Aug 26th, 2019 - CIB non-Gaussianity: Whitening of the Maps

On Friday (the 23rd), we discussed the prospects of picking out the non-Gaussianity of the CIB maps through a whitening process where the [math]\displaystyle{  a_{\ell m}  }[/math]'s are divided by the square root of [math]\displaystyle{  C_{\ell}  }[/math], then transformed into maps. Below are the results of six different maps whitened and zoomed in: 

(1) an NSIDE 1024 CMB map generated from CAMB theory [math]\displaystyle{ C_{\ell} }[/math]

(2) a non-Gaussian map created by [math]\displaystyle{ (1) + 10 \times (1)^2 }[/math] (NSIDE = 1024)

(3) the Planck SEVEM map (https://pla.esac.esa.int/#maps) (NSIDE = 2048)

(4) the Websky CIB map (NSIDE downgraded to 2048)

(5) the Websky CIB lensed map (NSIDE downgraded to 2048)

(6) the CIB halo kappa map (NSIDE downgraded to 2048)

Zoom-in maps

For each map, the range of the color bars are: [math]\displaystyle{ \mu \pm 3\sigma }[/math], with [math]\displaystyle{ \mu }[/math] being the means.

(1) (2)

(3) (4)

(5) (6)

The first map should set the standard for a whitened Gaussian map, the second one looks different (as it must be non-Gaussian from the definition), the third one seems to have some kind of structure in it (but it's a Planck map), and (4), (5), (6) have similarities but seem pretty Gaussian.

Below are the CMB (and its non-Gaussian version) and CIB (CIB, CIB lensed, CIB kappa) related zoom-ins switching back and forth.

CMB

CIB

Histograms

I also checked the histograms; the red dashed lines are the means.

(1) (2)

(3) (4)

(5) (6)

We see that (1) (CMB) and (3) Planck SEVEM are close to Gaussian, while (2) is highly non-Gaussian, and (4), (5), and (6) are weakly non-Gaussian.

So far, it seems rather difficult to search for coherent phases in the CIB map.