Performance-based Fisher optimization for CMB-S4, v3

 (Victor Buza)

This posting is in the style of the v2 optimization posting, which lead to the definition of the noise spectra that in turn were used to define Data Challenge 2.0. In this posting I try to update the previous optimization with the most up to date baseline that most recently appeared in the CDT report. The difference between v2 and v3 is the lack of 10/15 GHz channels, and the improved optimization resolution.

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 0:
Numbers corresponding to the v2 Optimization for DC2.0

\(f_{sky}\)Type of det-yrsEffort in the following channelTotal Effort
\(10\)\(15\)\(20\)\(30\)\(40\) \(85\) \(95\) \(145\) \(155\) \(220\) \(270\) \(DL\)
0.03 150 GHz Equivalent 1.7k 1.7k1.7k 25.0k 25.0k 187.5k 187.5k 67.5k 67.5k 57.5k 57.7k320k 1000k
Actual 8 16 30 1.0k 1.8k 60.2k 75.2k 63.0k 72.0k 118.1k 186.3k 299.0k 882k
Actual (1/4) 2 4 8 250 450 15.0k 18.8k 15.8k 18.0k 29.5k 46.6k 74.8k 220.5k

Table 1:
Numbers corresponding to this \(N_l\) posting for DC2.0.

Going from the previous table to this one we had decided to drop the 10 and 15 GHz channels, and up the percentage of effort in this lower window from 0.5% to 3.0%. This of course deviated from the optimal path, and necessitated that some channels get slightly less effort (in particular 30/40, 85/95, and DL).

\(f_{sky}\)Type of det-yrsEffort in the following channelTotal Effort
\(20\)\(30\)\(40\) \(85\) \(95\) \(145\) \(155\) \(220\) \(270\) \(DL\)
0.03 150 GHz Equivalent 30.0k 22.5k 22.5k 182.5k 182.5k 67.5k 67.5k 57.5k 57.7k310k 1000k
Actual 530 900 1.6k 58.6k 73.2k 63.0k 72.0k 118.1k 186.3k 289.7k 864k
Actual (1/4) 130 225 400 14.7k 18.3k 31.5k 18.0k 29.5k 46.6k 72.4k 216k

Table 2:
For the CDT report, it was decided that slightly more effort was necessary in order to achieve the desired science goal. Instead of re-optimizing, it was decided to simply scale the Table 1 numbers by \(\sqrt{7/6}\) (except the 20 GHz channel). The numbers in this table correspond to the numbers in the CDT report.
\(f_{sky}\)Type of det-yrsEffort in the following channelTotal Effort
\(20\)\(30\)\(40\) \(85\) \(95\) \(145\) \(155\) \(220\) \(270\) \(DL\)
0.03 150 GHz Equivalent 30.0k 26.1k 26.1k 211.7k 211.7k 78.3k 78.3k 66.7k 66.7k359.6k 1160k
Actual 530 1040 1.9k 68.0k 84.0k 72.0k 84.0k 136.0k 216.0k 336.0k 1000k
Actual (1/4) 130 260 470 17.0k 21.0k 18.0k 21.0k 34.0k 54.0k 84.0k 250k

Table 3:
Updated Optimization numbers. Comparing to Table 2, we can see that the full optimization agrees perfectly with the scaled version in the 85/95 and 220/DL channels, while preferring slightly more effort in 30/40, 145/155, and slightly less effort in 270.
\(f_{sky}\)Type of det-yrsEffort in the following channelTotal Effort
\(20\)\(30\)\(40\) \(85\) \(95\) \(145\) \(155\) \(220\) \(270\) \(DL\)
0.03 150 GHz Equivalent 32.5k 37.5k 37.5k 208.7k 208.7k 85.0k 85.0k 62.5k 62.5k360.0k 1160k
Actual 580 1500 2.7k 67.0k 84.0k 79.0k 90.0k 134.0k 203.0k 336.0k 1000k
Actual (1/4) 145 375 670 17.0k 21.0k 20.0k 22.5k 34.0k 51.0k 84.0k 250k