Geometry of dust rings in protoplanetary disks: the case of LkCa 15

Abstract

Dust properties in proto-planetary disks shape the pathways for planet formation. Here, we present a method to measure these properties in moderately inclined dust rings. Our method exploits the simple geometric fact that, for such a ring, its ansae appear brighter because our line of sight traverses a longer path through the ring material, and appear broader because the minor axis are foreshortened by projection. The resultant patterns of apparent brightness and width can used to constrain three parameters: the intrinsic ring width, its vertical thickness and its optical depth. We apply this method to ALMA archival images of the LkCa 15 disk, in Bands 7, 6 and 3. We find that the optical depth of its main ring drops from 1.6 at 0.89mm to 0.4 at 3mm. Simultaneously, both the ring width and the ring height decrease from about two to one gas scale heights. Such wavelength-dependent morphology can only be explained by the presence of multiple grain populations. If we adopt a simple two-size model, we infer that the ring contains a massive population of small grains (size < 20 micron; total mass ~ 100 earth masses) that are broadly distributed, and a less massive population of large grains (size > 200 micron) that are more spatially concentrated. This large surplus of small grains is not predicted by models of dust coagulation, but it naturally explains the fluffy ring in LkCa 15, and possibly rings in other disks.