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.

Background

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 limited resolution 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 then subdominant compared to the signal over the full range of multipoles of interest to the gravitational wave search.

Cl Nl 20GHz LAT 19.pngS-N 20GHz LAT 19.png

The biases for the two configurations derived from 1000 simulations 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

Any realistic analysis would include a marginalization over residual foregrounds, but it should be kept in mind that the this relies on assumptions about the scale dependence of synchrotron emission. Because it is dangerous to rely on an extrapolation in unknown foreground properties when claiming a detection of primordial gravitational waves, I will quote numbers only without marginalization over residual foregrounds. This provides a measure how well the maps can be cleaned without additional modeling.

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 one would expect, especially 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

For these noise levels, the point of diminishing return appears to be around 30 arcmin. Considering the ratio between synchrotron and noise power

S-N 20GHz 11-30 19.png

we approximately expect a ratio larger than 50 between synchrotron and noise power on the scales that causes the bias is required. An alternative route to estimate this is to compare the contribution of primordial B-modes with r=5e-4 to the synchrotron amplitude in the CMB bands. At l=150 and 95 GHz is expected to be ~57, so that a synchrotron rejection at this level or better is required for an unbiased measurement.

Any configuration that ensures this should successfully remove the bias. A natural question is whether the 30 and 40 GHz channels on the current delensing LAT configuration could be sufficient, especially given the higher sensitivity of the delensing LAT from recent studies for delensing. This plot

S-N-20-40GHz-V3R0.png

shows that it does not appear to be the case for the V3R0 configuration. It also shows that the signal-to-noise ratio on the synchrotron template is significantly higher with one 20 GHz tube than with two 30/40 GHz tubes. However, if 20 GHz detectors present a major technological challenge, it would be worth revisiting the low frequency sensitivity of the delensing LAT in more detail. For the V3R0 LF+ configuration the signal-to-noise ratio for a synchrotron spectral index of -3.1 begins to be comparable between 1 tube at 20 GHz and 4 at 30/40 GHz

S-N-20-40GHz-V3R0 LF+.png

Steeper spectral indices would further favor a 20 GHz band whereas a shallower slope would begin to favor 30/40 GHz. (Of course, even then removing the 20 GHz tube leads to a significant hit.)

Faraday Rotation

The utility of 20 GHz maps has been questioned because the amount of Faraday rotation is proportional to the square of the wavelength. Existing data and models suggest that this should not be a concern.

S-PASS, which operates at 2.3 GHz, has detected the effect at low galactic latitudes, but not at high galactic latitudes. This map shows the rotation measure in rad/m^2

S-PASS rm.gif

Many pixels are missing because so that it cannot be used very directly, but it gives a rough idea of the magnitude of the rotation measure that is expected in the southern hole.

A recent data-driven model with complete coverage that can be used to estimate the effect is described here https://arxiv.org/abs/1903.06735. In the deep patch, it predicts the following


Hutschenreuter rm pole deep.gifHutschenreuter rm pole deep std.gif

It may be worth incorporating this into our map-based simulations, but for now we can conservatively interpret this as an upper limit on the rotation measure of <30 rad/m^2. This corresponds to Faraday rotation by angle < 0.4 degrees. This leads to an upper limit on the rotation of the Stokes parameters of < 0.8 degrees. Correspondingly, accounting only for Faraday rotation, at the map level one would conservatively expect a correlation above > 98.5% between the synchrotron emission at 20 GHz and in the CMB bands.