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Register a new userTorques felt by solid accreting planets
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Zsolt Regaly
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The solid material of protoplanetary discs forms an asymmetric pattern around a low-mass planet (M_p<=10M_Earth) due to the combined effect of dust-gas interaction and the gravitational attraction of the planet. Recently, it has been shown that although the total solid mass is negligible compared to that of gas in protoplanetary discs, a positive torque can be emerged by a certain size solid species. The torque magnitude can overcome that of gas which may result in outward planetary migration. In this study, we show that the accretion of solid species by the planet strengthens the magnitude of solid torque being either positive or negative. We run two-dimensional, high-resolution (1.5Kx3K) global hydrodynamic simulations of an embedded low-mass planet in a protoplanetary disc. The solid material is handled as a pressureless fluid. Strong accretion of well-coupled solid species by a M_p<0.3M_Earth protoplanet results in the formation of such a strongly asymmetric solid pattern close to the planet that the positive solid torque can overcome that of gas by two times. However, the accretion of solids in the pebble regime results in increased magnitude negative torque felt by protoplanets and strengthened positive torque for Earth-mass planets. For M_p>=3M_Earth planets the magnitude of the solid torque is positive, however, independent of the accretion strength investigated. We conclude that the migration of solid accreting planets can be substantially departed from the canonical type-I prediction.
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The migration of low-mass planets is driven by the differential Lindblad torque and the corotation torque in non-magnetic viscous models of protoplanetary discs. The corotation torque has recently received detailed attention as it may slow down, stall, or reverse migration. In laminar viscous disc models, the long-term evolution of the corotation torque is intimately related to viscous and thermal diffusion processes in the planets horseshoe region. This paper examines the properties of the corotation torque in discs where MHD turbulence develops as a result of the magnetorotational instability, considering a weak initial toroidal magnetic field. We present results of 3D MHD simulations carried out with two different codes. Non-ideal MHD effects and the discs vertical stratification are neglected, and locally isothermal disc models are considered. The running time-averaged torque exerted by the disc on a fixed planet is evaluated in three disc models. We first present results with an inner disc cavity (planet trap). As in viscous disc models, the planet is found to experience a positive running time-averaged torque over several hundred orbits, which highlights the existence of an unsaturated corotation torque maintained in the long term in MHD turbulent discs. Two disc models with initial power-law density and temperature profiles are also adopted, in which the time-averaged torque is found to be in decent agreement with its counterpart in laminar viscous disc models with similar viscosity at the planet location. Detailed analysis of the averaged torque density distributions indicates that the differential Lindblad torque takes very similar values in MHD turbulent and laminar viscous discs, and there exists an unsaturated corotation torque in MHD turbulent discs. This analysis also reveals the existence of an additional corotation torque in weakly magnetized discs.
We study torques on migrating low-mass planets in locally isothermal discs. Previous work on low-mass planets generally kept the planet on a fixed orbit, after which the torque on the planet was measured. In addition to these static torques, when the planet is allowed to migrate it experiences dynamical torques, which are proportional to the migration rate and whose sign depends on the background vortensity gradient. We show that in discs a few times more massive than the Minimum Mass Solar Nebula, these dynamical torques can have a profound impact on planet migration. Inward migration can be slowed down significantly, and if static torques lead to outward migration, dynamical torques can take over, taking the planet beyond zero-torque lines set by saturation of the corotation torque in a runaway fashion. This means the region in non-isothermal discs where outward migration is possible can be larger than what would be concluded from static torques alone.
A key process in planet formation is the exchange of angular momentum between a growing planet and the protoplanetary disc, which makes the planet migrate through the disc. Several works show that in general low-mass and intermediate-mass planets migrate towards the central star, unless corotation torques become dominant. Recently, a new kind of torque, called the thermal torque, was proposed as a new source that can generate outward migration of low-mass planets. While the Lindblad and corotation torques depend mostly on the properties of the protoplanetary disc and on the planet mass, the thermal torque depends also on the luminosity of the planet, arising mainly from the accretion of solids. Thus, the accretion of solids plays an important role not only in the formation of the planet but also in its migration process. In a previous work, we evaluated the thermal torque effects on planetary growth and migration mainly in the planetesimal accretion paradigm. In this new work, we study the role of the thermal torque within the pebble accretion paradigm. Computations are carried out consistently in the framework of a global model of planet formation that includes disc evolution, dust growth and evolution, and pebble formation. We also incorporate updated prescriptions of the thermal torque derived from high resolution hydrodynamical simulations. Our simulations show that the thermal torque generates extended regions of outward migration in low viscosity discs. This has a significant impact in the formation of the planets.
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