# Low ell noise from past and current telescopes

*Colin Bischoff, 2018-09-13*

This posting documents (and slightly expands on) slides 6 and 7 from my presentation **Noise forecasting for small-area survey** from the 2018 Princeton workshop.

I use the products from my posting **2018 August 10: Achieved performance roundup** which consist of noise bandpowers (N_l) and f_sky as a function of ell for many recently published CMB polarization results.

I fit the N_l to a model of white plus 1/ell^alpha noise. The first figure shows the ell_knee (i.e. the scale at which the N_l is twice the white noise level) plotted vs telescope aperture. The main takeaway is that past experiments divide into two categories -- small aperture experiments (BICEP/Keck, ABS, QUIET) with ell_knee of ~50 and larger aperture experiments (POLARBEAR, ACTpol, SPTpol) with ell_knee of ~450.

Some additional notes:

- For POLARBEAR, I was unable to simultaneously solve for N_l and f_sky (because they haven't published their EE error bars). As a fall back, I assumed an effective sky area of 25 square-degrees that is constant in ell. From discussion with Yuji Chinone, it sounds like the size of the BB error bar in POLARBEAR's lowest ell bin is driven by lack of modes over such a small sky area but my analysis attributes it to excess low-ell noise. We expect to see very different results for upcoming POLARBEAR results, which cover a much larger sky area and use a rapidly-rotating half-wave plate.
- The bottom left corner of the figure includes seven different (but not wholly independent) BICEP/Keck points: BICEP2 (150 GHz), BKP (150 GHz), BK14 (95 and 150 GHz), and BK15 (95, 150, and 220 GHz).
- For QUIET, the power with smaller ell_knee is 43 GHz and the point with higher ell_knee is 95 GHz, perhaps reflecting a difference in atmospheric noise.
- Rather than focusing on aperture size, an alternate interpretation of this plot is to divide the experiments into a group with heavily baffled / enclosed telescopes (BICEP/Keck, ABS, QUIET) and a group with less baffling.

Figure 1 suggests that it is possible to achieve equally low ell_knee from both South Pole and Atacama sites. A potential objection to this claim is that the Atacama-based small-aperture telescopes (ABS and QUIET) both have significantly higher white noise than BICEP/Keck. If the low ell noise does not integrate down, then an ABS-like experiment with BICEP/Keck white noise level could end up completely dominated by the low ell noise.

To explore this question, I examine the multiple data points from BICEP/Keck at 95 and 150 GHz (Figure 2). The figure shows white noise power on the x-axis vs noise power at ell=50 on the y-axis. To guide the eye, I drew dotted lines from the origin through the first 150 GHz data point (BICEP2) and first 95 GHz data point (BK14). If low ell noise integrates down with white noise, then we would expect subsequent data points to lie on these lines. In fact, we see that the points fall slightly above the line. This indicates that the low ell noise is not integrating down quite as well as the white noise. However, it doesn't seem to be a large effect and the 150 GHz low ell noise does seem to integrate down properly from BKP through BK15 (albeit over a much shorter lever arm). It's hard to make a firm statement without a deeper study, but my takeaway is that we can expect the low ell noise to mostly integrate down as sensitivity improves.

A slightly different question that would be interesting to investigate is whether the low ell noise integrates down with *increased detector count*. If we hypothesize that this noise has atmospheric origin, then it should integrate down over time because the atmosphere fluctuates. However, if all the detectors in a large focal plane see common-mode atmospheric noise, then adding more detectors may not yield the expected improvement to the low ell noise. An interesting test would be to compare Keck Array 95 GHz noise (288 detectors per focal plane) to BICEP3 95 GHz noise (~2400 detectors).