[Paper Review] Planet-Disk Interactions

Sijme-Jan Paardekooper, Ruobing Dong+5 more|arXiv (Cornell University)|Mar 17, 2022

Astrophysics and Star Formation StudiesPhysics and Astronomy31 citations

TL;DR

This review summarizes how embedded planets interact with protoplanetary disks across migration regimes, including new insights on thermal torques, gap opening, and observational signatures.

ABSTRACT

Planet-disk interactions, where an embedded massive body interacts gravitationally with the protoplanetary disk it was formed in, can play an important role in reshaping both the disk and the orbit of the planet. Spiral density waves are launched into the disk by the planet, which, if they are strong enough, can lead to the formation of a gap. Both effects are observable with current instruments. The back-reaction of perturbations induced in the disk, both wave-like and non-wavelike, is a change in orbital elements of the planet. The efficiency of orbital migration is a long-standing problem in planet formation theory. We discuss recent progress in planet-disk interactions for different planet masses and disk parameters, in particular the level of turbulence, and progress in modeling observational signatures of embedded planets.

Motivation & Objective

• Clarify the main dynamical regimes of planet-disk interaction (Type I–III, gap opening, and gas-dflow through gaps).
• Assess how disk properties (turbulence, viscosity, temperature, diffusion) alter planetary torques and migration.
• Summarize recent progress on thermal torques, heating effects, and their impact on low-mass planets.
• Discuss gap-opening criteria and the evolving understanding of Type II migration.
• Highlight observational signatures and modeling tools for embedded planets in disks.

Proposed method

• Describe the basic flow structures around embedded planets and identify wavelike and non-wavelike responses.
• Present the classical and generalized torque prescriptions for Type I migration, including corotation (horseshoe) and Lindblad torques.
• Explain gap-opening criteria and the transition to Type II migration, incorporating recent simulations (e.g., q ≳ 5 h^{5/2} α^{1/2}).
• Introduce thermal diffusion and the cold/hot thermal torques, with analytic forms such as the thermal torque equation (Γ_thermal) and the luminosity threshold (L_c).
• Discuss dynamical corotation torques and their dependence on vortensity in the coorbital region, including non-viscous and magnetically driven inflow cases.
• Review observational and modeling tools used to study disk-planet interactions and their signatures.

Experimental results

Research questions

• RQ1 What are the dominant regimes of planet-disk interaction as a function of planet mass, disk viscosity, and scale height?
• RQ2 How do thermal diffusion and planetary heating modify the torque on low-mass planets (thermal torques and heating torques) and migration outcomes?
• RQ3 Under what conditions does a planet open a gap, and how does the gap depth and structure influence Type II migration?
• RQ4 How do corotation torques and dynamical corotation torques behave under varying viscosity, turbulence, and migration rates?
• RQ5 What observable signatures arise from planet-disk interactions, and how can models connect to current disk observations?

Key findings

• Thermal diffusion introduces a significant thermal torque that can dominate the net torque on very low-mass planets, often inward, and can be reversed by planetary heating (L>0).
• A generalized dynamical corotation torque framework describes how migration and vortensity contrasts drive torques in low-viscosity or magnetically stressed disks.
• The gap-opening criterion has been refined to q ≳ 5 h^{5/2} α^{1/2}, showing even Neptune-mass planets can open gaps in low-viscosity disks.
• Type II migration is not strictly tied to disk viscous accretion; gap-crossing flows allow planets to migrate with the gap, and a Kanagawa et al. (2018) model links migration to gap structure.
• Thermal effects, including the cold finger and heating torques, can alter eccentricity and inclination evolution over time.
• Observational advances (spiral arms, gaps, and kinematic signatures) are enabling detection and characterization of embedded planets and their disk responses.