Noise comparison between DM and Low-ℓ BB sims

Hits maps

First, we can compare the hits maps shown in Figure 1. Both the DM and Low-ℓ BB sims use hits maps made by Reijo, but they do have some differences. The Low-ℓ BB sims use the same hits maps at all frequencies, while the DM sims use one hits map for 30/40 GHz, a second one for 85/145 and 95/155, and a third hits map for 220/270 GHz. The DM 220/270 GHz hits map covers a notably larger sky area, despite the fact that all SATs should have similar field of view. Table 1 lists the effective \(f_\mathrm{sky}\) for each hit map, following equation A.1 of the DSR with weighting equal to the hits map (i.e. inverse noise variance weighting). At frequencies other than 220 and 270 GHz, the DM sims have \(f_\mathrm{sky}\) that is smaller by ∼20%, so we might expect \(\mathcal{N}_\ell\) to be ∼20% lower as well, if the total sensitivities are equal. For 220 and 270 GHz, the DM sims have \(f_\mathrm{sky}\) that is 33% higher.

Figure 1:

Relative hit maps for Data Challenge 06b sims (left) and Data Management sims (right). Note that the DC 06b sims use the same hit map for all frequencies, while the hit map for the DM sims varies with frequency.

Table 1:

Effective \(f_\mathrm{sky}\) for the hits maps used in DM and Low-ℓ BB sims.

Frequency	DC 06b \(f_\mathrm{eff}^\mathrm{noise}\)	DM sim \(f_\mathrm{eff}^\mathrm{noise}\)
30 GHz	2.955%	2.427%
40 GHz		2.427%
85 GHz		2.418%
95 GHz
145 GHz
155 GHz
220 GHz		3.916%
270 GHz		3.916%

Noise spectra

Next, Figure 2 shows the \(\mathcal{N}_\ell\) calculated from these maps, after weighting by the hits map (inverse noise variance weighting). The power spectrum estimator is anafast—no pure-B estimator is needed since the noise power is symmetric between E and B. For EE and BB, the dashed black line indicates the \(\mathcal{N}_\ell\) corresponding to the “Q/U rms” line from DSR Table 2-1. Note that the maps analyzed here were generated after the bug fix described here.

For EE or BB, the white noise level of the Low-ℓ BB sims agrees will with the DSR noise level at all eight frequencies. For the DM sims, the agreement is very good at 95 GHz, but the white \(N_\ell\) is low at other frequencies. The white \(N_\ell^{BB}\) values are listed in Table 2 below.

For TT, the noise levels agree between both sims for 30 and 40 GHz, but the DM sims are much noisier (∼3 orders of magnitude) for all other frequencies. This may have to do with the atmospheric model used for the DM sims, or perhaps it is a bug.

In EE and BB, the DM sims don't have excess low-ℓ noise, which is expected. They will contain excess low-ℓ noise if detector bandpass mismatches are turned on, in which case atmospheric fluctuations will leak into polarization.

Both sets of simulations have similar cut-offs in noise below ℓ ∼ 30. For the Low-ℓ BB sims, this feature is added by hand. For the DM sims, it presumably comes from the timestream filtering.

Figure 2:

Comparison of noise spectra between Data Management reference design sim (red) vs five realizations of Low-ℓ BB Data Challenge 06 sims (grey). Black dashed lines correspond to the polarization white noise level that is listed in bottom row of DSR Table 2-1.

Frequency	DSR Table 2-1 \(\mathcal{N}_\ell^{BB}\) \([\mu K^2]\)	Low-ℓ BB sim \(\mathcal{N}_\ell^{BB}\) \([\mu K^2]\)	DM sim \(\mathcal{N}_\ell^{BB}\) \([\mu K^2]\)
30 GHz	1.04e-06	0.97e-06	0.63e-06
40 GHz	1.71e-06	1.55e-06	0.67e-06
85 GHz	6.55e-08	6.16e-08	3.65e-08
95 GHz	5.15e-08	4.75e-08	4.78e-08
145 GHz	1.22e-07	1.26e-07	0.28e-07
155 GHz	1.43e-07	1.44e-07	0.55e-08
220 GHz	1.04e-06	0.95e-06	0.53e-06
270 GHz	3.05e-06	2.81e-06	1.62e-06

Frequency

DSR Table 2-1 \(\mathcal{N}_\ell^{BB}\) \([\mu K^2]\)

Low-ℓ BB sim \(\mathcal{N}_\ell^{BB}\) \([\mu K^2]\)

DM sim \(\mathcal{N}_\ell^{BB}\) \([\mu K^2]\)

30 GHz

1.04e-06

0.97e-06

0.63e-06

40 GHz

1.71e-06

1.55e-06

0.67e-06

85 GHz

6.55e-08

6.16e-08

3.65e-08

95 GHz

5.15e-08

4.75e-08

4.78e-08

145 GHz

1.22e-07

1.26e-07

0.28e-07

155 GHz

1.43e-07

1.44e-07

0.55e-08

220 GHz

1.04e-06

0.95e-06

0.53e-06

270 GHz

3.05e-06

2.81e-06

1.62e-06

Next steps

Andrea has produced CMB signal sims (ΛCDM, r=0). I have started looking at these, to understand the filtering that has gone into the DM sim maps and how much this affects our interpretation of the noise. In the process of tracking down the cause of the discrepancies seen above, we should improve and centralize the sim documentation.