# Tophat bands for Data Challenge

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Colin Bischoff -- 2016-11-02, updated 2016-11-04

In the process of science book forecasting, we came up with eight bands chosen to split up the four atmospheric windows. These bandpasses are listed in Table 1 of Victor's 2016-05-31 posting. I used the center frequencies and fractional bandwidths (Δν / ν). I then shifted the 215 GHz band up slightly (to 220 GHz) and widened the 270 GHz band (to 22%) to close a small gap between those bands.

For each band, I calculated

• relative brightness of a dust-type signal with βd = 1.59 and Td = 19.5 K; compared to 353 GHz reference frequency
• relative brightness of a synchrotron-type signal with βsync = -3.0; compared to 23 GHz reference frequency

This calculation requires us to specify the convention that we use for our tophat bandpass. I define this tophat to be such that a single-moded antenna (AΩ scales as λ2) would have uniform response as a function of frequency to a beam-filling Rayleigh-Jeans source. Before we start generating signal simulations, it would be a good idea to check that people generating foreground models agree on this calculation.

The figure below shows calculated atmospheric brightness spectra (at zenith) for South Pole at 0.5 mm PWV and Atacama at 1.0 mm PWV (both are near median values). Atmospheric spectra are courtesy of Denis Barkats, generated using am. I plotted the tophat bands on top of these spectra, with the height of each rectangle equal to the band-averaged brightness temperature using the South Pole spectrum. Also shown (in green) are the BICEP2 / Keck Array 150 GHz bandpass and the Keck Array 95 and 220 GHz bandpasses, for comparison.

The table includes a column that gives the overlap fraction for pairs of bands that split each atmospheric window. This fraction is defined as the ratio between the width of the intersection and the width of the union. Note that it is quite small for the low and high frequency windows, but substantial for the 90 GHz and 150 GHz windows.

The specific choice of how to split each atmospheric window into two bands was made for the Science Book forecasting effort. The procedure used to come up with the split was to separate two overlapping bands as far as possible while still keeping the calculated per-detector NET within 10-15% of the NET for a detector that spans the full window (see right-hand column of table). There may be room for further optimization of the band definitions, especially with more detailed models of atmosphere and detector performance. It is also likely that they will be changed down the line due to instrumental considerations. For example, if we use multichroic detectors, we would end up with pairs of bands that have little to no overlap. See Adrian's discussion of split vs staggered bands here.

Name center [GHz] width [GHz] dust scale factor
from 353 GHz
sync scale factor
from 23 GHz
Tsky (Pole) [K] Tsky (Atacama) [K] overlap fraction per-detector NET
[μK sqrt(s)]
30 30.00 9.00 0.0059 0.3876 6.3 5.2 2% 244
40 40.00 12.00 0.0076 0.1352 12.0 8.8 306
85 85.00 20.40 0.0179 0.0104 14.5 10.9 37% 346
95 95.00 22.80 0.0210 0.0074 11.7 9.2 295
145 145.00 31.90 0.0454 0.0024 10.5 10.3 53% 350
155 155.00 34.10 0.0526 0.0021 10.9 11.7 368
220 220.00 48.40 0.1368 0.0012 16.4 18.6 4% 738
270 270.00 59.40 0.2848 0.0010 21.4 24.5 1277
Keck 95 95.46 25.77 0.0212 0.0074 11.9 9.3
B2/Keck 150 148.92 43.52 0.0481 0.0023 11.9 12.0
Keck 220 228.27 48.02 0.1545 0.0012 16.9 19.1

Code used for calculations and plots in this posting: tophat_bandpass.py