# R-forecasting: high and low ell coordination

On this page we discuss and provide links for coordinating the optimization between high and low ell surveys.

Summary of plan:

**Delensing:**

Colin H. ran his foreground-cleaning code for the following cases:

fsky = [0.03, 0.05, 0.1, 0.15, 0.2, 0.3, 0.4]

Ndet_highres = 40k, 70k, 100k, 200k, 300k, 500k, 1000k

where we assume observing is for 5 years (so multiply by 5 to get detector-years). He produces Nl^BB and Nl^EE for each case. Here is a summary of the procedure:

The goal of the analysis is to optimize frequency channels (given an fsky value) for the detection of C_ell^kk via the EB estimator. There are eight possible frequency channels: 27/39/90/150/155/220/230/270 GHz. The telescope dish size is fixed to 5 m (if it were increased to 6 m, the overall S/N would improve but I suspect the frequency optimization would not change). The sky fractions considered are listed above. The maximum polarization multipole used is ell_max = 5000. The per-band sensitivity calculation includes a 20% efficiency factor that accounts for data cuts and calendar-year cuts, based on achieved ACT data. The sky model consists of:

- polarized Galactic dust

- polarized Galactic synchrotron (including a dust-correlated component)

- polarized Poisson radio point sources (amplitude matching Erminia/Dan's work in the N_eff forecasting)

- atmospheric noise, following Matthew Hasselfield's model (assumed frequency-independent, which is pessimistic)

- CMB (r=0)

The amplitudes of the dust and synchrotron components are assumed to follow a toy scaling \propto sqrt(fsky), with the values at fsky=0.01 set to the BICEP region amplitudes. In tests where the amplitudes are held fixed, the optimization results do not change much, since the EB estimator is getting most of its S/N from an ell-range where the instrumental noise is dominant. Note that I maintain EE/BB = 2 in the model.

For every Ndet/fsky/frequency-channel-arrangement option, I run a harmonic-space ILC calculation that simultaneously satisfies the following criteria at each multipole:

- unit response to CMB blackbody SED

- zero response to a fiducial polarized dust SED

- zero response to a fiducial polarized synchrotron SED

- minimum variance

The explicit "deprojection" of polarized dust and synchrotron is important: if one only imposes minimum variance, then these components are faint enough at high ell that the ILC simply minimizes instrumental noise. In that case, the C_ell^kk optimization trivially prefers all the detectors at the primary CMB channel (90 or 150), since these have the lowest instrumental noise levels. However, we are worried about small residuals from these foregrounds in the lensing reconstruction, so we will want to remove them as best as possible, at the price of increased instrumental noise in the final map. (Similarly, the SMICA map used in Planck lensing reconstruction does not deproject tSZ, and is susceptible to reconstruction biases due to tSZ (which are instead handled by masking clusters); if this had been explicitly deprojected, the SMICA map noise would increase somewhat, but the susceptibility to the tSZ bias would be greatly reduced/eliminated with no need for masking.)

The final outcome is a post-component separation noise curve for the EE and BB power spectra, N_ell^EE and N_ell^BB, respectively. The optimal noise curves for each fsky and Ndet option are provided in the tar file linked below. The columns within each file are [ell] [N_ell], where the latter is in units of uK^2, with no factors of ell*(ell+1) etc.

The post-component separation N_ell files are here (for 40k, 70k, 100k, 200k, 300k, 500k, 1000k):

I have also included a separate set of files containing the per-band sensitivities [uK-arcmin] obtained by the optimization for each fsky/Ndet option. The columns in these files are [frequency] [noise] [FWHM], in units of GHz, uK-arcmin, and arcmin, respectively. For cases where some frequency channels are not included in the optimal configuration, those channels have noise values >10^8 uK-arcmin in these files, so should be easy to identify and discard.

The channel sensitivity files are here (for 40k, 70k, 100k, 200k, 300k, 500k, 1000k):

Victor is set up to turn those curves into delensing fractions.

**Low-res survey:**

Victor then runs his code for the following fsky fractions and Ndet.

fsky = [0.03, 0.05, 0.1, 0.15, 0.2, 0.3, 0.4]

Ndet_lowres = 40k, 70k, 100k, 200k, 300k, 500k, 1000k

That will mean calculating his cov mat for each case above, and then exploring combinations with delensing fractions from Colin's curves.

We will end up with a set of combinations of fsky, Ndet_low, and Net_high that reaches the S4 sigma(r) target. Of those, we will identify the ones where Ntot=Ndet_lowres + Net_highres is minimized.