Background on 20 GHz channel

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This posting summarizes the analyses that led to the decision to move the 20 GHz channel from the SATs to the delensing LAT.


During the CDT studies, we noticed a bias on r for one of the foreground models for the configuration under study at the time. The configuration was not designated with an official data challenge number. It can either be thought of as the configuration obtained from configuration 02 by rescaling by a factor sqrt(7/6), or equivalently as configuration 04 but with a 20 GHz channel on the SATs rather than the delensing LAT. For completeness, here is the performance table for a 4-year survey

Frequency (GHz) 20 30 40 85 95 145 155 220 270
Beam FWHM (arcmin) 76.6 76.6 57.5 27.0 24.2 15.9 14.8 10.7 8.5
white noise level TT (uK-arcmin) 16.66 10.62 10.07 2.01 1.59 4.53 4.53 11.61 15.84
ell knee TT 500 175 175 175 175 230 230 230 230
1/f exponent TT -4.1 -4.1 -4.1 -4.1 -4.1 -3.8 -3.8 -3.8 -3.8
white noise level EE (uK-arcmin) 13.94 8.88 8.42 1.67 1.32 2.12 2.12 5.43 7.42
ell knee EE 200 50 50 50 50 65 65 65 65
1/f exponent EE -2.0 -2.0 -2.0 -2.0 -2.0 -3.0 -3.0 -3.0 -3.0
white noise level BB (uK-arcmin) 13.6 8.67 8.22 1.64 1.30 2.03 2.03 5.19 7.08
ell knee BB 200 50 50 50 50 60 60 60 60
1/f exponent BB -2.0 -2.0 -2.0 -2.0 -2.0 -3.0 -3.0 -3.0 -3.0
ell min 30 30 30 30 30 30 30 30 30
nside 512 512 512 512 512 512 512 512 512

The foreground model that first displayed the bias was model 06, which is based on MHD simulations of the ISM.

Closer inspection of the ILC results revealed that the bias was caused by synchrotron residuals in bins 4-6. This can be seen in the figure below. The blue points and error bars indicate the ILC spectrum, red and green data points show the synchrotron and dust residuals, respectively. The uncertainties are derived from 1000 simulations.

11.06 ILC.png

The bias was subsequently confirmed with a second MHD-based foreground model with a somewhat different model of synchrotron emission.

A comparison of the noise and synchrotron power spectra for this configuration at 20 GHz suggests that this is caused by the large beam at low frequencies and the associated drop in the signal-to-noise ratio on the synchrotron template

Cl Nl 20GHz.png11.06 S-N 20GHz.png

The analogous plots for the higher frequency channels show that the increase in resolution at 40 GHz at the noise levels considered is insufficient to compensate for the rapid drop of synchrotron emission with frequency.

Compensating for this through an increase in the number of detectors appeared challenging, which motivated a study of the bias as a function of beam size and sensitivity at low frequency.

The idea was put forward to have 20 GHz detectors on the delensing LAT instead of the SAT, which solved this problem. The noise is subdominant compared to the signal over the full range of multipoles of interest to the gravitational wave search.

Cl Nl 20GHz LAT.pngS-N 20GHz LAT.png

The biases for the two configurations were

Bias (no marginalization) Bias (with marginalization)
20 GHz on SAT 4.1e-4 1.1e-4
20 GHz on LAT 1.4e-4 0.1e-4

The marginalization over residual foregrounds relies on assumptions about the scale dependence of synchrotron emission, and it may be dangerous to rely on an extrapolation in unknown foreground properties when claiming a detection of primordial gravitational waves. So below I will quote numbers only without marginalization over residual foregrounds.

A range of configurations and foreground models were studied. I will show what I consider the most relevant subset which varies the resolution at 20 GHz. All parameters other than the resolution at 20 GHz are as in the performance table above, in particular lknee at 20 GHz was taken to be 200 throughout.

Because the synchrotron spectrum in foreground model 06 is harder than expected at high latitude, I will quote results for foreground model 08, which is an MHD-based model with energy spectrum for relativistic electrons informed by PAMELA for which the synchrotron spectrum is consistent with expectations based on WMAP.

For a 4-year survey, and foreground model 08, the biases without marginalization over residual foregrounds (assumptions about the scale dependence of the synchrotron spectrum) are

Beam FWHM @ 20 GHz Bias
76.6 2.8e-4
60.0 2.1e-4
45.0 1.5e-4
30.0 1.2e-4
15.0 1.0e-4
11.0 1.0e-4