 6400 Mpcs, z = 2.6065 to 2.9752 )

- [math]\displaystyle{ C_{\ell} }[/math], [math]\displaystyle{ b_{\ell} }[/math] Comparison, [math]\displaystyle{ C_{\ell} }[/math] and [math]\displaystyle{ b_{\ell} }[/math] Fractional Difference Comparison

Cl shell 16-1.png Bl shell 16-1 log.png Cl fd binned shell 16-1.png Bl fd shell 16-1.png 

 Shell 17  (6400 ~ 6800 Mpcs, z = 2.9752 to 3.4004 )

- [math]\displaystyle{ C_{\ell} }[/math], [math]\displaystyle{ b_{\ell} }[/math] Comparison, [math]\displaystyle{ C_{\ell} }[/math] and [math]\displaystyle{ b_{\ell} }[/math] Fractional Difference Comparison

Cl shell 17-1.png Bl shell 17-1 log.png Cl fd binned shell 17-1.png Bl fd shell 17-1.png 

 Shell 18  (6800 ~ 7200 Mpcs, z = 3.4004 to 3.8948 )

- [math]\displaystyle{ C_{\ell} }[/math], [math]\displaystyle{ b_{\ell} }[/math] Comparison, [math]\displaystyle{ C_{\ell} }[/math] and [math]\displaystyle{ b_{\ell} }[/math] Fractional Difference Comparison

Cl shell 18-1.png Bl shell 18-1 log.png Cl fd binned shell 18-1.png Bl fd shell 18-1.png 

 Shell 19  (7200 ~ 7600 Mpcs, z = 3.8948 to 4.5000 )

- [math]\displaystyle{ C_{\ell} }[/math], [math]\displaystyle{ b_{\ell} }[/math] Comparison, [math]\displaystyle{ C_{\ell} }[/math] and [math]\displaystyle{ b_{\ell} }[/math] Fractional Difference Comparison

Cl shell 19-1.png Bl shell 19-1 log.png Cl fd binned shell 19-1.png Bl fd shell 19-1.png

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