\(N_l\) spectra for the CMB-S4 data challenge, and updated \(\sigma_r\) checkpoints

 (Victor Buza)

Updated 2017-01-31 to include the new \(\sigma_r\) checkpoints that switch to the \(f_{sky}=3\%\) baseline, and take into account the slight updates to the bandpasses and NET's as well as turn dust decorrelation on.

This posting presents the \(N_l\) spectra to be used for Phase 1 of the CMB-S4 data challenge. These spectra are based on the exact same noise specifications that went into the calculations and results presented in the CMB S4 Science Book Chapter 2. The documentation and evolution of these specifications have been layed out through multiple postings on the CMB S4 wiki. Below is a useful historical recap:

1. Experiment Specification and \(N_l\) fitting

In this posting I do the following things:

A few things to keep in mind:

As mentioned in the posting above, the effort distributions in the tables below were calculated given an optimized solution for a minimal \(\sigma_r\), taking into account contributions from foregrounds and CMB lensing. The assumed unit of effort is equivalent to 500 det-yrs at 150 GHz. For other channels, the number of detectors is calculated as \(n_{det,150}\times \left(\frac{\nu}{150}\right)^2\), i.e. assuming comparable focal plane area. A conversion between the (150 equivalent) number of det-yrs and (actual) number of det-yrs is given for each band. This is just one way to implement a detector cost-function, and other suggestions are welcomed.

Table 1:
Case: \(r=0\), Total effort: \(10^6\) det-yrs (150 equiv)

Note: Given the assumed level of foreground complexity, the fully optimal solution presented in this posting does not necessarily divide effort among all of the eight bands. To combat this, an equal force split among bands in each atmospheric window has been implemented. You will notice an equal amount of 150 equiv det-yrs being assigned to each of the two bands in each of the atmospheric windows. This effect introduces deviations from the optimal solution which are discussed in the posting linked above. All map-depths are quoted for (Q or U, E or B) polarization.

In addition to the numbers in the tables, I also provide the full \(N_{l,\{BB,EE,TT\}}\), \(\mu K_{CMB}^2\) to which I fit -- {Nl(BB), r=0, fsky=3%}, {Nl(EE), r=0, fsky=3%}, {Nl(TT), r=0, fsky=3%}. And the actual fits, linked in the headers below.
\(f_{sky}=0.03\)Analytic Fitting parameters (BB)Analytic Fitting parameters (EE)Analytic Fitting parameters (TT)
\(\nu\),GHz# det-yrs
(150 equiv)
# det-yrs
FWHM, arcmin \(\sigma_{map}\),
\(\mu K\)-arcmin
\(l_{knee}\) \(\gamma\) \(\sigma_{map}\),
\(\mu K\)-arcmin
\(l_{knee}\) \(\gamma\) \(\sigma_{map}\),
\(\mu K\)-arcmin
\(l_{knee}\) \(\gamma\)
30 27,500 1,100 76.6 10.59 50 -2.0 10.85 50 -2.0 12.97 175 -4.1
40 27,500 1,960 57.5 10.79 50 -2.0 11.06 50 -2.0 13.22 175 -4.1
85 201,250 64,620 27.0 1.88 50 -2.0 1.93 50 -2.0 2.30 175 -4.1
95 201,250 80,720 24.2 1.54 50 -2.0 1.58 50 -2.0 1.89 175 -4.1
145 68,750 64,420 15.9 2.38 60 -3.0 2.49 65 -3.0 5.31 230 -3.8
155 68,750 73,410 14.8 2.45 60 -3.0 2.56 65 -3.0 5.48 230 -3.8
215 56,250 115,560 10.7 5.30 60 -3.0 5.55 65 -3.0 11.86 230 -3.8
270 56,250 182,250 8.5 7.93 60 -3.0 8.30 65 -3.0 17.72 230 -3.8
Total Degree Scale Effort 707,500 583,870
Total Arcmin Scale Effort 292,500 273,325
Total Effort 1,000,000 857,190

2. Using our full framework to arrive at updated \(\sigma_r\) checkpoints

This section is the updated equivalent of Sections 2 of the 2016 May 13: σ(r) forecasting checkpoints and 2016 June 3: σ(r) forecasting checkpoints, V2 postings. The updates consist in switching to the \(f_{sky}=3\%\) baseline, turning dust decorrelation on, and using the slightly updated bandpasses and NET's described in Colin's November 4th posting.

As before, in this section I use fully descriptive BPCM's, and the assumptions below, as inputs to the Fisher Forecasting framework, to arrive at \(\sigma_r\) constraints. However, the \(N_l\) files above should be compatible with the used BPCM's.

Table 2:
I marginalize over the fully dimensional Fisher Matrix to arrive at the following \(\sigma_r\) results. Using the total arcminute scale effort specified in the table above, and our assumptions about delensing (found in Section 1 of the June 3rd posting), one can calculate that it corresponds to \(A_L=0.10\) , i.e. 90% of the lensing power is removed; \(A_L=1\) stands for no-delensing included, and \(A_L=0\) stands for perfect delensing.

\(f_{sky}=0.03\)CMB-S4 BookUpdated
\(\sigma_r(r=0, A_L=0), \times 10^{-3}\)0.580.61
\(\sigma_r(r=0, A_L=0.1), \times 10^{-3}\)0.870.91
\(\sigma_r(r=0, A_L=1), \times 10^{-3}\)3.783.82