Sims with nominal Chile and Pole masks II
August 27 2018, Clem Pryke (Oct 31: updated second plot to add numerical values in plot titles)
In Sims with nominal Chile and Pole masks I showed two more realistic sky masks. In this post I start making sims using them and pushing them through the BK style re-analysis pipeline. Below is a plot showing spectra of the first 300 realizations of lensed-LCDM and noise as seen through the three masks: the previous circular idealized f_sky 3% mask, the nominal Chile mask and the BICEP3 2017 as observed mask. In column 1 (left-most) we see the lLCDM spectra with their familiar forms (plotted as D_l - i.e. l(l+1)C_l). In column 2 we see the standard deviations of these - as expected the largest mask has the smallest sample variance and the smallest mask has the largest sample variance. In column 3 we see the noise spectra - plotted as straight C_l (without l^2 scaling) on log scale so we can see the expected white+1/f form. In column 4 we see the standard deviation of the noise - for BB this is presumably close to proportional to sigma(r) in the noise limited regime (i.e. for strong de-lensing).
(sqrt(2)*mean/std)^2 is the effective degrees of freedom for an auto-spectrum bandpower (since bandpowers are chi^2 distributed and chi^2 distribution has mean of n and std of sqrt(2n)). The full sky degrees of freedom is 2l*delta(l) where delta(l) is the width of the bandpower. We can therefore calculate the f_sky effective for each bandpower as (1/(l*delta(l))*(mean/std)^2. The plot below shows this for signal (left column) and noise (middle column). (Note that the blue is from 1000 realizations whereas the red and green 300.) We see the expected result that the effective f_sky for noise is greater than for signal - since the noise rises up towards the edge of the mask it partially resists the apodization and there really are more modes in the apodized noise map. The right column shows the ratio middle/left - I think this is some sort of measure of mask edge to central-region'ness.