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Register a new userCorotation torques experienced by planets embedded in weakly magnetized turbulent discs
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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.
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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.
We present the results of hydrodynamical simulations of the orbital evolution of planets undergoing runaway gas accretion in radiative discs. We consider accreting disc models with constant mass flux through the disc, and where radiative cooling balances the effect of viscous heating and stellar irradiation. We assume that 20-30 $M_oplus$ giant planet cores are formed in the region where viscous heating dominates and migrate outward under the action of a strong corotation torque. In the case where gas accretion is neglected, we find evidence for strong dynamical torques in accreting discs with accretion rates ${dot M}gtrsim 7times 10^{-8} ;M_odot/yr$. Their main effect is to increase outward migration rates by a factor of $sim 2$ typically. In the presence of gas accretion, however, runaway outward migration is observed with the planet passing through the zero-torque radius and the transition between the viscous heating and stellar heating dominated regimes. The ability for an accreting planet to enter a fast migration regime is found to depend strongly on the planet growth rate, but can occur for values of the mass flux through the disc of ${dot M}gtrsim 5times 10^{-8} ;M_odot/yr$. We find that an episode of runaway outward migration can cause an accreting planet formed in the 5-10 AU region to temporarily orbit at star-planet separations as large as $sim$60-70 AU. However, increase in the amplitude of the Lindblad torque associated with planet growth plus change in the streamline topology near the planet systematically cause the direction of migration to be reversed. Our results indicate that a planet can reach large orbital distances under the combined effect of dynamical torques and gas accretion, but an alternative mechanism is required to explain the presence of massive planets on wide orbits.
As of today ten circumbinary planets orbiting solar type main sequence stars have been discovered. Nearly all of them orbit around the central binary very closely to the region of instability where it is difficult to form them in situ. It is assumed that they formed further out and migrated to their observed position. We extend previous studies to a more realistic thermal disc structure and determine what parameter influence the final parking location of a planet around a binary star. We perform two-dimensional numerical simulations of viscous accretion discs around a central binary that include viscous heating and radiative cooling from the disc surfaces. We vary the binary eccentricity as well as disc viscosity and mass. Concerning the disc evolution we find that it can take well over 100000 binary orbits until an equilibrium state is reached. As seen previously, we find that the central cavity opened by the binary becomes eccentric and precesses slowly in a prograde sense. Embedded planets migrate to the inner edge of the disc. In cases of lower disc viscosity they migrate further in maintaining a circular orbit, while for high viscosity they are parked further out on an eccentric orbit. The final location of an embedded planet is linked to its ability to open a gap in the disc. Gap opening planets separate inner from outer disc, preventing eccentricity excitation in the latter and making it more circular. This allows embedded planets to migrate closer to the binary, in agreement with the observations. The necessary condition for gap opening and the final planet position depend on the planet mass and disc viscosity.
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.
Over the last few years instruments such as VLT/SPHERE and Subaru/HiCIAO have been able to take detailed scattered light images of protoplanetary discs. Many of the features observed in these discs are generally suspected to be caused by an embedded planet, and understanding the cause of these features requires detailed theoretical models. In this work we investigate disc-planet interactions using the PLUTO code to run 2D and 3D hydrodynamic simulations of protoplanetary discs with embedded 30 M$_{oplus}$ and 300 M$_{oplus}$ planets on both an inclined ($i = 2.86^{circ}$) and non-inclined orbit, using an $alpha$-viscosity of $4 times 10^{-3}$. We produce synthetic scattered-light images of these discs at emph{H-band} wavelengths using the radiative transfer code RADMC3D. We find that while the surface density evolution in 2D and 3D simulations of inclined and non-inclined planets remain fairly similar, their observational appearance is remarkably different. Most of the features seen in the synthetic emph{H-band} images are connected to density variations of the disc at around 3.3 scale heights above and below the midplane, which emphasizes the need for 3D simulations. Planets on sustained orbital inclinations disrupt the discs upper-atmosphere and produce radically different observable features and intensity profiles, including shadowing effects and intensity variation in the order of 10-20 times the surrounding background. The vertical optical depth to the disc midplane for emph{H-band} wavelengths is $tau approx 20$ in the disc gap created by the high-mass planet. We conclude that direct imaging of planets embedded in the disc remains difficult to observe, even for massive planets in the gap.
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