TheBicep2/Keck Arraymatrix-purified 150 GHz 2D angular power spectra are binned and averaged into 1D angular power spectra. The autospectra forBicep2 or Keck Arrayare evaluated individually and the cross-spectra of the two experiments are evaluated. As an example, Figure 5.5 shows the Keck Array 1D autospectra. The lensed-ΛCDM model is a good fit to all angular power spectra, with the exception ofBB at low`, where a strong excess is observed.
The Keck Arraydata are also compared toBicep2 for consistency between the two experiments. This can be done by a simple jackknife between the maps or by comparing the autospectra and cross-spectra of the experiments. To test the compatibility of the resulting bandpowers with null we compare them to the differences of signal+noise simulations that share common input skies. In such tests it is necessary that the simulations contain power roughly equal to the real sky as the cross terms between signal and noise increase the fluctuation of the differences even for perfectly common sky coverage. We added power to the signal simulations that matches the amplitude of the signal in excess of ΛCDM in bandpowers 1–5. (The origin of the extra signal over ΛCDM is not important here—only its approximate amplitude.) The results are shown in Figure 5.6. We then proceed to calculate the PTE of theχand χ2 statistics versus the simulated distributions for the two bandpower ranges and give the results in Table 5.2. In both the figure and the table we note the effect of the two bandpowers at ` ≈220 that are high with respect to lensed-ΛCDM in B2xB2 (as noted in theBicep2Results Paper) but not in KxK and B2xK—as expected these also show up in the map difference. Again note that the PTE values are correlated (both along and between rows of the table) so overinterpretation should be avoided. Our conclusion is that theBicep2andKeck Arraydata are consistent—especially in the lowest five bandpowers, where an IGW contribution would be strongest.
0 2000 4000 6000 TT
l(l+1)Cl/2π [µK2]
0 100 200 300
−1 0 1
TT jack − χ2 PTE = 0.02
−50 0 50 100 150 TE
0 100 200 300
−0.1 0
0.1 TE jack − χ2 PTE = 0.31
0 5 10
15 EE − χ2 PTE = 0.04
0 100 200 300
−0.01 0
0.01 EE jack − χ2 PTE = 0.25
0 100 200 300
−0.01 0 0.01 0.02 0.03 0.04
0.05 BB − χ2 PTE = 2.7×10−7
BB jack − χ2 PTE = 0.96
−5 0 5
TB
0 100 200 300
−0.4
−0.2 0
0.2 TB jack − χ2 PTE = 0.07
−0.1
−0.05 0 0.05
0.1 EB − χ2 PTE = 0.93
0 100 200 300
−0.01 0
0.01 EB jack − χ2 PTE = 0.67
Multipole
Figure 5.5: Keck Arraypower spectrum results for signal (black points) and early/late season jackknife (blue points). The solid red curves show the lensed-ΛCDM theory expectations. The error bars are the standard deviations of the lensed-ΛCDM+noise simulations and hence contain no sample variance on any additional signal component. The probability to exceed (PTE) the observed value of a simple χ2 statistic is given (as evaluated against the simulations). Note the very differenty-axis scales for the jackknife spectra (other thanBB). See the text for additional discussion of theBBspectrum. (Note that the calibration procedure usesEB to set the overall polarization angle so T B andEB as plotted above cannot be used to measure astrophysical polarization rotation.)
−0.01 0 0.01 0.02 0.03 0.04 0.05
Multipole l(l+1)C lBB /2π[µK2 ]
B2xB2 KxK B2xK
0 50 100 150 200 250 300
−0.01
−0.005 0 0.005
Multipole l(l+1)C lBB /2π[µK2 ]
Map Jack B2xB2−B2xK B2xB2−KxK B2xK−KxK
Figure 5.6: Upper: Comparison of theKeck Array BB auto spectrum, theBicep2auto spectrum, and the cross-spectrum taken between the two. The error bars are the standard deviation of the lensed-ΛCDM+noise simulations and are not appropriate for comparison of the data values. (For clarity theKeck Arrayand cross- spectrum points are offset horizontally.) Lower: Four compatibility tests between theB-modes measured by Bicep2andKeck Array. The “map jack” takes the difference of theQandU maps, divides by a factor of two, and calculates theBBspectrum. The other three sets of points are the differences of the spectra shown in the upper panel divided by a factor of four. In each case the error bars are the standard deviation of the pairwise differences of signal+noise simulations that share common input skies—comparison of each set of these points (individually) with null is an appropriate test of the compatibility of the experiments—see text for details.
Table 5.2: Bicep2/Keck Arraycompatibility test PTE values from χ2 andχ-like (sum of deviation) tests Jackknife Bandpowers Bandpowers Bandpowers Bandpowers
1–5χ2 1–9χ2 1–5χ 1–9χ
Map jackknife
EE 0.034 0.048 0.106 0.028
BB 0.561 0.695 0.054 0.018
EB 0.741 0.754 0.405 0.651
Spectral jackknife B2-cross
EE 0.112 0.092 0.068 0.078
BB 0.687 0.387 0.052 0.008
EB 0.555 0.224 0.212 0.234
Spectral jackknife B2-Keck
EE 0.138 0.128 0.066 0.126
BB 0.920 0.485 0.200 0.022
EB 0.511 0.214 0.210 0.200
Spectral jackknife cross-Keck
EE 0.176 0.204 0.074 0.202
BB 0.880 0.966 0.643 0.435
EB 0.361 0.437 0.443 0.188
Inasmuch as the two experiments are consistent with each other and measuring the same sky at the same spectral band, their accumulation quantities can be combined to average maps, which is equivalent to a noise weighted combination of the maps. This results in Qand U maps that have a depth of 57 nK deg (3.4µK arcmin) over an effective area of 400 square degrees for an equivalent survey weight of 248000µK−2 (see Table 5.1).
The observation regions and strategies are sufficiently similar that it is found empirically using simulations that the purification matrix of either experiment delivers adequate B-mode purity when applied to the combined map (with contamination equivalent tor <10−3).
The finalBB spectrum is shown in Figure 5.7 and is inconsistent with the lensed-ΛCDM expectation at
>6σ(for either bandpowers 1–5 or 1–9). The lensed-ΛCDM+noise error bars as plotted are approximately a factor two smaller than those of the previousBicep2only results—saturation on the (small) sample variance of the lensing component is occurring—the noise component is a factor 2.3 times smaller. All the spectra (includingT T,EEetc.) are available for download athttp://bicepkeck.org/together with the ancillary data, noise information, etc., required to use them.