Formation of multiple dust rings and gaps in protoplanetary discs by a single migrating planet. A parameter study in locally isothermal discs

Abstract

ALMA observations show that large protoplanetary discs usually contain multiple concentric dust rings separated by dark gaps. A natural explanation is dust-trapping at the edges of gaps opened by newly formed planets. However, planets typically migrate inward on timescales shorter than disc lifetimes, seemingly at odds with rings at large radii. We aim to investigate the conditions under which migrating planets can form long-lived, multi-ringed structures out to $r\sim 150$ au to constrain the parameter space for the planetary origin hypothesis of rings. Using the FargoCPT hydrodynamics code, we ran two-dimensional, locally isothermal disc models with a single migrating planet, varying disc aspect ratio, viscosity ($\alpha$), and planetary mass. In all models, the planet eventually stalls in a deep gap. At $\alpha \le 10^{-4}$, secondary spirals launched by the planet can open additional gaps at smaller radii. When planets exceed twice the local thermal mass before stalling, they enter a regime of alternating slow and type-III rapid migration, leaving partial gaps outside their orbit. The gap edges consistently feature pressure maxima that trap dust. These begin as large vortices at $\alpha \le 10^{-4}$, but gradually smear out into rings before dissipating. The type-III remnant rings dissipate quickly at $\alpha =10^{-3}$, but persist for at least 300-500 kyr at $\alpha \le 10^{-4}$. Both smear-out and dissipation timescales increase with lower $\alpha$. Our results show that migrating planets can reproduce observed multi-ringed structures in discs with $\alpha \lesssim 10^{-4}$ through their stall ($r\lesssim 50$ au), secondary gap-opening ($r\lesssim 20$ au), and type-III migration remnants (extending to $r\sim 150$ au for Jupiter-mass planets in sufficiently massive discs). Longer simulations will be required to compare the statistics of ring-to-vortex occurrence to observations.

20 pages, 14 figures, accepted for publication in A&A; v2 changes: language edits and one additional reference (arXiv:2305.01493)