Aliased power in noise maps
After exchanging some plots with Raphael, he has pointed out that the noise maps generated for Data Challenge 1 show evidence of aliasing. This can be seen in Figure 1.
- The black line shows the noise model specified for the data challenge.
- The blue and orange curves are both calculated from full-sky, nside=512 noise maps (realization 0000 of 95 GHz noise). I used healpy.anafast for power spectrum calculations.
- The map used for the blue line was generated using synfast with nlmax=2048 (note that aℓm are calculated out to ℓ=4096).
- For the orange line, I used a map generated from the same aℓm but with nlmax=1535, which is 3*nside - 1.
The blue curve shows a clear excess starting around ℓ = 1100, presumably from aliasing. In contrast, the orange curve rolls off slowly starting at ℓ = 800.
This aliasing is not a problem for the signal maps (lensed-ΛCDM, Gaussian dust, Gaussian sync), even though they also use nlmax = 2048 because those maps have been smoothed by the instrument beam (8.5 arcmin at 270 GHz). Figure 2 shows the same comparison as Figure 1, except for Gaussian dust at 270 GHz (frequency with the least beam smoothing). In this case, the discrepancy between nlmax = 2048 and 1535 is very small (note the logarithmic y-axis), but both calculated power spectra diverge from the model above ℓ = 600.
My conclusion from looking at these spectra is that the choice of nlmax is unlikely to impact r estimates, because it only shows up at ℓ > 1000. Going forward, it probably is a good idea to use nlmax = 3*nside - 1, though we see from Figure 1 that this leads to an Nℓ discrepancy with the opposite sign.