Noise levels in BK15 for S4 sims.

1. Introduction.

2. Plots.

In figure 3 of the BK15 paper we plot the noise bandpowers normalized by \(\ell_c (\ell_c+1)/(2\pi)\), where \(\ell_c\) are the fiducial bandpowers, but we plot them at the position of the bin center computed by weighted_ellbins.m, integrating \(\ell\) in the bandpower window function (bpwf).

In this posting, we start from the noise bandpowers from the BK15 analysis and fit a 1/f noise model, as described in this posting.

Here we study 3 different cases, where the same \(\ell_c\) is used for the normalization and for the position:

• We use the fiducial \(\ell_c\), which are the same for any field or frequency, as is used in the likelihood definition. This is the choice that was made for the previous DCs.
• We use the usual bpwf weighted \(\ell_c\), as used for the bin position in the BK15 paper, though it is more adapted for a signal flat in \(D_\ell\).
• We use the flat-\(C_\ell\) weighted \(\ell_c\), where we add an extra \(\ell^2\) factor in front of the bpwf. This is probably the most adapted for the noise bandpowers, which are flat in C_ell.

Note that we fit the noise parameters to the mean of the BK15 noise bandpowers, whereas the previous DCs used the bias removed from the bandpowers which also include a correction of the E-to-B leakage. Since the E-to-B leakage is powerspectrum-method dependent, it might be more "stable" to use the mean of the bandpowers. Here we check that the effect is anyway negligible.

3. Tables.

Note that here we report the white noise level in terms of map depth, i.e. the square root of the usual noise level in [\(\mu K^2\)] divided by \(\Omega_{\rm pix}\), as defined in this posting.

4. Table for sims.

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.
We use the fiducial \(\ell_c\) here, as was used for the DC4 numbers.
Note that we obtain map depth at 150 GHz that are only roughly twice higher than, say, DC4 155 GHz. Note again that this is for a \(f_{\rm sky}\) of roughly 1% whereas the DC4 numbers are for 3%.
Note that we used the same fractional bandwidth as in DC4 or 5: 0.22 for 150 and 220GHz, and 0.24 for 95GHz.

The parameter file can be downloaded here.