# UNDER CONSTRUCTION

Below are transcripts of email threads that led to the N(l) definitions used in Delensing sensitivity - preliminary results. These will be converted to more legible and official documentation soon (by me, Tom C.).

## Polarized N(l)

From: Raphael Flauger <flauger@physics.ucsd.edu>
Subject: Re: South Pole atmosphere
Date: May 22, 2020 at 8:10:23 PM CDT
To: Thomas Crawford <tcrawfor@kicp.uchicago.edu>
Cc: Jeffrey J Mcmahon <jjm@uchicago.edu>, Jessica Avva <jessica.avva@gmail.com>,  Bradford Benson <bbenson@astro.uchicago.edu>

Hi Tom,

thanks! For BK what I have is based on reverse engineering from noise spectra and covariance matrices. So this is definitely more convenient :)

Best,

Raphael

On Fri, May 22, 2020 at 11:13 AM Thomas Crawford <tcrawfor@kicp.uchicago.edu> wrote:
Hi Raphael -

Attached is a pickle file with the 1d transfer function Jessica estimated for the map run from which she extracted Q/U noise spectra. It's the "power" transfer function (i.e., what you would correct C(ell) with). We'll include the TT transfer function when we pass along the TT noise curves.

Tom

--
Tom Crawford
University of Chicago
Department of Astronomy & Astrophysics
773-702-1564

On May 20, 2020, at 6:07 PM, Bradford Benson <bbenson@astro.uchicago.edu> wrote:

Hi Raphael,

On May 20, 2020, at 5:46 PM, Raphael Flauger <flauger@physics.ucsd.edu> wrote:

I was also surprised (mostly because the behavior of the slopes as a function of frequency is quite different from the SATs), but I really don't have intuition for what the slopes should be. If it's dominated by atmosphere, one could try to understand the physics, although the time scale wouldn't be right to do that this time around.

Anyway, since I don't understand it, I would follow the data, but I'm also happy to just us -2.6 across the board if you think that's more realistic. Could something like this indicate that we don't understand how it will average down (given that the 220 GHz maps are much less sensitive)? Is it easy to do splits on the lower frequency channels with comparable sensitivity to 220 GHz and look at those? For what we're doing now I think what we have might be good enough, but if it's easy perhaps one could take a look.

I think it likely means that the low-ell signal in the SPT-3G polarization data is not purely leaked atmosphere, or is something else entirely (e.g., the detector readout electronics, ground / RFI pickup, detector / cryostat temperature fluctuations, etc.).  So you might think CMB-S4 should do better, assuming it improves on whatever is limiting things for 3G, such that S4 is truly atmosphere limited.  Or conversely, you might think that the low-ell CMB-S4 performance is likely to be limited by some other systematic, in which case it will be hard to predict the S4 performance solely from SPT-3G.

Along those lines, I think I now agree with you, that we shouldn’t overthink its true physical origin and just use the fit values, since we are using SPT-3G as demonstration of achieved performance.  So I think it makes sense to go ahead with your previously suggested table of ell-knees and alpha.

Regarding lmin, it's just a parameter that is trivial to change. I just mentioned it because I have to pick something, and these spectra suggest 30 is overly optimistic. I can see how much it depends on this.

Sounds good.

Best,

Raphael

On Tue, May 19, 2020 at 10:40 PM Bradford Benson <bbenson@astro.uchicago.edu> wrote:

Hi Raphael, Tom,

On May 19, 2020, at 11:12 AM, Raphael Flauger <flauger@physics.ucsd.edu> wrote:

Hi Tom,

thanks.

Just to confirm that I'm using the data correctly, these dictionaries contain the standard deviation of Q, U noise in uK-arcmin as a function of scale, and I have to square them and convert to uK^2 to get N_\ell, correct? Doing that, I find the following numbers

{'90':
{'noise': 13.41293610924204, 'lknee': 138.91437047497493, 'alpha': -2.692635972676584},
'150':
{'noise': 13.355935721921394, 'lknee': 192.05036619725882, 'alpha': -2.564750987240382},
'220':
{'noise': 49.904078366542684, 'lknee': 188.9652441904766, 'alpha': -2.184254665752176}
}

Here 'noise' are the Q/U white noise levels in uK-arcmin. The spectra/fits are attached.
These QU noise levels would be consistent with the SPT-3G polarization noise for the 2019 season, so I think you are doing it correctly.

So for this range of frequencies, we could round to something like
Freq  ell-knee  alpha
93     140         -2.7
145    190        -2.6
225    190        -2.2

So some guess along the lines of Brad's table could be

Freq  ell-knee  alpha
27     150         -2.7
39     150         -2.7
93     150         -2.7
145    200        -2.6
225    200        -2.2
278    200        -2.2

but you probably have better intuition how to read the fits and extrapolate to higher and lower frequencies.

Another question I have is about the part of the plot that isn't shown, namely below \ell=80 where the spectra turn over. My forecasts also take \ell_min as an input. Based on your spectra, it perhaps seems reasonable to set that to \ell=80? Previously I set it to 30 (just because that was the number we had used for the SATs and I needed some number and was used for LAT Fisher forecasts.) Or will this get better? (For delensing I'm planning to take l_min for BB = 200 as in the map-based analyses. So I'm really asking about l_min for EE.)

