Migrating super-Earths in low-viscosity discs: unveiling the roles of feedback, vortices, and laminar accretion flows

Abstract

We present the highest resolution study to date of super-Earths migrating in inviscid and low-viscosity discs, motivated by the connection to laminar, wind-driven models of protoplanetary discs. Our models unveil the critical role of vortices in determining the migration behaviour for partial gap-opening planets. Vortices form in pressure maxima at gap edges, and prevent the disc-feedback stopping of migration for intermediate planets in low-viscosity and inviscid discs, contrary to the concept of the 'inertial limit' or 'disc feedback' halting predicted from analytical models. Vortices may also form in the corotation region, and can dramatically modify migration behaviour through direct gravitational interaction with the planet. These features become apparent at high resolution, and for all but the highest viscosities there exist significant difficulties in obtaining numerically converged results. The migration of partial gap-opening planets, however, clearly becomes chaotic for sufficiently low viscosities. At moderate viscosity, a smooth disc-feedback regime is found in which migration can slow substantially, and the migration time-scale observed corresponds to migration being driven by diffusive relaxation of the gap edges. At high viscosity classical Type I migration is recovered. For Jupiter-analogue planets in inviscid discs, a wide, deep gap is formed. Transient Type II migration occurs over radial length-scales corresponding to the gap width, beyond which migration can stall. Finally, we examine the particle trapping driven by structures left in inviscid discs by a migrating planet, and find that particle traps in the form of multiple rings and vortices can persist long after the planet has passed. In this case, the observation of particle traps by submillimetre interferometers such as ALMA cannot be used to infer the current presence of an adjacent planet.

Intermittent planet migration and the formation of multiple dust rings and gaps in protoplanetary discs

“…These small-scale vortices, which are better resolved in the 1512×2250 simulation, thus tend to extend the runaway phase, and bring the planet closer to the grid's inner boundary. Similar results have been obtained by McNally et al (2019), who examined intermittent runaway migration in low-viscosity and inviscid disk models, and found that con-vergence in resolution was increasingly difficult to achieve, if achievable at all, upon decreasing viscosity. Although, in our simulations, stages of decelerated migration last shorter when increasing resolution, a pressure maximum does form when migration decelerates, but it is smoother, the density of dust trapped at this location is therefore smaller, and so is the intensity of the corresponding bright ring.…”

“…As already stated in Section 3.1, Lin & Papaloizou (2010) and McNally et al (2019) have obtained a similar scenario of intermittent migration. Although in these mod-els gas vortices form at the edges of the planet gap due to the Rossby-Wave Instability, the intermittent episodes of runaway migration can also be accounted for by the time evolution of the inverse vortensity of the gas crossing the planet's orbit.…”

“…• Intermittent migration: the intermediate curves for Σ0 = 10 −3 (in red) show non-steady (or non-smooth) orbital evolution, with several short stages of runaway migration which impart a stair-case shape to the curves. Lin & Papaloizou (2010) and McNally et al (2019) have reported results of hydrodynamical simulations with similar multiple episodes of runaway migration, which were obtained in inviscid or low-viscosity disk models. These intermittent stages of runaway migration are related to the time evolution of the coorbital vorticity-weighted mass deficit of the planet (Masset & Papaloizou 2003).…”

“…Progressive advectiondiffusion of vortensity in the horseshoe region, and shock formation inside the gap's inner edge, reinstate inward migration. The oscillations in the planet's orbital radius described by McNally et al (2019) terial in the coorbital region. These secondary U-turns help at once brake the planet's migration and replenish the reservoir of dust particles ahead of the planet before the pending runaway phase.…”

“…We shall focus on the migration of moderately massive planets (typically around a Saturn mass) in fairly massive disks, which are subject to rapid runaway migration (Masset & Papaloizou 2003). Such planets can undergo multiple stages of intermittent runaway migration (Lin & Papaloizou 2010;McNally et al 2019). We find that these multiple stages of intermittent runaway migration lead to the formation of several dust rings and therefore sequences of dark and bright rings in the (sub-)mm continuum.…”