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Register a new userSimulating planet migration in globally evolving disks
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Numerical simulations of planet-disk interactions are usually performed with hydro-codes that -- because they consider only an annulus of the disk, over a 2D grid -- can not take into account the global evolution of the disk. However, the latter governs planetary migration of type II, so that the accuracy of the planetary evolution can be questioned. To develop an algorithm that models the local planet-disk interactions together with the global viscous evolution of the disk, we surround the usual 2D grid with a 1D grid ranging over the real extension of the disk. The 1D and 2D grids are coupled at their common boundaries via ghost rings, paying particular attention to the fluxes at the interface, especially the flux of angular momentum carried by waves. The computation is done in the frame centered on the center of mass to ensure angular momentum conservation. The global evolution of the disk and the local planet-disk interactions are both well described and the feedback of one on the other can be studied with this algorithm, for a negligible additional computing cost with respect to usual algorithms.
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We describe 2D hydrodynamic simulations of the migration of low-mass planets ($leq 30 M_{oplus}$) in nearly laminar disks (viscosity parameter $alpha < 10^{-3}$) over timescales of several thousand orbit periods. We consider disk masses of 1, 2, and 5 times the minimum mass solar nebula, disk thickness parameters of $H/r = 0.035$ and 0.05, and a variety of $alpha$ values and planet masses. Disk self-gravity is fully included. Previous analytic work has suggested that Type I planet migration can be halted in disks of sufficiently low turbulent viscosity, for $alpha sim 10^{-4}$. The halting is due to a feedback effect of breaking density waves that results in a slight mass redistribution and consequently an increased outward torque contribution. The simulations confirm the existence of a critical mass ($M_{cr} sim 10 M_{oplus}$) beyond which migration halts in nearly laminar disks. For $alpha ga 10^{-3}$, density feedback effects are washed out and Type I migration persists. The critical masses are in good agreement with the analytic model of Rafikov (2002). In addition, for $alpha la 10^{-4}$ steep density gradients produce a vortex instability, resulting in a small time-varying eccentricity in the planets orbit and a slight outward migration. Migration in nearly laminar disks may be sufficiently slow to reconcile the timescales of migration theory with those of giant planet formation in the core accretion model.
Planet migration originally refers to protoplanetary disks, which are more massive and dense than typical accretion disks in binary systems. We study planet migration in an accretion disk in a binary system consisting of a solar-like star hosting a planet and a red giant donor star. The accretion disk is fed by a stellar wind. %, disk self-gravity is neglected. We use the $alpha$-disk model and consider that the stellar wind is time-dependent. Assuming the disk is quasi-stationary we calculate its temperature and surface density profiles. In addition to the standard disk model, when matter is captured by the disk at its outer edge, we study the situation when the stellar wind delivers matter on the whole disc surface inside the accretion radius with the rate depending on distance from the central star. Implying that a planet experiences classical type I/II migration we calculate migration time for a planet on a circular orbit coplanar with the disk. Potentially, rapid inward planet migration can result in a planet-star merger which can be accompanied by an optical or/and UV/X-ray transient. We calculate timescale of migration for different parameters of planets and binaries. Our results demonstrate that planets can fall on their host stars within the lifetime of the late-type donor for realistic sets of parameters.
The increasing number of newly detected exoplanets at short orbital periods raises questions about their formation and migration histories. A particular puzzle that requires explanation arises from one of the key results of the Kepler mission, namely the increase in the planetary occurrence rate with orbital period up to 10 days for F, G, K and M stars. We investigate the conditions for planet formation and migration near the dust sublimation front in protostellar disks around young Sun-like stars. For this analysis we use iterative 2D radiation hydrostatic disk models which include irradiation by the star, and dust sublimation and deposition depending on the local temperature and vapor pressure. We perform a parameter study by varying the magnetized turbulence onset temperature, the accretion stress, the dust mass fraction, and the mass accretion rate. Our models feature a gas-only inner disk, a silicate sublimation front and dust rim starting at around 0.08 au, an ionization transition zone with a corresponding density jump, and a pressure maximum which acts as a pebble trap at around 0.12 au. Migration torque maps show Earth- and super-Earth-mass planets halt in our model disks at orbital periods ranging from 10 to 22 days. Such periods are in good agreement with both the inferred location of the innermost planets in multiplanetary systems, and the break in planet occurrence rates from the Kepler sample at 10 days. In particular, models with small grains depleted produce a trap located at a 10-day orbital period, while models with a higher abundance of small grains present a trap at around a 17-day orbital period. The snow line lies at 1.6 au, near where the occurrence rate of the giant planets peaks. We conclude that the dust sublimation zone is crucial for forming close-in planets, especially when considering tightly packed super-Earth systems.
We consider the radial migration of vortices in two-dimensional isothermal gaseous disks. We find that a vortex core, orbiting at the local gas velocity, induces velocity perturbations that propagate away from the vortex as density waves. The resulting spiral wave pattern is reminiscent of an embedded planet. There are two main causes for asymmetries in these wakes: geometrical effects tend to favor the outer wave, while a radial vortensity gradient leads to an asymmetric vortex core, which favors the wave at the side that has the lowest density. In the case of asymmetric waves, which we always find except for a disk of constant pressure, there is a net exchange of angular momentum between the vortex and the surrounding disk, which leads to orbital migration of the vortex. Numerical hydrodynamical simulations show that this migration can be very rapid, on a time scale of a few thousand orbits, for vortices with a size comparable to the scale height of the disk. We discuss the possible effects of vortex migration on planet formation scenarios.
The known exoplanet population displays a great diversity of orbital architectures, and explaining the origin of this is a major challenge for planet formation theories. The gravitational interaction between young planets and their protoplanetary disks provides one way in which planetary orbits can be shaped during the formation epoch. Disk-planet interactions are strongly influenced by the structure and physical processes that drive the evolution of the protoplanetary disk. In this review we focus on how disk-planet interactions drive the migration of planets when different assumptions are made about the physics of angular momentum transport, and how it drives accretion flows in protoplanetary disk models. In particular, we consider migration in discs where: (i) accretion flows arise because turbulence diffusively transports angular momentum; (ii) laminar accretion flows are confined to thin, ionised layers near disk surfaces and are driven by the launching of magneto-centrifugal winds, with the midplane being completely inert; (iii) laminar accretion flows pervade the full column density of the disc, and are driven by a combination of large scale horizontal and vertical magnetic fields.
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