Background on 20 GHz channel

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This posting summarizes the analyses that led to the CDT decision to move the 20 GHz channel from the SATs to the delensing LAT, and provides some additional background.

Summary of CDT results

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 (hopefully more realistic) spectral dependence 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 (approximately a factor 8 at map level between 20 and 40 GHz).

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 move the 20 GHz detectors from the SAT to the delensing LAT. 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

Signal-to-noise considerations

For the noise levels of the CDT configuration, 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 see that this corresponds to a ratio of approximately 50 between synchrotron and noise power on the scales that cause the bias. Perhaps an intuitive way to understand this is to compare the contribution of primordial B-modes with r=5e-4 to the synchrotron amplitude in the CMB bands. Here this is shown for a synchrotron spectral index of -3.1

Cl sync95 Cl5e4 3p1.png

At l=150 the ratio between power in synchrotron emission and a tensor signal with r=5e-4 is around 50, so that a synchrotron rejection at the very least at this level is required for an unbiased measurement. Of course, the synchrotron contamination at 150 GHz is lower and this depends on the relative sensitivities between these channels, but for the current configuration the ILC weights for 85/95 GHz dominate those of 145/155 GHz (by roughly a factor 3).

Any configuration that ensures a rejection well above this level should successfully remove the bias. The sensitivity of the instrument has increased significantly since the CDT so that the bias must also be reduced further. For the DSR configuration with the following performance expectation

Frequency (GHz) 20 30 40 85 95 145 155 220 270
Beam FWHM (arcmin) 11.0 72.8 72.8 25.5 22.7 25.5 22.7 13.0 13.0
noise T (uK-arcmin) 11.94 5.64 7.14 1.41 1.24 2.71 2.90 7.50 12.85
l_knee T 700 150 150 150 150 230 230 230 230
exponent T -4.4 -4.4 -4.4 -4.4 -4.4 -3.8 -3.8 -3.8 -3.8
noise E (uK-arcmin) 8.44 3.74 4.73 0.93 0.82 1.25 1.34 3.48 8.08
l_knee E 200 60 60 60 60 65 65 65 65
exponent E -2.0 -2.2 -2.2 -2.2 -2.2 -3.1 -3.1 -3.1 -3.1
noise B (uK-arcmin) 8.44 3.53 4.46 0.88 0.78 1.23 1.34 3.48 5.97
l_knee B 200 60 60 60 60 60 60 60 60
exponent B -2.0 -1.7 -1.7 -1.7 -1.7 -3.0 -3.0 -3.0 -3.0

the ratio between synchrotron and noise power has improved by more than a factor 2 so that synchrotron rejection from the 20 GHz channel has improved in line with the improvement in sensitivity

S-N 20GHz DSR.png

In the context of the delensing LAT sensitivity study summarized [1], the delensing LAT sensitivities have been refined, which has increased the expected white noise levels at 20 GHz. Map-based simulations should be used to confirm that the current levels of sensitivity at 20 GHz are sufficient to 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 for the V3R0 baseline configuration


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, and the sensitivities at 30/40 GHz are most likely insufficient to reject synchrotron radiation at the required level. it does not appear to be the case for the V3R0 configuration.

However, if 20 GHz detectors present a major technological challenge, it may 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 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. So decorrelation between the 20 GHz band and the CMB bands caused by Faraday rotation does not appear to be problematic.