Detection and Removal of B-mode Dust Foregrounds with Signatures of
  Statistical Anisotropy
  Searches for inflationary gravitational wave signals in the CMB B-mode
polarisation 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 polarised 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 $r\sim0.001$ at $2\sigma$, 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.
