# Noise levels for a DSR-like Data Challenge.

B. Racine

In this short posting, we report the noise levels scaled from the achieved BK15 noise bandpowers to the DSR-like ones.
Update Sept 30 2019: changed the beam FWHM grouping and added param files without detector count scalings.

## 1. Introduction.

In this posting, our goal is to create a parameter file describing the noise properties to be used for the DSR-like data challenge (DC5?). This will be used to construct noise spectra and synthesize noise maps for the S4 map based analysis. Example of such noise parameters for the different data challenges are shown here.
Note that all these past Data Challenges were using BK14 noise spectra as inputs, while using preliminary 220 GHz survey weights. In the current posting, our achieved performances come from BK15.

## 2. Noise fit.

A few soft choices have to be made when going from our noise simulations to the S4 predicted noise levels, and have been discussed in this posting about BK15 noise levels. We here make the same choices, using the "fiducial" bin center, as well as the mean of the noise spectra.
Note also that the noise spectra in figure 3 of the BK15 paper have had a suppression factor applied, which includes filtering and beam deconvolution. When fitting the 1/f noise model, we need to take out the effect of the beam. We here use a gaussian beam instead of the actual measured beam, which has negligible impact.

We fit a 1/f model to the BK15 noise bandpowers: $$$N_\ell^{fit} = N_0 \left(1+\left(\frac{l}{l_{\rm knee}}\right)^{\alpha}\right),$$$ In order to keep the different DC parameters consistent, we convert the $$N_0$$ white noise level, in $$\mu K^2$$, to a map depth $$\sigma_{\rm map}$$, in $$\mu K$$-arcmin : $$$\sigma_{\rm map}= \sqrt{ N_0 * (180/\pi)^2*60^2}.$$$ We then get the noise parameters reported in this posting and shown here in figure 1.

## 3. Noise rescaling.

We can then rescale the noise levels, using ideal NETs for BK detectors as well as for the S4 detectors. The ideal NETs per detector were calculated with NETlib.py and are the same as in previous DC:

• $${\rm NET}_{\rm S4, ideal}$$ = 214, 177, 224, 270, 238, 309, 331, 747 and 1281 $$\mu K_{\rm CMB}\sqrt{s}$$ for the nine S4 bands,
• $${\rm NET}_{\rm BK15, ideal}$$ = 287.6, 313.1 and 837.7 $$\mu K_{\rm CMB}\sqrt{s}$$ for the BK15 bands.
We also scale according to the number of detectors-years. We use :
• $$N_{\rm det-yr, S4} = N_{\rm det per tube} * N_{\rm tube} * N_{\rm years}$$= [135, 288, 288, 3524, 3524, 3524, 3524, 8438, 8438].*[1,2,2,6,6,6,6,4,4]*7.
Note that the 135 detectors per tube at 20 GHz correspond to the channel on the delensing LAT at Pole.
• $$N_{\rm det-yr, BK15}$$ = 288*4, 512*11.2 and 512*2.
The nominal number of 150GHz receiver years in BK150 is 17. The number 11.2 comes from assuming 30k survey weight per receiver-year, which was substantially exceeded by BICEP2 and was typical of the best of the Keck 150GHz focal planes.
We scale the 20, 30, 40, 85 and 95 GHz S4 channels from the 95 GHz BK15 inputs, the 145 and 155 GHz from the 150 GHz BK15 inputs and the 220 and 270 GHz from the 220 GHz BK15 inputs. Note that for the 20GHz channel, which is placed on the delensing LAT, we use different shape parameters ($$l_{\rm knee}$$ and $$\alpha$$), based on SPT measurements.
The overall scaling is then: $$$\sigma_{\rm map, S4} = \sigma_{\rm map, BK15} \frac{{\rm NET}_{\rm S4, ideal}}{{\rm NET}_{\rm BK15, ideal}} \sqrt{\frac{N_{\rm det-yr, BK15}}{N_{\rm det-yr, S4}}}$$$
Note that contrary to previous DC, we don't rescale by a factor of $$\sqrt{3}$$, so these levels would correspond to an observation of the BK15 patch with S4 sensitivity. The scaling to different hitmaps will be performed on the go using the ratios of the $$\rm f_{\rm sky,noise}$$, defined as: \begin{align} {\rm f_{\rm sky,noise}} &= \frac{\Omega_{pix}}{4\pi} \frac{(\sum_i h_i)^2}{\sum_i h_i^{2}}, \end{align} We then get the noise power spectra plotted in figure 2

## 4. Tables.

Here we propose a table to be used for the S4 sims, with some rounded up values, in the spirit of what is reported here.
Note again that these noise levels have not been rescaled to a specific observing strategy.

The parameter file can be downloaded here. We also provide a file that has been scaled by the relative NET, but not by the relative detector count, here.
Update Sept 30 2019: Note that in the original table, we used a different grouping of the beam size, based on table 2-1 of the DSR, whereas we now updated to table 3-1, which has the proper dichroic coupling. Note that in the Fisher exercise, the grouping from table 2-1 waqs used. We checked on a number of cases that the effect on $$\sigma(r)$$ is below 0.2%.

Parameters\Frequencies (GHz) 20 30 40 85 95 145 155 220 270
Bandwidth (GHz) 5 9 12 20.4 22.8 31.9 34.1 48.4 59.4
Beam FWHM (arcmin) 11 72.8 72.8 25.5 22.7 25.5 22.7 13 13
$$\sigma_{\rm map} [\mu \rm K-arcmin]$$ TT 8.99 3.6 4.55 0.91 0.8 1.83 1.96 4.93 8.45
$$\ell_{\rm knee}$$ TT 500 150 150 150 150 230 230 220 220
$$\alpha$$ TT -4.3 -4.3 -4.3 -4.3 -4.3 -3.8 -3.8 -4 -4
$$\sigma_{\rm map} [\mu \rm K-arcmin]$$ EE 6.09 2.44 3.09 0.61 0.54 0.85 0.91 2.34 4.02
$$\ell_{\rm knee}$$ EE 200 65 65 65 65 65 65 60 60
$$\alpha$$ EE -1.9 -1.9 -1.9 -1.9 -1.9 -3 -3 -3.1 -3.1
$$\sigma_{\rm map} [\mu \rm K-arcmin]$$ BB 5.6 2.24 2.84 0.56 0.5 0.83 0.89 2.28 3.91
$$\ell_{\rm knee}$$ BB 200 75 75 75 75 60 60 60 60
$$\alpha$$ BB -1.5 -1.5 -1.5 -1.5 -1.5 -2.8 -2.8 -2.9 -2.9
$$\ell_{\rm min}$$ 30 30 30 30 30 30 30 30 30
nside 512 512 512 512 512 512 512 512 512