Feb 13, 2019 - Top hats and Poisson maps

I first tried to reproduce Pavel's results with top hat filters, then did some filtering analysis using a Poisson map (for 32 bands).

1. Top hat filters -defined f = np.zeros(nside*3), f[l_min:l_max]=1, map = hp.almxfl(alm, f) for each l_band (top-hat filters with sharp edges)

The plots match Pavel's which are shown below (the nside for my maps = 2048, for Pavel's, nside = 4096, which is why the x-axis scales are twice as mine).

2. Poisson map analysis - I generated a Poisson map with the same mean as the total unlensed sims-map, and a similar variance as well. The mean of the sims map and Poisson map are both around 0.45, while the variances are 5.6443*10e-5, 5.6252*10e-5 respectively. As the np.random.poisson module generates only natural numbers, I first multiplied an arbitrary constant to the mean of the sims map to define the Poisson array and then divided the factor out later (factor:800 in this case). If the Poisson array is defined to have the same mean as the sims map (0.45), then the array are basically mostly 0's with a few 1, 2, 3's, which is extremely inaccurate.

The resulting map is as below. Left is the Poisson map, while right is the original unlensed map from sims. The sims map certainly seems to have larger scale fluctuations.

I was not able to get a Cl plot of the Poisson map, as the matplotlib.plot module would break down when I tried so after using hp.anafast to convert the Poisson map into Cls. So I moved on to the top-hat filtered, and (original) band-filtered statistics of the Poisson map.

-Top hat filtered

The plots show a quite similar trend with the skewness and kurtosis of the top-hat filtered sims maps.

-Original band filtered

Comparing these to the sims-maps' skewness and kurtosis below,

the Poisson map's skewness and kurtosis are completely different. I will check again to see if I had actually filtered the Poisson and sims maps using the same filters.