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Register a new userNumerical simulations of type III planetary migration: II. Inward migration of massive planets
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We present a numerical study of rapid, so called type III migration for Jupitersized planets embedded in a protoplanetary disc. We limit ourselves to the case of inward migration, and study in detail its evolution and physics, concentrating on the structure of the corotation and circumplanetary regions, and processes for stopping migration. We also consider the dependence of the migration behaviour on several key parameters. We perform this study using the results of global, two-dimensional hydrodynamical simulations with adaptive mesh refinement. The initial conditions are chosen to satisfy the condition for rapid inward migration. We find that type III migration can be divided into two regimes, fast and slow. The structure of the coorbital region, mass accumulation rate, and migration behaviour differ between these two regimes. All our simulations show a transition from the fast to the slow regime, ending type III migration well before reaching the star. The stopping radius is found to be larger for more massive planets and less massive discs. A sharp density drop is also found to be an efficient stopping mechanism. In the fast migration limit the migration rate and induced eccentricity are lower for less massive discs, but almost do not depend on planet mass. Eccentricity is damped on the migration time scale.
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We present a numerical study of rapid, so called type III migration for Jupiter-sized planets embedded in a protoplanetary disc. We limit ourselves to the case of outward migration, and study in detail its evolution and physics, concentrating on the structure of the co-rotation and circumplanetary regions, and processes for stopping migration. We also consider the dependence of the migration behaviour on several key parameters. We perform this study using global, two-dimensional hydrodynamical simulations with adaptive mesh refinement. We find that the outward directed type III migration can be started if the initial conditions support $Z > 1$, that corresponds to initial value $M_rmn{Delta} ga 1.5$. Unlike the inward directed migration, in the outward migration the migration rate increases due to the growing of the volume of the co-orbital region. We find the migration to be strongly dependent on the rate of the mass accumulation in the circumplanetary disc, leading to two possible regimes of migration, fast and slow. The structure of the co-orbital region and the stopping mechanism differ between these two regimes.
Planetary systems are born in the disks of gas, dust and rocky fragments that surround newly formed stars. Solid content assembles into ever-larger rocky fragments that eventually become planetary embryos. These then continue their growth by accreting leftover material in the disc. Concurrently, tidal effects in the disc cause a radial drift in the embryo orbits, a process known as migration. Fast inward migration is predicted by theory for embryos smaller than three to five Earth masses. With only inward migration, these embryos can only rarely become giant planets located at Earths distance from the Sun and beyond, in contrast with observations. Here we report that asymmetries in the temperature rise associated with accreting infalling material produce a force (which gives rise to an effect that we call heating torque) that counteracts inward migration. This provides a channel for the formation of giant planets and also explains the strong planet-metallicity correlation found between the incidence of giant planets and the heavy-element abundance of the host stars.
During their formation, emerging protoplanets tidally interact with their natal disks. Proto-gas-giant planets, with Hills radius larger than the disk thickness, open gaps and quench gas flow in the vicinity of their orbits. It is usually assumed that their type II migration is coupled to the viscous evolution of the disk. Although this hypothesis provides an explanation for the origin of close-in planets, it also encounter predicament on the retention of long-period orbits for most gas giant planets. Moreover, numerical simulations indicate that planets migrations are not solely determined by the viscous diffusion of their natal disk. Here we carry out a series of hydrodynamic simulations combined with analytic studies to examine the transition between different paradigms of type II migration. We find a range of planetary mass for which gas continues to flow through a severely depleted gap so that the surface density distribution in the disk region beyond the gap is maintained in a quasi-steady state. The associated gap profile modifies the location of corotation & Lindblad resonances. In the proximity of the planets orbit, high-order Lindblad & corotation torque are weakened by the gas depletion in the gap while low-order Lindblad torques near the gap walls preserves their magnitude. Consequently, the intrinsic surface density distribution of the disk determines delicately both pace and direction of planets type II migration. We show that this effect might stall the inward migration of giant planets and preserve them in disk regions where the surface density is steep.
Studies of planet migration derived from disc planet interactions began before the discovery of exoplanets. The potential importance of migration for determining orbital architectures being realised, the field received greater attention soon after the initial discoveries of exoplanets. Early studies based on very simple disc models indicated very fast migration times for low mass planets that raised questions about its relevance. However, more recent studies, made possible with improving resources, that considered improved physics and disc models revealed processes that could halt or reverse this migration. That in turn led to a focus on special regions in the disc where migration could be halted. In this way the migration of low mass planets could be reconciled with formation theories. In the case of giant planets which have a nonlinear interaction with the disc, the migration should be slower and coupled to the evolution of the disc. The latter needs to be considered more fully to make future progress in all cases. Here we are primarily concerned with processes where migration is connected with the presence of the protopolanetary disk. Migration may also be induced by disc-free gravitational interactions amongst planets or with binary companions. This is only briefly discussed here.
Multiple planet systems provide an ideal laboratory for probing exoplanet composition, formation history and potential habitability. For the TRAPPIST-1 planets, the planetary radii are well established from transits (Gillon et al., 2016, Gillon et al., 2017), with reasonable mass estimates coming from transit timing variations (Gillon et al., 2017, Wang et al., 2017) and dynamical modeling (Quarles et al., 2017). The low bulk densities of the TRAPPIST-1 planets demand significant volatile content. Here we show using mass-radius-composition models, that TRAPPIST-1f and g likely contain substantial ($geq50$ wt%) water/ice, with b and c being significantly drier ($leq15$ wt%). We propose this gradient of water mass fractions implies planets f and g formed outside the primordial snow line whereas b and c formed inside. We find that compared to planets in our solar system that also formed within the snow line, TRAPPIST-1b and c contain hundreds more oceans worth of water. We demonstrate the extent and timescale of migration in the TRAPPIST-1 system depends on how rapidly the planets formed and the relative location of the primordial snow line. This work provides a framework for understanding the differences between the protoplanetary disks of our solar system versus M dwarfs. Our results provide key insights into the volatile budgets, timescales of planet formation, and migration history of likely the most common planetary host in the Galaxy.
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