# Sigma(r) vs r plots in prep for the DSR, polarization galactic mask.

B. Racine, R. Flauger

Yet another posting about $$\sigma(r)$$ vs. $$r$$ plots.
WARNING, This is preliminary.
In this posting, we use galactic masks defined in polarization to throw away areas of the sky that are highly contaminated.
Updated on May 15th to add the case where Chile's observing efficiency is half the one at Pole, as well as a few missing clicks.

## Introduction

In this recent posting, we proposed some $$\sigma(r)$$ vs. $$r$$ plots for the DSR.

In a subsequent posting, we updated our results with a more realistic handling of the joint observations, and studied the effect of the 20GHz channel on the constraints. We also tried to very naively boost the foreground level in the shallow part of the Chile map, since it is hitting a region with more foreground.

In the current posting, we instead apply a mask to the hitmap used for the Fisher forecast (thus reducing the number of modes used in the high foreground regions.)
As in the last posting (as mentioned in this posting):
• We switched to rescaling from the BK inverse noise variance weightings (since they should be removed from the BK bpcm and noise levels), instead of the naive 1% scaling.
• We are also combining the Pole and Chile dataset at the hitcount level instead of adding in inverse quadrature as we used to in the post-CDT spreadsheet (see section 2).
• We are still using the mean site NET, and decided not to apply the relative efficiency corrections explained in this posting.
• Since the 20GHz channel is on the delensing LAT, it is only able to observe the patches that will be delensed, i.e. not the shallow chile one. Previously we had ignored that fact and were rescaling the 20GHz channel as the other channels. We are now accounting for the fact that there is only one 20GHz tube, at Pole. Note that we also take into account that if all the tubes are in Chile, we can still use the 20GHz from Pole on the deep delensed patch, as well as for the combined case, but of course never more than one tube in total.

## 1: $$\sigma(r)$$ vs r for different hitcount maps.

The current DSR configuration is a 18 tubes configuration (slightly updated since the spreadsheet, now [2,2,6,6,6,6,4,4] tubes, each with [288, 288, 3524, 3524, 3524, 3524, 8438, 8438] detector per tube for [20, 30, 40, 85, 95, 145, 155, 220, 270] GHz, and 135 at 20GHz on a LAT).
We also show other configurations for comparison: 6 (1,2,2,1), 9 (1,3,3,2), 12 (1,4,4,3) in addition to 18 (2,6,6,4), where this notation shows the dichroic coupling.
Note that these configurations have been chosen so that they can sum to the default 18 tubes over 2 sites. This is studied in the next section.

In figure 1, we show the $$\sigma(r)$$ vs r plots for different configurations, with or without decorrelation, after applying different cuts based on the polarized foreground levels.

## 2: $$\sigma(r)$$ Tables for combined observations.

In the post DSR spreadsheet, we were combining the constraints as a weighted average of independent results, i.e. summing the $$\sigma(r)$$ in inverse quadrature. Here instead, we are combining at the map level, by simply summing the hitmaps for the overlapping deep patch. These new combined observations then go through Raphael's ILC to compute the residual signals and the corresponding "more optimal" scalings (see appendix A). For the Chile observations, we still add the shallow part in inverse quadrature (Since the patches don't overlap by definition, this is an ok approximation, even though they are measuring the same $$\ell$$ mode.)

## 3: $$\sigma(r)$$ vs r for the combined observations.

In this plot, we show the $$\sigma(r)$$ vs r for a total of 18 tubes, but split in different ways over the 2 sites.

## 4: $$\sigma(r)$$ vs r with bands for the foreground cut used.

In this section, we show $$\sigma(r)$$ vs r plots, adding cuts based on the polarization intensity. Here we use the galactic masks introduced briefly in appendix B.

## Appendix A: Scaling factors.

This part need to be documented more, but meanwhile, here are some notes from Raphael defining the new scaling factors, and how to rescale the BPCM: here (pdf scan of Raphael's notes).

The 4 scaling factors introduced in the notes above are plotted here as a function of the value of r for the different masks. They can be downloaded in this tarball. They were plotted for the unmasked version in this posting

## Appendix B: Galactic mask of polarized emission.

Here we show the different hitmaps as well as the new masks introduced. These have been produced by Raphael, based on Planck polarized intensity.

Comments on figure 7:

• For the 04 to 04d maps, 04 is the reference mask, with peak value at unity. The other masks have been rescaled to have the same total number of hits (i.e. same sum).
• Note that for the Chile deep and Pole wide, we use the inverse covariance maps to compute the weights, which includes has higher noise when observing at low latitude. This only takes into account the relative effect due to this higher noise, for now we don't use the overall scaling in the forecasting.
• For the Pole wide and Chile deep, we show the inverse of the covariance maps reported in this posting and this posting.
• Note the fact that signal $$f_{\rm sky}$$ is larger for the shallow map than for the full chile map, which is maybe counter-intuitive at first. This is because we are here using definitions assuming a inverse noise variance weighting. This will wash out the signal in the full chile deep mask due to the shallow part.