I know this is what the fits are giving, however It is a little odd to me that the alpha’s in the high frequency bands are less steep than the alphas in the low-frequency bands.  So its a bit OCD and its so small that it shouldn’t really matter, but maybe you should just make the 225 and 278 GHz alphas = -2.6 (i.e, the same as the 150s).  The 150, 225, and 278 GHz bands should have a similar loading from water vapor, so if the knee was due to atmosphere, I would expect them to have a similar alpha.

Re the ell_min for EE, with ell-knees in the ~150-200 range, its unlikely the LAT contributes significantly below ell ~ 80 (i.e., compared to the SATs), so that should be fine for these baseline forecasts.  However, I am anticipating that someone (i.e., Carlstrom) will ask in the near future what could be gained if the LAT ell-knees were lower (i.e., because this is one of the motivations for building a TMA at the South Pole, that it could provide sensitivity margin).  So if its not a big hassle for your forecast machinery and will make this request easier if it comes later, you might just go ahead and leave ell_min to be ~30 (or the same as the SATs).

Tom, feel free to weigh in as well, but that seems sensible to me.

Best,

Raphael

On Tue, May 19, 2020 at 6:15 AM Thomas Crawford <tcrawfor@kicp.uchicago.edu> wrote:
Oops, I forgot the contents of that file knew about the custom SPT-3G software. The attached file should just be flat numpy arrays.

Tom

--
Tom Crawford
University of Chicago
Department of Astronomy & Astrophysics
773-702-1564

On May 18, 2020, at 11:10 PM, Raphael Flauger <flauger@physics.ucsd.edu> wrote:

Hi Tom,

definitely possible that it's a user error on my end, but I don't seem to be able to open it. I get
ModuleNotFoundError: No module named 'spt3g'
which sounds like it may use some information from that module? If the numbers I sent fit the data, we could use those, but I'm also happy to redo the fit properly if you can easily make a version I can open.
Best,
Raphael

On Mon, May 18, 2020 at 7:19 PM Thomas Crawford <tcrawfor@kicp.uchicago.edu> wrote:
Ha! Sorry to make you scrape the figure; the .pkl file with spectra is attached.

I was indeed just being lazy. Also, there is a typo; the model spectra as plotted are alpha = 3, not alpha = 4. But yes, yours are clearly better fits.

--
Tom Crawford
University of Chicago
Department of Astronomy & Astrophysics
773-702-1564

On May 18, 2020, at 8:03 PM, Raphael Flauger <flauger@physics.ucsd.edu> wrote:

Hi Tom, hi Jessica,

thanks, for looking into it and sending the new results. The spectra look nice.

Is there a reason not to fit to them? For a cheap digitization of your data, I find the following parameters

lknee        alpha
90 GHz         148          -2.39
150 GHz       205          -2.34
220 GHz       191          -2.14

I'm attaching the corresponding plot. It might be more proper to fit to the actual data. I'm happy to do the fit if it takes too much time, and you can share them. If you have time, you could do the fit, if not, perhaps Jeff/Brad can use this table (or a rounded version thereof) since I don't think they would change much (but they are noticeably different from the by eye numbers)?

Is the scaling currently proposed to get from detector NETs to map white noise levels consistent with what you find?

Best,

Raphael

On Mon, May 18, 2020 at 1:55 PM Thomas Crawford <tcrawfor@kicp.uchicago.edu> wrote:
Hi Jeff & Brad & Raphael -

Attached is our best current guess at debiased (i.e., filter-transfer-function-corrected) polarization noise in the three SPT-3G bands. All the work was done by Berkeley grad student Jessica Avva (cc'ed). We think there are ways to improve this (hopefully by a lot), but this is where we are now.

This plot uses data from the full 2019 season (including about 3 months when the sun was up and weather was not as good), the maps were made with a 19th-order polynomial subtracted from each detector's data over each 100-degree (in azimuth) scan across the field, and detector sensitivity to atmosphere was matched between detectors in a pixel by calibrating to elevation nods. The poly-filter transfer function (which cuts off at around ell ~ 40 in the scan direction) was estimated from simulations and deconvolved from the raw noise spectra, which are azimuthal averages of 2d noise PSDs constructed from many semi-independent data splits. The plot shows the average of the Q and U N(\ell) spectra. The numbers in the plot legend for ell_knee and alpha are estimated by eye. They fit quite well at the beginning of the noise roll-up then overestimate the measured noise at the low-ell end.

Let me and Jessica know if you have questions.

Tom

<qu_noise_3g_tf_corrected.png>

--
Tom Crawford
University of Chicago
Department of Astronomy & Astrophysics
773-702-1564

On May 13, 2020, at 1:48 PM, Jeffrey J Mcmahon <jjm@uchicago.edu> wrote:

no problem!  Just making sure I didn’t miss anything.

We have the noise model setup, code to generate N_ell setup, (just need to change parameters to be consistent with what you send, and we are merging this with the S4 component separation code to produce cloned N_ell…

This should be tougher in the next few days.

On May 13, 2020, at 1:47 PM, Thomas Crawford <tcrawfor@kicp.uchicago.edu> wrote:

Still being worked on. Sorry, I know it's been promised for a while.

--
Tom Crawford
University of Chicago
Department of Astronomy & Astrophysics
773-702-1564

On May 13, 2020, at 1:46 PM, Jeffrey J Mcmahon <jjm@uchicago.edu> wrote:

Hi Tom,

Do you have a South Pole atmospheric model (for N_ell) that Alec can implement and merge with the noise model?