How \(N_\ell\) integrates down with \(N_{\mathrm{det}}\) in B3 2017 data.

Follow-up to 20201116_noise_int_down_K17_18 using per-pair coadds.

— Baibhav Singari

The behavior of noise in the pixel space as a function of number of receivers coadded has been investigated in 20201027_noise_scaling_withrx for Keck 2012/13 data. The behavior of \(N_\ell\) with number of coadded receivers for Keck 2013,2017 and 2018 has been investigated in 20201116_noise_int_down and 20201116_noise_int_down_K17_18, where we observe that the average \(N_\ell\) for \(10 \lt l \lt 100\) (bandpowers 2 and 3) shows deviation from simple scaling as a function of number of detectors. Also, the \(TT\) spectrum for the Keck 2013 and B2 has been investigated in 20210330_noise_int_down_t. This posting is a follow-up to the same in order to investigate the scaling of \(BB\) and \(TT\) \(N_\ell\) with number of detectors in BICEP 3 using per-pair coadded maps for BICEP 3 2017 data.

BICEP3 has got the same number of pairs as K2013- about 1200, but at 95 GHz rather than 150 GHz.We want to see if the excess noise effect is band dependent. We accumulate 5021 tags for 2017 and create the per-pair coadded map (jack02) for the analysis. The data-products used for this analysis are are stored in maps/5901 and aps/5901.

We use the jack02 per phase coadded map, equally divide the pairs into 8 groups of 155 pairs each (after shuffling), and accumulate over them so as to cover the entire focal plane each time with an increasing density of detectors.

Fig.1a: The polarization weight maps \(1/Q_{\mathrm{var}} + 1/U_{\mathrm{var}}\) as a function of the number of accumulated pairs.
Fig.1b: Array layouts as projected on sky with the 8 subsets of pairs (for which the polarization weights have been shown in the previous figure) in increasing order of density of detector pairs on focal plane.

We then simulate 100 realizations of \(N_\ell\) for each of these 8 combinations of accumulated tiles. We plot those in Fig.2a (Note: \(N_\ell\) has been divided by a factor of \( \ell(\ell+1)/2\pi\) to plot the 'raw \(N_\ell\)' ). We then take the mean of those 100 realizations and plot in Fig 2.b.

Fig.2a: First 100 realizations of \(N_\ell\) plotted. Realizations with different number of accumulated receivers have been plotted with different colors. The \(N_\ell\) has been divided by a factor of \( \ell(\ell+1)/2\pi\) to plot the raw \(N_\ell\).
Fig.2b: The mean of the 100 realizations of \(N_\ell\) plotted in Fig.2a.

The high \(\ell\) component integrated faster than the low \(\ell\) component as a function of number of accumulated receivers. To illustrate it better we plot the mean \(N_\ell\) in bandpowers 2 and 3 (in blue) and in the range \(200 \lt \ell \lt 400\) (in red).

Fig.3: Left panel: The mean \(N_\ell\) for \(\ell \gt 10\) as a function of number of detectors. Right panel: The mean \(N_\ell\) in different \(\ell\) ranges has been plotted as a function of total polarized map weights. The 8 points are for 155, 310, 465, 620, 775, 930, 1085 and 1240 accumulated pairs respectively. The dotted lines show the expected \(N_\ell\) from the total polarized weight (extrapolated value from the second point based on map weight).

The mean \(N_\ell\) integrates with \(N_{\det}\) closely in accordance with expectations (for \(\ell \gt 10\)). Subdividing into low \(\ell\) (bandpowers 2 and 3) and high \(\ell\) range, the mean \(N_\ell\) in the low \(\ell\) range scales almost similarly compared to the high \(\ell\) range. Although, the mean \(N_\ell\) for the low \(\ell\) range has a deviation from the expectation (around 15 percent), the deviation is not as high as seen in case of Keck data. The reason these B3 \(N_\ell\) spectra turn down at lower \(\ell\), as compared to Keck data, is because of the poly and scansync filtering. This filtering also suppresses the low \(\ell\) power for 150/220GHz but there the \(1/f\) noise is strong enough that it still kicks up to lower \(\ell\) even after the filtering.

The individual pol weight maps from the 8 combinations are here.

TT \(N_\ell\) for B3


Fig.4: Top panel: Same as figure 2, but for TT; i.e., the individual TT \(N_\ell\) vs \(\ell\)(left) and the mean of the 100 realizations(right). Bottom left panel: The mean TT \(N_\ell\) for \(\ell \gt 10\) as a function of number of detectors. Bottom right panel: The mean TT \(N_\ell\) in different \(\ell\) ranges has been plotted as a function of total polarized map weights. The 8 points are for 155, 310, 465, 620, 775, 930, 1085 and 1240 accumulated pairs respectively. The dotted lines show the expected \(N_\ell\) from the total polarized weight (extrapolated value from the first point based on map weight).

Summary

For BB \(N_\ell\):
  1. The \(N_\ell\) for BICEP 3 integrates much better with \(N_{det}\) as compared to Keck 2013/17/18 data.
  2. The mean \(N_\ell\) for \(10 \lt \ell \lt 100\) (mean in bandpowers 2 and 3) is much closer to the mean \(N_\ell\) in the high \(\ell\) range (as compared to the Keck case).
  3. The mean \(N_\ell\) values in the low \(\ell\) range tend to the value of the mean in the high \(\ell\) range for high number of \(N_{det}\). As the number of detectors are increased the \(N_\ell\) vs \(\ell\) is almost flat.
  4. The trend of the mean \(N_\ell\) being higher in the low \(\ell\) region as compared to the high \(\ell\) region (in case of Keck data) has been reversed with the BICEP 3 dataset.
  5. The deviation of \(N_\ell\) from expectation in the low \(\ell\) regime is around 15 % from the expected number, which is much less than the deviation from expectation with Keck dataset which had the data from higher frequency bands.
For TT \(N_\ell\):
  1. The mean in the low \(\ell\) bandpower(\(\sim 40\)) doesn't scale down at all, it remains constant no matter how many pairs are coadded.
  2. The TT \(N_\ell\) is \(1/f\) dominated which flattens out only at the highest \(\ell\).

Code

Codes for the posting are in here.
make_noise_sims.m is for creating the xxx6 jack02 realizations. make_aps_jack02.m is for creating the aps for the noise realizations. plot_aps_B32017_jack02.m and plot_aps_B32017_TT_jack02.m for creating all the plots in the posting.