Eccentric disks as a gateway to giant planet outward migration

¹ Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, Milano 20133, Italy
² Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
³ School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, UK

^★ Corresponding author: chiara.scardoni@unimi.it

Received: 1 September 2025
Accepted: 19 September 2025

Abstract

Context. Recent studies on the planet-dominated regime of type II migration have demonstrated the presence of a correlation between the direction of massive planet migration and the parameter K that describes the depth of the gap opened by the planet. Indeed, it has been reported that high (low) values for the K parameter correspond to an outward (inward) migration.

Aims. In this paper, we aim to understand the mechanism driving inward and outward migration and why these mechanisms are correlated with the gap depth.

Methods. We performed a suite of 2D, live-planet, long-term simulations of massive planets migrating in disks with the hydro-code FARGO3D. We focused on a range of planet masses (1–13 m_J) and disk aspect ratios (from 0.03 to 0.1). We analyzed the evolution of orbital elements and gap structure. We also studied the torque contributions from outer Lindblad resonances to investigate their role in the migration outcome.

Results. We find that while all planets initially migrate inward, those with high enough K values eventually enter a phase in which the torque reverses sign and migration turns outward, until the point where it stalls. This behavior is associated with eccentricity growth in the outer disk and changes in the gap structure. We identified the surface density ratio at the 1:2 and 1:3 outer Lindblad resonances as a key output diagnostic that are correlated with the migration direction. In general, this ratio regulates the migration for all the cases where the massive planet remains in an almost circular orbit and the outer gap region exhibits moderate eccentricity. This characteristic sequence of inward-reversal-outward-stalling can occur for a variety of K values. Thus, further work is required to identify the simulation input parameters that determine the onset of this sequence.

Conclusions. Our results suggest that outward migration in the planet-dominated regime is primarily governed by the relative importance of the 1:2 and 1:3 resonances. Therefore, the gap profiles play a crucial role in determining the direction of migration.