This posting presents the \(N_l\) spectra to be used for Phase 2 of the CMB-S4 data challenge and is the analogue of this posting for Phase 1. These noise spectra are based on the most recent optimization, which includes extra low frequency bands. The documentation and evolution of these specifications have been layed out through multiple postings on the CMB S4 wiki. Below is a useful historical recap that builds on the posting linked above (for Phase1), and includes work from many people:

- 2016 December 20: N_ell spectra for the CMB-S4 data challenge, and updated σ(r) checkpoints
- 2017 January 12: Maps for CMB-S4 data challenge 1
- 2017 January 30: Aliased power in noise maps
- 2017 February 24: BK-Style processing of DC1 maps to spectra
- 2017 March 17: S4 DC1.0 analysis
- 2017 March 20: CMBS4 Band sensitivity comparison follow-up
- 2017 March 23: 01.00 sim input maps
- 2017 March 27: 01.01 sim input maps - first try
- 2017 March 28: Adding higher res delensing "band"
- 2017 March 29: CMB-S4 frequency bands v1.99
- 2017 April 04: Updated Performance-based Fisher optimization for CMB-S4
- 2017 March 31: Data Challenge analysis - DC1.0, DC1.1, DC1.2
- 2017 April 04: Updated Performance-based Fisher optimization for CMB-S4
- 2017 April 18: BK-style power spectra for 1000 realizations of v01.00–02 CMB-S4 simulation maps
- 2017 May 8: Checking PySM maps
- 2017 May 15: Rev 2 PySM a2d4f1s3 maps

In this posting I do the following things:

- As before, I present the actual \(N_l\)'s that went into the forecasts (interpolated on \(l=[30,320]\)), and I'm providing noise fit parameters so that they directly match the \(N_l\)'s rather than following some map-depth prescription (that, for instance, conserves survey weight; as was done in Table 2 of the June 3rd posting). In order to offer Clem simple to use analytic \(N_l\)'s for {TT,EE,BB} for making noise maps, I parametrize the noise as follows: \[ N_{l,fit} = \frac{l(l+1)}{2\pi}\frac{\Omega_{pix}}{B_l^2}\left(1+\left(\frac{l}{l_{knee}}\right)^\gamma\right)\sigma_{map}^2 \] and fit for {\(\sigma_{map}\), \(\gamma\), \(l_{knee}\)}. Above, \(B^2_{l} = \exp(-\frac{l(l+1)\theta^2}{8log(2)})\), and \(\theta\) is the FWHM (in radians) of the Gaussian beam, \(\Omega_{pix}=4\pi\)/(# square arminutes on the sky), and \(\sigma_{map}\) is the map-noise in \(\mu K\)-arcmin.

- As mentioned in the March 31st posting, all the scalings are done from achieved BK performances. For frequencies at which we currently do not have data, we scale from the closest frequency that we have an achieved survey weight for, as that is the performance that should guide us. Prior to the CMB-S4 science book, we had a reasonably accurate measurement of our 220 GHz survey weight, but not of the 220 GHz \(N_l\)'s; hence, for the 215 and 270 channels, we assume noise properties similar to BK_150, while scaling from the BK_220 survey weight. This effectively means that we need to parametrize two noise spectra: BK_95 and BK_150. You will see that the table below reflects that.
- Given that TT and EE were not used in the forecasts for Chapter 2 of the S4 Sciencebook, nor in the most recent optimization, there are no direct calculations of the scalings that take us from BK to S4. Here, for TT and EE, I apply the same noise scalings that were applied to BK BB spectra.

As mentioned in the posting above, the effort distributions in the tables below were calculated given an optimized solution for a minimal \(\sigma_r\), taking into account contributions from foregrounds and CMB lensing. 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. A conversion between the (150 equivalent) number of det-yrs and (actual) number of det-yrs is given for each band. This is just one way to implement a detector cost-function, and other suggestions are welcomed.

\(f_{sky}=0.03\) | Analytic Fitting parameters (BB) | Analytic Fitting parameters (EE) | Analytic Fitting parameters (TT) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

\(\nu\),GHz | # det-yrs (150 equiv) | # det-yrs (actual) | FWHM, arcmin | \(\sigma_{map}\), \(\mu K\)-arcmin | \(l_{knee}\) | \(\gamma\) | \(\sigma_{map}\), \(\mu K\)-arcmin | \(l_{knee}\) | \(\gamma\) | \(\sigma_{map}\), \(\mu K\)-arcmin | \(l_{knee}\) | \(\gamma\) |

20 | 30,000 | 533 | 76.6 | 14.69 | 50 | -2.0 | 15.06 | 50 | -2.0 | 17.99 | 175 | -4.1 |

30 | 22,500 | 900 | 76.6 | 9.36 | 50 | -2.0 | 9.59 | 50 | -2.0 | 11.47 | 175 | -4.1 |

40 | 22,500 | 1,600 | 57.5 | 8.88 | 50 | -2.0 | 9.10 | 50 | -2.0 | 10.88 | 175 | -4.1 |

85 | 182,500 | 58,600 | 27.0 | 1.77 | 50 | -2.0 | 1.81 | 50 | -2.0 | 2.17 | 175 | -4.1 |

95 | 182,500 | 73,200 | 24.2 | 1.40 | 50 | -2.0 | 1.43 | 50 | -2.0 | 1.72 | 175 | -4.1 |

145 | 67,500 | 63,075 | 15.9 | 2.19 | 60 | -3.0 | 2.29 | 65 | -3.0 | 4.89 | 230 | -3.8 |

155 | 67,500 | 72,075 | 14.8 | 2.19 | 60 | -3.0 | 2.29 | 65 | -3.0 | 4.89 | 230 | -3.8 |

220 | 57,500 | 118,130 | 10.7 | 5.61 | 60 | -3.0 | 5.87 | 65 | -3.0 | 12.54 | 230 | -3.8 |

270 | 57,500 | 186,300 | 8.5 | 7.65 | 60 | -3.0 | 8.01 | 65 | -3.0 | 17.11 | 230 | -3.8 |

Total Degree Scale Effort | 690,000 | 574,420 | ||||||||||

Total Arcmin Scale Effort | 310,000 | 289,680 | ||||||||||

Total Effort | 1,000,000 | 864,100 |