# Tophat bands for Data Challenge

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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 started from the bandpass files and calculated tophats with the same band center and width. While the band centers are close to the nominal values, the band widths that I derive are significantly larger than what is listed in Victor's table.

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

The scaling factors calculate for non-tophat vs tophat bands agree to better than 1%.

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 (beam solid angle 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 for South Pole at 0.5 mm PWV and Atacama at 1.0 mm PWV (both are near median values). 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. Atmospheric spectra are courtesy of Denis Barkats, generated using am.

Name center [GHz] width [GHz] dust scale factor
from 353 GHz
sync scale factor
from 23 GHz
Tsky (Pole) [K] Tsky (Atacama) [K]
30 30.57 12.18 0.0060 0.3757 6.5 5.4
40 40.76 16.24 0.0078 0.1311 14.1 10.2
85 86.22 29.91 0.0183 0.0103 15.7 11.7
95 96.36 33.42 0.0216 0.0074 13.7 10.4
145 146.49 43.17 0.0465 0.0024 11.6 11.2
155 156.60 46.14 0.0540 0.0021 13.4 15.3
215 217.21 64.01 0.1310 0.0012 19.6 23.7
270 271.66 62.11 0.2918 0.0010 21.8 25.0

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

Colin Bischoff, 2016-11-01