Seeing the Unseen: A Method to Detect Unresolved Rings in Protoplanetary Disks

While high-resolution Atacama Large Millimeter/submillimeter Array (ALMA) observations reveal a wealth of substructure in protoplanetary disks, they remain incapable of resolving the types of small-scale dust structures predicted, for example, by numerical simulations of the streaming instability. In this article, we propose a method to find evidence for unresolved, optically thick dusty rings in protoplanetary disks. We demonstrate that, in presence of unresolved rings, the brightness of an inclined disk exhibits a distinctive emission peak at the minor axis. Furthermore, the azimuthal brightness depends on both the geometry of the rings and the dust optical properties; we can therefore use the azimuthal brightness variations to both detect unresolved rings and probe their properties. By analyzing the azimuthal brightness in the test case of ringlike substructures formed by streaming instability, we show that the resulting peak is likely detectable by ALMA for typical disk parameters. Moreover, we present an analytic model that not only qualitatively but also quantitatively reproduces the peak found in the simulations, validating its applicability to infer the presence of unresolved rings in observations and characterize their optical properties and shape. This will contribute to the identification of disk regions where streaming instability (and thus planet formation) is occurring.