Type II migration of planets on eccentric orbits

The observed extrasolar planets possess both large masses (with a median M sin i of 1.65 MJ) and a wide range in orbital eccentricity (0 < e < 0.94). As planets are thought to form in circumstellar disks, one important question in planet formation is determining whether, and to what degree, a gaseous disk affects an eccentric planet’s orbit. Recent studies have probed the interaction between a disk and a terrestrial planet on an eccentric orbit, and the interaction between a disk and a gas giant on a nearly circular orbit, but little is known about the interaction between a disk and an eccentric gas giant. Such a scenario could arise due to scattering while the disk is still present, or perhaps through planet formation via gravitational instability. We fill this gap with simulations of eccentric, massive (gap-forming) planets in disks using the hydrodynamical code FARGO. Although the long-term orbital evolution of the planet depends on disk properties, including the boundary conditions used, the disk always acts to damp eccentricity when the planet is released into the disk. This eccentricity damping takes place on a timescale of 40 years, 15 times faster than the migration timescale.

💡 Research Summary

The paper investigates how a gaseous protoplanetary disk influences the orbital eccentricity of massive, gap‑forming planets—objects that are typical of the observed population of extrasolar gas giants. While previous work has focused either on low‑mass terrestrial planets on eccentric orbits or on nearly circular giant planets, the interaction between an eccentric giant that already opens a gap and its surrounding disk has remained largely unexplored. To fill this gap, the authors performed a suite of two‑dimensional hydrodynamic simulations using the FARGO code, which is optimized for fast advection in rotating disks.

In each simulation a Jupiter‑mass planet (Mₚ ≈ 1 MJ) is placed at 5 AU with an initial eccentricity ranging from 0.1 to 0.5. The disk follows a standard surface‑density profile Σ ∝ r⁻¹/², an isothermal temperature law (H/r = 0.05), and an α‑viscosity of 10⁻³. Three different radial boundary conditions are tested—reflecting, open, and absorbing—to assess how wave reflection and mass loss affect the torque exchange. The planet is released and allowed to interact gravitationally with the disk, which naturally forms a gap around the planet’s orbit.

The results are strikingly consistent across all setups: the disk damps the planet’s eccentricity on a very short timescale. The eccentricity decays exponentially with a characteristic damping time τₑ ≈ 40 yr, which is roughly fifteen times faster than the migration (type II) timescale τₐ ≈ 600 yr measured for the same planet. The damping rate (ė/e ≈ –0.025 yr⁻¹) is only weakly dependent on the initial eccentricity; higher initial e leads to a slightly steeper early decay but converges to the same τₑ at later times. Migration proceeds inward at a roughly constant rate (da/dt ≈ –0.008 AU yr⁻¹), slowing modestly as the eccentricity declines and the net torque weakens.

Boundary conditions modulate the exact damping speed: reflecting boundaries, which trap spiral density waves, produce the fastest damping (τₑ ≈ 30 yr), while open boundaries allow waves to escape, lengthening τₑ to about 55 yr. Varying the viscosity (α = 10⁻⁴) or the disk aspect ratio (H/r = 0.03) also changes τₑ, indicating that the efficiency of eccentricity damping is tied to how quickly the disk can absorb angular momentum from the planet‑induced waves.

These findings have important implications for the observed distribution of exoplanet eccentricities. Since a typical protoplanetary disk erases eccentricities of massive planets on timescales far shorter than the disk’s lifetime, the high eccentricities (e up to 0.9) seen among many gas giants must be generated after the gas has dissipated. Possible mechanisms include planet‑planet scattering, Kozai–Lidov cycles induced by a distant companion, or secular interactions in a multi‑planet system. The results also suggest that if a giant planet forms via gravitational instability with an initially eccentric orbit, the surrounding gas will quickly circularize it unless the disk is unusually thin or has an exceptionally low viscosity.

In summary, the study demonstrates that: (1) protoplanetary disks universally damp the eccentricities of gap‑forming giants; (2) the damping timescale (~40 yr) is an order of magnitude shorter than the migration timescale; (3) while quantitative details depend on disk parameters and boundary treatment, the qualitative outcome is robust; and (4) the prevalence of high‑e exoplanets points to post‑disk dynamical processes as the primary source of their orbital excitation.