Updated Performance-based Fisher optimization for CMB-S4

 (Victor Buza)
Updated 2017-04-21: Added "Split" path option; Added "fsky=0.01" option; Added "Window 0-4" option; Added summary table.

As we are gearing up for increasingly more complex data challenges, we want to expand the set of available frequencies in order to explore any potential benefit to parameter constraints. As with DC1.0, the next version of the data challenge maps need to be informed by a thorough performance-based optimization (for the small S4 survey, this is an optimization over \(\sigma_r\)).

On March 31st 2017, the Forecasting group had agreed on new band definitions which have been documented in this posting.

In this posting I optimize for \(\sigma_r\) given these new band definitions. The framework that I use is entirely equivalent to the perfromance based framework described in this posting, which was used for the Science Book Inflation forecasts.

1. Worked-out Example; Experiment Specification

Below, similar to Section 2 and 3 of the posting linked above, I present an application of this framework to an optimization grounded in achieved performance.

2. Parameter Constraints; \(\sigma_r\) performance

Figure 1:

(Top, Left) Optimal path indicating the total number of det-yrs, and the individual distribution of det-yrs at each point.
(Top, Right) Individual map depths for every channel, in \(\mu K\)-arcmin. Calculated from the accumulated weights in each channel, scaled from achieved performances.
(Bottom, Left) Ratio of the total effort that is spent on delensing, as a function of total effort, and the effective RMS lensing residual as a function of total effort.
(Bottom, Right) Resulting \(\sigma(r)\) constraints for each level of delensing.

Table 1:
This table offers a summary of the pager above for the Sync Decorrelation "On" setting, at 1M det-yrs (150 equiv).

One can note that the inclusion of Window 0 sees the formal optimal solution change by dedicating some effort to Window 0, and at the same time changing the effort distribution in the other Widdows. Including Window 0 improves \(\sigma_r\) by roughly 20% in almost all cases.
\(f_{sky}\)Windows IncludedEffort in \(\sigma_r\) (\(\times 10^{-3}\))Effective \(A_L\)Path
\(W_0\)\(W_1\)\(W_2\) \(W_3\) \(W_4\) \(W_{DL}\)
0.01 W0-4 1.0% 10.0% 31.5% 13.5% 8.75% 35.25% 0.56 0.048 Optimal
0.60 0.048 Split
W1-4 --- 11.25% 29.0% 19.0% 11.25% 30.0% 0.69 0.052 Optimal
0.71 0.052 Split
0.03 W0-4 0.5% 5.0% 37.5% 13.5% 11.5% 32.0% 0.65 0.088 Optimal
0.70 0.088 Split
W1-4 --- 11.25% 34.75% 16.0% 11.5% 27.0% 0.79 0.096 Optimal
0.84 0.096 Split
0.10 W0-4 3.0% 2.5% 41.5% 15.0% 11.5% 26.5% 0.78 0.18 Optimal
0.86 0.18 Split
W1-4 --- 8.5% 39.0% 15.0% 14.0% 23.5% 0.95 0.19 Optimal
1.05 0.19 Split

3. To come soon: