# Characterization of simulations for configurations 30-33

## Contents

## Noise characterization

To characterize the noise properties of the simulations, we provide a plot for each configuration comparing the average of the noise spectra obtained from the simulations with the expectation based on the input noise model.

In addition to the expected average, we can also predict the scatter we expect analytically. For each configuration, we show a plot comparing the predicted standard deviation for the noise spectra with that obtained from the simulations.

Finally, we show sample realizations of the noise maps for the Stokes Q parameter for the different frequency bands.

The theoretical expectation and simulations typically agree to within a few per cent. The lowest bin is an exception and (just like in the data challenge simulations) the noise estimated from the simulations exceeds the theory curve by as much as 20 per cent. This is caused by the prescription used here (and in the community more generally) to generate the apodized noise maps, which assumes that reweighting pixels by Nobs leaves the power spectrum unchanged. This assumption fails as on scales that approach scales on which the hits map varies. This could be corrected but has not been done here.

### Configuration 30

#### Comparison of simulation average with noise model

#### Comparison of noise variance with expectation based on noise model and weight map

### Configuration 31

#### Comparison of simulation average with noise model

#### Comparison of noise variance with expectation based on noise model and weight map

### Configuration 32

#### Comparison of simulation average with noise model

#### Comparison of noise variance with expectation based on noise model and weight map

### Configuration 33

#### Comparison of simulation average with noise model

#### Comparison of noise variance with expectation based on noise model and weight map

## Sample noise realizations

### Configuration 30

#### Noise realization 0001

#### Noise realization 0002

### Configuration 31

#### Noise realization 0001

#### Noise realization 0002

### Configuration 32

#### Noise realization 0001

#### Noise realization 0002

### Configuration 33

#### Noise realization 0001

#### Noise realization 0002

## CMB characterization

Here we provide plots comparing the CMB power spectra measured from the CMB maps to the theory prediction. The average of measured auto spectra is shown as points, the theoretical prediction is shown in the form of circles. This serves a dual purpose. On the one hand it shows that the simulations have AL=0.082 as desired. On the other hand it shows that the estimator is unbiased over the range of multipoles relevant for the B-mode search with CMB-S4. For the multipole range around the recombination peak, this is true even at the level of precision of 1000 simulations. For multipoles larger than 230 the 1000 simulations allow to detect a bias, but it remains small compared to cosmic variance.