May 21, 2019 - Using George's source catalog

George made a catalog of sources that go into the CIB map. Their fluxes are later normalized by a constant, that we can determine by comparison with the map - the total flux of the map (4.18 MJy) should be equal the sum of fluxes of the sources. Using the related scaling, we can make a histogram of the source flux densities:

This plot agrees with what Jason has. We checked that the total flux when calculating either the left or right bin values instead of the center only change the normalization by 0.1%.

Using results from [1], the corresponding power spectrum and bispectrum are

[math]\displaystyle{ \begin{array}{lcl} C_\ell &=& \frac{1}{4\pi} \sum_\mathrm{bins} S_i^2 N_i = 1400\, \mathrm{Jy^2/sr}\\ b_{\ell_1\ell_2\ell_3} &=& \frac{1}{4\pi} \sum_\mathrm{bins} S_i^3 N_i = 360\, \mathrm{Jy^3/sr} . \end{array} }[/math]

Contributions to reduced bispectrum from sources

It is interesting to ask which sources contribute to the reduced bispectrum assuming the Poisson limit. It turns out that the brightest sources are responsible.

Top hat skewness

Now we can compare the skewness from the top-hat filtered maps with theoretical expectations from the previous post. While we see linear trend at high [math]\displaystyle{ \ell }[/math], the amplitude is about a factor of 2.5 too high in the map.