Planet-Disk Interaction in Disks with Cooling: Basic Theory

• Published in: The Astrophysical journal Vol. 892; no. 1; pp. 65 - 84
• Main Authors: Miranda, Ryan, Rafikov, Roman R.
• Format: Journal Article
• Language: English
• Published: Philadelphia The American Astronomical Society 20.03.2020; IOP Publishing
• Subjects: Angular momentum; Angular momentum flux; Approximation; Astrophysics; Computer simulation; Cooling; Cooling effects; Damping; Density; Diagnostic systems; Gravitation theory; Hydrodynamics; Linear damping; Mathematical analysis; Momentum flux; Numerical simulations; Perturbation methods; Perturbation theory; Planet formation; Planets; Protoplanetary disks; Thermodynamics
• ISSN: 0004-637X; 1538-4357
• DOI: 10.3847/1538-4357/ab791a

Gravitational coupling between young planets and their parent disks is often explored using numerical simulations, which typically treat the disk thermodynamics in a highly simplified manner. In particular, many studies adopt the locally isothermal approximation, in which the disk temperature is a fixed function of the stellocentric distance. We explore the dynamics of planet-driven density waves in disks with more general thermodynamics, in which the temperature is relaxed toward an equilibrium profile on a finite cooling timescale tc. We use both linear perturbation theory and direct numerical simulations to examine the global structure of density waves launched by planets in such disks. A key diagnostic used in this study is the behavior of the wave angular momentum flux (AMF), which directly determines the evolution of the underlying disk. The AMF of free waves is constant for slowly cooling (adiabatic) disks but scales with the disk temperature for rapidly cooling (and locally isothermal) disks. However, cooling must be extremely fast, with β = tc 10−3 for the locally isothermal approximation to provide a good description of density wave dynamics in the linear regime (relaxing to β 10−2 when nonlinear effects are important). For intermediate cooling timescales, density waves are subject to a strong linear damping. This modifies the appearance of planet-driven spiral arms and the characteristics of axisymmetric structures produced by massive planets: in disks with β 0.1-1, a near-thermal mass planet opens only a single wide gap around its orbit, in contrast to the several narrow gaps produced when cooling is either faster or slower.