Deprojecting and constraining the vertical thickness of exoKuiper belts

Constraining the vertical and radial structure of debris discs is crucial to understanding their formation, evolution, and dynamics. To measure both the radial and vertical structure, a disc must be sufficiently inclined. However, if a disc is too close to edge-on, deprojecting its emission becomes non-trivial. In this paper we show how FRANKENSTEIN, a non-parametric tool to extract the radial brightness profile of circumstellar discs, can be used to deproject their emission at any inclination as long as they are optically thin and axisymmetric. Furthermore, we extend FRANKENSTEIN to account for the vertical thickness of an optically thin disc (H(r)) and show how it can be constrained by sampling its posterior probability distribution and assuming a functional form (e.g. constant h = H/r), while fitting the radial profile non-parametrically. We use this new method to determine the radial and vertical structures of 16 highly inclined debris discs observed by ALMA. We find a wide range of vertical aspect ratios, h, ranging from 0.020 ± 0.002 (AU Mic) to 0.20 ± 0.03 (HD 110058), which are consistent with parametric models. We find a tentative correlation between h and the disc fractional width, as expected if wide discs were more stirred. Assuming discs are self-stirred, the thinnest discs would require the presence of at least 500-km-sized planetesimals. The thickest discs would likely require the presence of planets. We also recover previously inferred and new radial structures, including a potential gap in the radial distribution of HD 61005. Finally, our new extension of FRANKENSTEIN also allows constraining how h varies as a function of radius, which we test on 49 Ceti, finding that h is consistent with being constant.