Performance-based Fisher optimization for CMB-S4, v3

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.

• For this particular example I assume nine S4 channels: {20, 30, 40, 85, 95, 145, 155, 215, 270} GHz, two WMAP channels: {23, 33} GHz and seven Planck channels: {30, 44, 70,100, 143, 217, 353} GHz.


• This example assumes 0.5m apertures, and scales the beams accordingly. Note: This is not true for the 20 GHz channel, which assumes a beam equivalent to the beam at 30 GHz (i.e we assume that the aperture scales by the required amount to keep the beam fixed to the one at 30).


• 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. The projections run out to a total of 3,000,000 det-yrs (3,000,000 det-yrs, if all at 150 GHz, would be equivalent to 500,000 detectors operating for 6 yrs -- this seems like a comfortable upper bound for what might be conceivable for S4. S4 scale surveys seem likely to be in the range of \(10^6\) to \(2.5\times10^6\) det-yrs).


• I first want to emphasize that the NET numbers that follow are only used to determine the scalings between different channels, and NOT to calculate sensitivities. All sensitivities are based on achieved performance. The ideal NET's per detector are assumed to be {214, 177, 224, 270, 238, 309, 331, 747, 1281} \(\mu\mathrm{K}_\mathrm{CMB} \sqrt{s}\). This is the last column of the table in the Band Definition posting. Note: These updated NET's are calculated for a 100mK bath, as opposed to 250mK before, and are therefore lower than before.


• The BPWF's, ell-binning, and ell-range are assumed to be l=[30,330]; yielding 9 bins with nominal centers at ell of {37.5, 72.5, 107.5, 142.5, 177.5, 212.5, 247.5, 282.5, 317.5}.


• The Fiducial Model for the Fisher forecasting is centered at \(r\) of 0, with \(A_{dust} = 4.25\) (best-fit value from BK14) and \(A_{sync}=3.8\) (95% upper limit from BK14). The spatial and frequency spectral indeces are centered at \(\beta_{dust}=1.59, \beta_{sync}=-3.10, \alpha_{dust}=-0.42, \alpha_{sync}=-0.6\), and the dust/sync correlation is centered at \(\epsilon=0\). I also introduce \(\delta_{dust}\) -- a dust decorrelation parameter (that is always ON), and \(\delta_{sync}\) -- a sync decorrelation parameter (that is always ON). The dust decorrelation parametrization is exactly as described in Section 5 of the initial optimization posting. The synchrotron decorrelation parameter is being introduced here for the first time, and has the same frequency and spatial form as the dust decorrelation parameter, but is normalized at (23GHz, 33GHz, l=80). While this parameter is let to freely vary in the Fisher optimization, I do center it at zero, given that we have no good information on this value.


• The Fisher matrix is 10-dimensional. The 10 parameters we are constraining are: {\(r, A_{dust}, \beta_{dust}, \alpha_{dust}, A_{sync}, \beta_{sync}, \alpha_{sync}, \epsilon, \delta_{dust}, \delta_{sync}\)}. Where \(\beta_{dust}\) and \(\beta_{sync}\) have Gaussian priors of \(0.11, 0.30\), and the rest have flat priors.


• As before, I implement delensing as an extra band in the optimization. See the description underneath Table 1 in this posting for a more in depth description on how this is done.

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.

• Optimal path Does not force any band-splitting; it purely shows the most optimal path.


• Split path Sums up all the effort in each atmospheric window, and then makes sure the amount of effort in each band (within an atmospheric window) is equivalent. (Note: the top left panel might have overlapping lines because of this; easiest to look on the top right panel). The delensing effort is included in the total effort similarly to the Optimal Path.