We present resolved Herschel images of circumbinary debris disks in the alpha CrB (HD139006) and beta Tri (HD13161) systems. We find that both disks are consistent with being aligned with the binary orbital planes. Though secular perturbations from the binary can align the disk, in both cases the alignment time at the distances at which the disk is resolved is greater than the stellar age, so we conclude that the coplanarity was primordial. Neither disk can be modelled as a narrow ring, requiring extended radial distributions. To satisfy both the Herschel and mid-IR images of the alpha CrB disk, we construct a model that extends from 1-300AU, whose radial profile is broadly consistent with a picture where planetesimal collisions are excited by secular perturbations from the binary. However, this model is also consistent with stirring by other mechanisms, such as the formation of Pluto-sized objects. The beta Tri disk model extends from 50-400AU. A model with depleted (rather than empty) inner regions also reproduces the observations and is consistent with binary and other stirring mechanisms. As part of the modelling process, we find that the Herschel PACS beam varies by as much as 10% at 70um and a few % at 100um. The 70um variation can therefore hinder image interpretation, particularly for poorly resolved objects. The number of systems in which circumbinary debris disk orientations have been compared with the binary plane is now four. More systems are needed, but a picture in which disks around very close binaries (alpha CrB, beta Tri, and HD 98800, with periods of a few weeks to a year) are aligned, and disks around wider binaries (99 Her, with a 50 yr period) are misaligned, may be emerging. This picture is qualitatively consistent with the expectation that the protoplanetary disks from which the debris emerged are more likely to be aligned if their binaries have shorter periods.
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