# BK-style power spectra for 1000 realizations of v02.00–06 CMB-S4 simulation maps

— J. Willmert, C. Bischoff, V. Buza

Updated: 2017 Aug 14 — Added 02.03 and 02.04
Updated: 2017 Sep 08 — Added 02.05 and 02.06

## Final pager

The power spectra presented here are analyzed from the input HEALPix maps using the S2HAT and PS2HAT libraries (see also arXiv:0903.2350). Custom MATLAB mex bindings interface to the (P)S2HAT library and permit us to finishing processing using the MATLAB pipeline used for standard BICEP/Keck analysis (i.e. our FFT steps are replaced with (P)S2HAT, but debiasing, suppression factor correction, etc follow the same code path as used in BK analysis; see for example arXiv:1403.3985 and arXiv:1603.05976 for more details on the BK pipeline).

Short summary of processing details:

• This posting makes use of and presents the 02.00, 02.01, and 02.02 maps as discussed in Experiment Definitions. 1000 realizations of noise and (variable $$A_L$$) lensed-ΛCDM + noise + foregrounds (aka combined) input maps have been processed to power spectra.
• No E-to-B leakage debias has been applied. The use of the PS2HAT library minimizes leakage such that this should be unnecessary (and no unlensed-ΛCDM sims were processed from which the debias would normally be taken).
• Suppression factors (from the beam function and any algorithmic/processing losses) are computed from so-called “direct BPWFs” for each frequency band. The cross-frequency BPWFs are assumed to be the geometric mean of the auto-frequency BPWFs. See BK-VII §7.3 for a complete description of the method.
• The “real” data points are just realization 0 of the combined maps data set.
 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.