Reading between the Rings: Observed Dust Ring Properties as Probes of Planet Masses

Abstract We hypothesize that dust rings in protoplanetary disks formed by an embedded planet should have properties that reflect the planet’s mass. We use 2D hydrodynamical simulations of planet–disk interactions to investigate this, focusing on planets ranging from 0.5–2.0× the pebble-isolation mass, for three different aspect ratios. We find the ring’s dust mass, peak location, and width to correlate with planet mass. We confirm a positive linear relationship between a planet’s Hill radius and the location of a ring’s density peak and demonstrate how this relationship can be used to constrain planet masses in observed systems by applying it to PDS 70. The dust ring width and mass change with planet mass for planet masses up to the pebble-isolation mass, beyond which they become constant. The steepness of the gas pressure radial profile is asymmetric, with the direction of the asymmetry being determined by whether the planet mass is above or below the pebble-isolation mass. We therefore propose a new way to define the pebble-isolation mass: the minimum planet mass that perturbs the gas enough for the pressure gradient interior to the pressure maximum to exceed the pressure gradient exterior to it. We discuss how our findings could be used to constrain or estimate planet masses from gas or dust observations of disks with measurable substructures and apply our results to five disks in the exoALMA sample to estimate planet masses and constrain disk aspect ratios. We also discuss how the potential for planetesimal formation in a ring varies with planet mass.