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Register a new userPlanet-disk interaction in disks with cooling: basic theory
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Ryan Miranda IAS
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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 towards an equilibrium profile on a finite cooling timescale $t_{rm c}$. 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 $beta = Omega t_{rm c} lesssim 10^{-3}$ for the locally isothermal approximation to provide a good description of density wave dynamics in the linear regime (relaxing to $beta lesssim 10^{-2}$ 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 $beta approx 0.1$ -- $1$, 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.
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Context. Structures in debris disks induced by planetdisk interaction are promising to provide valuable constraints on the existence and properties of embedded planets. Aims. We investigate the observability of structures in debris disks induced by planet-disk interaction. Methods. The observability of debris disks with the Atacama Large Millimeter/submillimeter Array (ALMA) is studied on the basis of a simple analytical disk model. Furthermore, N-body simulations are used to model the spatial dust distribution in debris disks under the influence of planet-disk interaction. Images at optical scattered light to millimeter thermal re-emission are computed. Available information about the expected capabilities of ALMA and the James Webb Space Telescope (JWST) are used to investigate the observability of characteristic disk structures through spatially resolved imaging. Results. Planet-disk interaction can result in prominent structures. This provides the opportunity of detecting and characterizing extrasolar planets in a range of masses and radial distances from the star that is not accessible to other techniques. Facilities that will be available in the near future are shown to provide the capabilities to spatially resolve and characterize structures in debris disks. Limitations are revealed and suggestions for possible instrument setups and observing strategies are given. In particular, ALMA is limited by its sensitivity to surface brightness, which requires a trade-off between sensitivity and spatial resolution. Space-based midinfrared observations will be able to detect and spatially resolve regions in debris disks even at a distance of several tens of AU from the star, where the emission from debris disks in this wavelength range is expected to be low. [Abridged]
High resolution ALMA observations revealed a variety of rich substructures in numerous protoplanetary disks. These structures consist of rings, gaps and asymmetric features. It is debated whether planets can be accounted for these substructures in the dust continuum. Characterizing the origin of asymmetries as seen in HD 163296 might lead to a better understanding of planet formation and the underlying physical parameters of the system. We test the possibility of the formation of the crescent-shaped asymmetry in the HD 163296 disk through planet-disk interaction. The goal is to obtain constraints on planet masses and eccentricities and disk viscosities. Two dimensional, multi-fluid, hydrodynamical simulations are performed with the FARGO3D code including three embedded planets. Dust is described with the pressureless fluid approach and is distributed over eight size bins. Resulting grids are post-processed with the radiative transfer code RADMC-3D and the CASA software to model synthetic observations. We find that the crescent-shaped asymmetry can be qualitatively modeled with a Jupiter mass planet at a radial distance of 48 au. Dust is trapped preferably in the trailing Lagrange point L5 with a mass of 10 to 15 earth masses. Increased values of eccentricity of the innermost Jupiter mass planet damages the stability of the crescent-shaped feature and does not reproduce the observed radial proximity to the first prominent ring in the system. Generally, a low level of viscosity ($alpha leq 2cdot10^{-3}$) is necessary to allow the existence of such a feature. Including dust feedback the leading point L4 can dominantly capture dust for dust grains with an initial Stokes number $leq 3.6cdot 10^{-2}$. The observational results suggest a negligible effect of dust feedback since only one such feature has been detected so far.
We carry out local three dimensional (3D) hydrodynamic simulations of planet-disk interaction in stratified disks with varied thermodynamic properties. We find that whenever the Brunt-Vaisala frequency (N) in the disk is nonzero, the planet exerts a strong torque on the disk in the vicinity of the planet, with a reduction in the traditional torque cutoff. In particular, this is true for adiabatic perturbations in disks with isothermal density structure, as should be typical for centrally irradiated protoplanetary disks. We identify this torque with buoyancy waves, which are excited (when N is non-zero) close to the planet, within one disk scale height from its orbit. These waves give rise to density perturbations with a characteristic 3D spatial pattern which is in close agreement with the linear dispersion relation for buoyancy waves. The torque due to these waves can amount to as much as several tens of per cent of the total planetary torque, which is not expected based on analytical calculations limited to axisymmetric or low-m modes. Buoyancy waves should be ubiquitous around planets in the inner, dense regions of protoplanetary disks, where they might possibly affect planet migration.
In this work, we study how the dust coagulation/fragmentation will influence the evolution and observational appearances of vortices induced by a massive planet embedded in a low viscosity disk by performing global 2D high-resolution hydrodynamical simulations. Within the vortex, due to its higher gas surface density and steeper pressure gradients, dust coagulation, fragmentation and drift (to the vortex center) are all quite efficient, producing dust particles ranging from micron to $sim 1.0 {rm cm}$, as well as overall high dust-to-gas ratio (above unity). In addition, the dust size distribution is quite non-uniform inside the vortex, with the mass weighted average dust size at the vortex center ($sim 4.0$ mm) being a factor of $sim10$ larger than other vortex regions. Both large ($sim$ mm) and small (tens of micron) particles contribute strongly to affect the gas motion within the vortex. As such, we find that the inclusion of dust coagulation has a significant impact on the vortex lifetime and the typical vortex lifetime is about 1000 orbits. After the initial gaseous vortex is destroyed, the dust spreads into a ring with a few remaining smaller gaseous vortices with a high dust concentration and a large maximum size ($sim$ mm). At late time, the synthetic dust continuum images for the coagulation case show as a ring inlaid with several hot spots at 1.33 mm band, while only distinct hot spots remain at 7.0 mm.
While numerical simulations have been playing a key role in the studies of planet-disk interaction, testing numerical results against observations has been limited so far. With the two directly imaged protoplanets embedded in its circumstellar disk, PDS 70 offers an ideal testbed for planet-disk interaction studies. Using two-dimensional hydrodynamic simulations we show that the observed features can be well explained with the two planets in formation, providing strong evidence that previously proposed theories of planet-disk interaction are in action, including resonant migration, particle trapping, size segregation, and filtration. Our simulations suggest that the two planets are likely in 2:1 mean motion resonance and can remain dynamically stable over million-year timescales. The growth of the planets at $10^{-8}-10^{-7}~M_{rm Jup}~{rm yr}^{-1}$, rates comparable to the estimates from H$alpha$ observations, does not destabilize the resonant configuration. Large grains are filtered at the gap edge and only small, (sub-)$mu$m grains can flow to the circumplanetary disks and the inner circumstellar disk. With the sub-millimeter continuum ring observed outward of the two directly imaged planets, PDS 70 provides the first observational evidence of particle filtration by gap-opening planets. The observed sub-millimeter continuum emission at the vicinity of the planets can be reproduced when (sub-)$mu$m grains survive over multiple circumplanetary disk gas viscous timescales and accumulate therein. One such possibility is if (sub-)$mu$m grains grow in size and remain trapped in pressure bumps, similar to what we find happening in circumstellar disks. We discuss potential implications to planet formation in the solar system and mature extrasolar planetary systems.
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