Detection and removal of B-mode dust foregrounds with signatures of statistical anisotropy

Searches for inflationary gravitational wave signals in the cosmic microwave background (CMB) B-mode polarization are expected to reach unprecedented power over the next decade. A major difficulty in these ongoing searches is that Galactic foregrounds such as dust can easily mimic inflationary signals. Though, typically, foregrounds are separated from primordial signals using the foregrounds' different frequency dependence, in this paper we investigate instead the extent to which the Galactic dust B-modes' statistical anisotropy can be used to distinguish them from inflationary B-modes, building on the work of Kamionkowski and Kovetz (2014). In our work, we extend existing anisotropy estimators and apply them to simulations of polarized dust to forecast their performance for future experiments. Considering the application of this method as a null-test for dust contamination to CMB-S4, we find that we can detect residual dust levels corresponding to r ~ 0.001 at 2σ, which implies that statistical anisotropy estimators will be a powerful diagnostic for foreground residuals (though our results show some dependence on the dust simulation used). Finally, considering applications beyond a simple null test, we demonstrate how anisotropy statistics can be used to construct an estimate of the dust B-mode map, which could potentially be used to clean the B-mode sky.