# ACTPol Nl from Naess 2014

At the Chicago CMB-S4 workshop (September 2016), the forecasting group stated our desire for more experiments to release their N_ell curves. Jo pointed out that this information can be extracted from the ACTPol data release that accompanied Næss et al (2014). I went ahead and did this exercise, using the code linked here: ACTPol_Naess_Nl.py.

Some notes:

• The Næss et al analysis uses data taken with ACTPol between September 11 and December 14, 2013. It is split between four patches, with total sky area of 270 square-degrees. The detector bandpasses are centered at 146 GHz.
• The publicly released likelihood code only calculates a likelihood for TT, TE, and EE spectra, and those are the only spectra included in the supplied bandpower covariance matrix. However, the tarball includes a file with BB bandpowers and error bars, which I used for this calculation.
• I assumed that the error bars for BB are given by (C_l + N_l) * sqrt(2 / dof), where C_l are expectation values calculated by applying the ACT polarized bandpower window functions (BblMean_Pol.dat) to a lensing BB theory spectrum and dof are bandpower degrees-of-freedom calculated as fsky * sum(2 * ell + 1) for tophat ell bins. For these data, delta-ell = 50 at low ell but grows to 800 for the few highest ell bins. My formula does not include any contribution to the BB error bar from E-to-B leakage, so these results are only accurate if that is a sub-dominant component.

After solving for N_ell, I fit it to a white plus 1/f model, A * (1 + (ell_knee / ell)^alpha) * B_ell^2, including B_ell^2 calculated for a 1.3 arcmin beam. The recovered N_ell and best fit model can be seen in the figure below. Note that both the figure and the fit parameters are N_ell, not l*(l+1) N_ell / (2*pi).

• White noise level, A = 8.8e-5 uK^2
• Ell knee = 646
• Power law slope, alpha = 2.1

The fit seems fairly good, which gives me confidence that I didn't mangle anything in my calculation. I also added curves corresponding to sqrt(2) times 11 or 17 uK-arcmin, which are the map noise levels quoted in the abstract of Næss et al. The factor of sqrt(2) is needed for polarized map depths, see Næss et al Section 3.1. Even ignoring the excess low-ell noise, these quoted white noise levels appear to be a bit optimistic.

I have also provided the N_ell curve (blue curve in above figure) in tabulated form here: Media:ACTPol_Naess_Nl.txt

Colin Bischoff, 2016-10-02