No evidence for dust B-mode decorrelation in Planck data

Constraints on inflationary $B$-modes using Cosmic Microwave Background polarization data commonly rely on either template cleaning or cross-spectra between maps at different frequencies to disentangle galactic foregrounds from the cosmological signal. Assumptions about how the foregrounds scale with frequency are therefore crucial to interpreting the data. Recent results from the Planck satellite collaboration claim significant evidence for a decorrelation in the polarization signal of the spatial pattern of galactic dust between 353 GHz and 217 GHz. Such a decorrelation would suppress power in the cross spectrum between high frequency maps, where the dust is strong, and lower frequency maps, where the sensitivity to cosmological $B$-modes is strongest. Alternatively, it would leave residuals in lower frequency maps cleaned with a template derived from the higher frequency maps. If not accounted for, both situations would result in an underestimate of the dust contribution and thus an upward bias on measurements of the tensor-to-scalar ratio, $r$. In this paper we revisit this measurement and find that the no-decorrelation hypothesis cannot be excluded with the Planck data. There are three main reasons for this: i) there is significant noise bias in cross spectra between Planck data splits that needs to be accounted for; ii) there is strong evidence for unknown instrumental systematics whose amplitude we estimate using alternative Planck data splits; iii) there are significant correlations between measurements in different sky patches that need to be taken into account when assessing the statistical significance. Between $\ell=55-90$ and over $72\%$ of the sky, the dust $BB$ correlation between 217 GHz and 353 GHz is $1.001^{+.004/.021}_{-.004/.000}$ ($68\%~stat./syst.$) and shows no significant trend with sky fraction.