# BK-style power spectra of 04/04b/04c/04d masks (adding BK14 mask)

— C. Pryke

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## Final pager

This posting follows from 20180925_bkfinal_04bc and simply adds results for mask 04d which is the BK14 mask. This is the mask for the BK14 results from which we are extrapolating in all of our "scaling from achieved performance" S4 calculations. We may be able to get insight from these as to whether the various extrapolations are behaving as we expect.

The situation is actually a little bit complicated. Victor took the BK14 bandpower covariance matrix and scaled it to a) increase the number of detector years, and b) change the effective sky area from BK14 (nominal 1%) to the circular 04 hit pattern (assumed to be 3%?). Noise spectra were taken from this and written into the 04/params.dat file. Full sky noise realizations were then generated with an additional scaling such that when the noise is blown up around the edge by 1/sqrt(hits) and then the map is re-analyzed with the hit pattern as apodization mask one recovers exactly the uK-arcmin in the params.dat file. This amounts to making the noise a little lower in the center of the map so that the "effective noise post apodization" is the desired level.

For the 04b (Chile) and 04c (BICEP2 2017) masks I then re-used these full sky noise realizations and simply blew up the noise according to 1/sqrt(hits) using the different hit patterns post normalization to have the same total number of hits. This step seems perfectly correct in terms of preserving the same amount of experimental effort and just re-deploying it on the sky in a different hit pattern.

For this latest 04d mask (BK14) I have done the same thing as for 04b and 04c - just redeployed the hits - in this case back to the BK14 pattern we started with.

So if all these steps were valid then the $$\sigma(r)$$ results from 04d will agree with BK14 scaled simply by detector-year effort ratios using Victor's Fisher code.

 Figure 1 Final Pager

### Legend for first half of the "Figure types":

• Thick red : lensed-ΛCDM scalars
• Thick black : Real data
• Colored : lensed-ΛCDM + noise + foreground realizations

### Legend for second half of the "Figure types":

#### spectra

• thick red : lensed-ΛCDM
• thin gray : s+n+f simulations with lensed-ΛCDM (sim type 5) and foregrounds (sim type 3) as signal, debiased with noise (sim type 6)
• thick gray : mean of sims (thin gray)
• red points with blue error bars : real data, debiased with the noise, uncertainties from the spread of the s+n+f sims (thin gray)

#### bp devs

• thin gray : s+n+f sims
• thin red : 1 sigma contours
• thin green : 2 sigma contours
• thick black + markers : real data
• red markers : bins that go into chi2 analysis

Note: The contours mark the simulated bandpower in each bin closest to the respective percentile.

#### chi2

• red vertical : real data
• blue : distribution from s+n+f sims
• green : chi2 probability distribution fitted to blue

#### sum bp devs

• red vertical : real data
• blue : distribution from s+n+f sims

#### uncertainties

• red : std of s+n+f sims
• blue : std of noise-only sims

Note: Remember that bandpower is a variance. Hence bandpower error bar is the std of a variance. This means noise and sample fluctuation components straight add, no quadrature — i.e. the difference between blue and red is the signal fluctatution component.

### Linked previous postings

[expt_defn]
CMB-S4 Data Challenge Experiment Definitions
[20170411_bkfinal_01.00]
BK-style power spectra for 1000 realizations of v01.00–02 CMB-S4 simulation maps (J. Willmert, C. Bischoff, V. Buza)