A Joint Analysis of BICEP2/Keck Array and Planck Data

TL;DR

This work addresses whether inflationary gravitational waves contribute to CMB B-modes by jointly analyzing BICEP2/Keck and Planck polarization data. It implements a multi-frequency likelihood that models dust polarization with a Planck-informed prior and jointly fits for $r$ and dust parameters across cross-spectra, yielding $r<0.12$ (95% CL) with a dust-dominated signal and a $7.0\sigma$ detection of lensing B-modes. The results are robust to data splits, priors, and the inclusion of synchrotron, and they demonstrate the necessity of multi-frequency dust cleaning in primordial B-mode searches. Overall, the analysis places stringent constraints on primordial gravitational waves while confirming dust contamination and strong lensing signatures in the B-mode polarization.

Abstract

We report the results of a joint analysis of data from BICEP2/Keck Array and Planck. BICEP2 and Keck Array have observed the same approximately 400 deg$^2$ patch of sky centered on RA 0h, Dec. $-57.5°$. The combined maps reach a depth of 57 nK deg in Stokes $Q$ and $U$ in a band centered at 150 GHz. Planck has observed the full sky in polarization at seven frequencies from 30 to 353 GHz, but much less deeply in any given region (1.2 $μ$K deg in $Q$ and $U$ at 143 GHz). We detect 150$\times$353 cross-correlation in $B$-modes at high significance. We fit the single- and cross-frequency power spectra at frequencies $\geq 150$ GHz to a lensed-$Λ$CDM model that includes dust and a possible contribution from inflationary gravitational waves (as parameterized by the tensor-to-scalar ratio $r$), using a prior on the frequency spectral behavior of polarized dust emission from previous \planck\ analysis of other regions of the sky. We find strong evidence for dust and no statistically significant evidence for tensor modes. We probe various model variations and extensions, including adding a synchrotron component in combination with lower frequency data, and find that these make little difference to the $r$ constraint. Finally we present an alternative analysis which is similar to a map-based cleaning of the dust contribution, and show that this gives similar constraints. The final result is expressed as a likelihood curve for $r$, and yields an upper limit $r_{0.05}<0.12$ at 95% confidence. Marginalizing over dust and $r$, lensing $B$-modes are detected at $7.0\,σ$ significance.

Figures (13)

• Figure 1: Planck 353 GHz $T$, $Q$, and $U$ maps before (left) and after (right) the application of BICEP2/ Keck filtering. In both cases the maps have been multiplied by the BICEP2/ Keck apodization mask. The Planck maps are presmoothed to the BICEP2/ Keck beam profile and have the mean value subtracted. The filtering, in particular the third order polynominal subtraction to suppress atmospheric pickup, removes large-angular scale signal along the BICEP2/ Keck scanning direction (parallel to the right ascension direction in the maps here).
• Figure 2: Single- and cross-frequency spectra between BICEP2/ Keck maps at 150 GHz and Planck maps at 353 GHz. The red curves show the lensed-$\Lambda$CDM expectations. The left column shows single-frequency spectra of the BICEP2, Keck Array and combined BICEP2/ Keck maps. The BICEP2 spectra are identical to those in BK-I, while the Keck Array and combined are as given in BK-V. The center column shows cross-frequency spectra between BICEP2/ Keck maps and Planck 353 GHz maps. The right column shows Planck 353 GHz data-split cross-spectra. In all cases the error bars are the standard deviations of lensed-$\Lambda$CDM+noise simulations and hence contain no sample variance on any other component. For $EE$ and $BB$ the $\chi^2$ and $\chi$ (sum of deviations) versus lensed-$\Lambda$CDM for the nine bandpowers shown is marked at upper/lower left (for the combined BICEP2/ Keck points and DS1$\times$DS2). In the bottom row (for $BB$) the center and right panels have a scaling applied such that signal from dust with the fiducial frequency spectrum would produce signal with the same apparent amplitude as in the 150 GHz panel on the left (as indicated by the right-side $y$-axes). We see from the significant excess apparent in the bottom center panel that a substantial amount of the signal detected at 150 GHz by BICEP2 and Keck Array indeed appears to be due to dust.
• Figure 3: $EE$ (left column) and $BB$ (right column) cross-spectra between BICEP2/ Keck maps and all of the polarized frequencies of Planck. In all cases the quantity plotted is $\ell(\ell+1)C_l/2\pi$ in units of $~\mu{\rm K}_{\mathrm{CMB}}^2$, and the red curves show the lensed-$\Lambda$CDM expectations. The error bars are the standard deviations of lensed-$\Lambda$CDM+noise simulations and hence contain no sample variance on any other component. Also note that the $y$-axis scales differ from panel to panel in the right column. The $\chi^2$ and $\chi$ (sum of deviations) versus lensed-$\Lambda$CDM for the five bandpowers shown is marked at upper left. There are no additional strong detections of deviation from lensed-$\Lambda$CDM over those already shown in Fig. \ref{['fig:spectra']} although BK150$\times$P217 shows some evidence of excess.
• Figure 4: Differences of B150$\times$P353 and K150$\times$P353 $BB$ cross-spectra. The error bars are the standard deviations of the pairwise differences of signal+noise simulations that share common input skies. The probability to exceed the observed values of $\chi^2$ and $\chi$ statistics, as evaluated against the simulations, is quoted for bandpower ranges 1--5 ($20<\ell<200$) and 1--9 ($20<\ell<330$). There is no evidence that these spectra are statistically incompatible.
• Figure 5: Differences of B150$\times$P353 $BB$ cross-spectra from the standard power spectrum estimator and alternate estimators. The error bars are the standard deviations of the pairwise differences of signal+noise simulations that share common input skies. The probability to exceed the observed values of $\chi^2$ and $\chi$ statistics, as evaluated against the simulations, is quoted for bandpower ranges 1--5 ($20<\ell<200$) and 1--9 ($20<\ell<330$). We see that the differences of the real spectra are consistent with the differences of the simulations.