# WAFTT results part 2

## Contents

### Observing schedules

This posting relies on the same observing schedules described by Reijo in the earlier posting Noise models and sky fractions for WAFTT.

### Depth Maps

The hits maps "without elevation penalty" provided by Reijo were converted to depth maps as described in Noise models and sky fractions for WAFTT. The depth maps here differ from the depth maps in Noise models and sky fractions for WAFTT in atmospheric model.

The depth maps can be found on NERSC, /global/cscratch1/sd/mhasse/cmb-s4/fskytaskforce/190311/:

- depth_el_min30.zip
- depth_el_min40.zip
- depth_el_min50.zip
- gal_masks_eq.zip (this archive contains Reijo's galactic masks, converted to same pixelization as the depth maps)

### Noise characteristics for minimum elevation of 50 degrees

Galactic cut (in %) | 0 | 10 | 20 | 30 | |
---|---|---|---|---|---|

Sky fraction (in %) | 57 | 52 | 45 | 39 | |

Effective sky fraction for noise (in %) | 52 | 47 | 41 | 35 | |

Effective sky fraction for signal (in %) | 47 | 43 | 37 | 32 |

Frequency (GHz) | 20 | 27 | 39 | 93 | 145 | 225 | 280 | |
---|---|---|---|---|---|---|---|---|

white noise level TT (uK-arcmin) | 51.9 | 17.5 | 9.7 | 1.6 | 1.7 | 5.3 | 12.7 | |

ell knee TT | 451 | 410 | 381 | 1254 | 4458 | 4370 | 4408 | |

1/f exponent TT (uK-arcmin) | -3.5 | -3.5 | -3.4 | -3.0 | -2.3 | -3.4 | -3.4 | |

white noise level E/B (uK-arcmin) | 73.3 | 24.8 | 13.7 | 2.3 | 2.4 | 7.5 | 17.9 | |

ell knee E/B | 700 | 467 | 467 | 467 | 467 | 467 | 467 | |

1/f exponent E/B (uK-arcmin) | -1.4 | -1.1 | -1.1 | -1.1 | -1.1 | -1.1 | -1.1 |

### Noise characteristics for minimum elevation of 40 degrees

Galactic cut (in %) | 0 | 10 | 20 | 30 | |
---|---|---|---|---|---|

Sky fraction (in %) | 68 | 63 | 55 | 48 | |

Effective sky fraction for noise (in %) | 63 | 58 | 51 | 44 | |

Effective sky fraction for signal (in %) | 59 | 54 | 47 | 41 |

Frequency (GHz) | 20 | 27 | 39 | 93 | 145 | 225 | 280 | |
---|---|---|---|---|---|---|---|---|

white noise level TT (uK-arcmin) | 58.1 | 19.6 | 11.0 | 1.8 | 1.9 | 6.1 | 14.6 | |

ell knee TT | 475 | 433 | 395 | 1315 | 4651 | 4511 | 4525 | |

1/f exponent TT (uK-arcmin) | -3.5 | -3.5 | -3.4 | -3.1 | -2.3 | -3.4 | -3.4 | |

white noise level E/B (uK-arcmin) | 82.2 | 27.7 | 15.5 | 2.6 | 2.7 | 8.6 | 20.6 | |

ell knee E/B | 700 | 467 | 467 | 467 | 467 | 467 | 467 | |

1/f exponent E/B (uK-arcmin) | -1.4 | -1.1 | -1.1 | -1.1 | -1.1 | -1.1 | -1.1 | |

White noise penalty (relative to f_sky scaling) | 1.00 | 1.00 | 1.00 | 1.00 | 1.01 | 1.03 | 1.04 |

### Noise characteristics for minimum elevation of 30 degrees

Galactic cut (in %) | 0 | 10 | 20 | 30 | |
---|---|---|---|---|---|

Sky fraction (in %) | 75 | 69 | 62 | 54 | |

Effective sky fraction for noise (in %) | 71 | 65 | 57 | 50 | |

Effective sky fraction for signal (in %) | 66 | 61 | 54 | 47 |

Frequency (GHz) | 20 | 27 | 39 | 93 | 145 | 225 | 280 | |
---|---|---|---|---|---|---|---|---|

white noise level TT (uK-arcmin) | 63.1 | 21.1 | 12.1 | 2.0 | 2.1 | 6.7 | 16.3 | |

ell knee TT | 502 | 458 | 410 | 1376 | 4820 | 4641 | 4632 | |

1/f exponent TT (uK-arcmin) | -3.5 | -3.4 | -3.4 | -3.1 | -2.3 | -3.4 | -3.4 | |

white noise level E/B (uK-arcmin) | 89.3 | 29.9 | 17.1 | 2.9 | 2.9 | 9.5 | 23.0 | |

ell knee E/B | 700 | 467 | 467 | 467 | 467 | 467 | 467 | |

1/f exponent E/B (uK-arcmin) | -1.4 | -1.1 | -1.1 | -1.1 | -1.1 | -1.1 | -1.1 | |

White noise penalty (relative to f_sky scaling) | 1.02 | 1.02 | 1.04 | 1.03 | 1.04 | 1.08 | 1.09 |

### Foreground model

### Forecast details

Here we will give the details of converting the numbers in the tables above to forecasts for light relic density N_{eff}. Many of the details are the same as in the previous iteration of WAFTT forecasting but are repeated here for clarity. The forecasts were done for LCDM+N_{eff}+M_{ν}, assuming BBN consistency to fix Y_{p}. TT, TE, EE, and φφ spectra were included, with the lensing reconstruction calculated using the minimum variance combination of quadratic estimators, including the improvement from iterative EB reconstruction. The small improvements which come from delensing T and E spectra (see https://arxiv.org/abs/1609.08143) were also included.

The TT and EE extragalactic foreground residuals and ILC noise curves were computed by Raphael using an extragalactic foreground model and point source removal provided by Kevin Huffenberger.

The S4-only ILC noise was combined with Planck, in an inverse variance sum, which is important to cover the low l temperature modes contaminated by the atmosphere for S4:

1 / N_{l}^{Planck+S4} = 1 / (N_{l}^{S4} + N_{l}^{Planck})

Contamination from extragalactic residuals was then added. For our purposes, these extragalactic foregrounds act much like an additional source of noise (modulo the correction from the beam). For example, point source residuals in TT affect the signal to noise of both TT and TE at high-l. Additionally, there is a cut imposed at l_{min} = 30, and we took l_{max} = 5000. A model for Planck temperature data was included for l < 30 on f_sky = 0.8.

The resulting noise curves were then used in a Fisher forecast to compute the errors. The sky fraction for S4 is shown in the tables above. Planck was assumed to cover an additional part of the sky, not observed by CMB-S4, i.e. f_{sky}^{Planck-only} = (1 - total S4 sky fraction) * (1 - galactic cut). The results for the forecasts are shown below.