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Register a new userMigrating Low-Mass Planets in Inviscid Dusty Protoplanetary Discs
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He-Feng Hsieh
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Disc-driven planet migration is integral to the formation of planetary systems. In standard, gas-dominated protoplanetary discs, low-mass planets or planetary cores undergo rapid inwards migration and are lost to the central star. However, several recent studies indicate that the solid component in protoplanetary discs can have a significant dynamical effect on disc-planet interaction, especially when the solid-to-gas mass ratio approaches unity or larger and the dust-on-gas drag forces become significant. As there are several ways to raise the solid abundance in protoplanetary discs, for example through disc winds and dust-trapping in pressure bumps, it is important to understand how planets migrate through a dusty environment. To this end, we study planet migration in dust-rich discs via a systematic set of high-resolution, two-dimensional numerical simulations. We show that the inwards migration of low-mass planets can be slowed down by dusty dynamical corotation torques. We also identify a new regime of stochastic migration applicable to discs with dust-to-gas mass ratios $gtrsim 0.3$ and particle Stokes numbers $gtrsim 0.03$. In these cases, disc-planet interaction leads to the continuous development of small-scale, intense dust vortices that scatter the planet, which can potentially halt or even reverse the inwards planet migration. We briefly discuss the observational implications of our results and highlight directions for future work.
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In the innermost regions of protoplanerary discs, the solid-to-gas ratio can be increased considerably by a number of processes, including photoevaporative and particle drift. MHD disc models also suggest the existence of a dead-zone at $Rlesssim 10$ AU, where the regions close to the midplane remain laminar. In this context, we use two-fluid hydrodynamical simulations to study the interaction between a low-mass planet ($sim 1.7 ;{rm M_oplus}$) on a fixed orbit and an inviscid pebble-rich disc with solid-to-gas ratio $epsilonge 0.5$. For pebbles with Stokes numbers St=0.1, 0.5, multiple dusty vortices are formed through the Rossby Wave Instability at the planet separatrix. Effects due to gas drag then lead to a strong enhancement in the solid-to-gas ratio, which can increase by a factor of $sim 10^3$ for marginally coupled particles with St=0.5. As in streaming instabilities, pebble clumps reorganize into filaments that may plausibly collapse to form planetesimals. When the planet is allowed to migrate in a MMSN disc, the vortex instability is delayed due to migration but sets in once inward migration stops due a strong positive pebble torque. Again, particle filaments evolving in a gap are formed in the disc while the planet undergoes an episode of outward migration. Our results suggest that vortex instabilities triggered by low-mass planets could play an important role in forming planetesimals in pebble-rich, inviscid discs, and may significantly modify the migration of low-mass planets. They also imply that planetary dust gaps may not necessarily contain planets if these migrated away.
Recent observations show that rings and gaps are ubiquitous in protoplanetary discs. These features are often interpreted as being due to the presence of planets; however, the effect of planetary migration on the observed morphology has not been investigated hitherto. In this work we investigate whether multiwavelength mm/submm observations can detect signatures of planet migration, using 2D dusty hydrodynamic simulations to model the structures generated by migrating planets and synthesising ALMA continuum observations at 0.85 and 3 mm. We identify three possible morphologies for a migrating planet: a slowly migrating planet is associated with a single ring outside the planets orbit, a rapidly migrating planet is associated with a single ring inside the planets orbit while a planet migrating at intermediate speed generates one ring on each side of the planets orbit. We argue that multiwavelength data can distinguish multiple rings produced by a migrating planet from other scenarios for creating multiple rings, such as multiple planets or discs with low viscosity. The signature of migration is that the outer ring has a lower spectral index, due to larger dust grains being trapped there. Of the recent ALMA observations revealing protoplanetary discs with multiple rings and gaps, we suggest that Elias 24 is the best candidate for a planet migrating in the intermediate speed regime.
Embedded planets disturb the density structure of the ambient disk and gravitational back-reaction will induce possibly a change in the planets orbital elements. The accurate determination of the forces acting on the planet requires careful numerical analysis. Recently, the validity of the often used fast orbital advection algorithm (FARGO) has been put into question, and special numerical resolution and stability requirements have been suggested. In this paper we study the process of planet-disk interaction for small mass planets of a few Earth masses, and reanalyze the numerical requirements to obtain converged and stable results. One focus lies on the applicability of the FARGO-algorithm. Additionally, we study the difference of two and three-dimensional simulations, compare global with local setups, as well as isothermal and adiabatic conditions. We study the influence of the planet on the disk through two- and three-dimensional hydrodynamical simulations. To strengthen our conclusions we perform a detailed numerical comparison where several upwind and Riemann-solver based codes are used with and without the FARGO-algorithm. With respect to the wake structure and the torque density acting on the planet we demonstrate that the FARGO-algorithm yields correct results, and that at a fraction of the regular cpu-time. We find that the resolution requirements for achieving convergent results in unshocked regions are rather modest and depend on the pressure scale height of the disk. By comparing the torque densities of 2D and 3D simulations we show that a suitable vertical averaging procedure for the force gives an excellent agreement between the two. We show that isothermal and adiabatic runs can differ considerably, even for adiabatic indices very close to unity.
Type-II migration of giant planets has a speed proportional to the discs viscosity for values of the alpha viscosity parameter larger than 1.e-4 . At lower viscosities previous studies, based on 2D simulations have shown that migration can be very chaotic and often characterized by phases of fast migration. The reason is that in low-viscosity discs vortices appear due to the Rossby-wave instability at the edges of the gap opened by the planet. Migration is then determined by vortex-planet interactions. Our aim is to study migration in low viscosity 3D discs. We performed numerical simulations using 2D (including self-gravity) and 3D codes. After selecting disc masses for which self-gravity is not important, 3D simulations without self-gravity can be safely used. In our nominal simulation only numerical viscosity is present. We then performed simulations with prescribed viscosity to assess the threshold below which the new migration processes appear. We show that for alpha viscosity <= 1.e-5 two migration modes are possible which differ from classical Type-II migration, in the sense that they are not proportional to the discs viscosity. The first occurs when the gap opened by the planet is not very deep. This occurs in 3D simulations and/or when a big vortex forms at the outer edge of the planetary gap, diffusing material into the gap. We call this type of migration vortex-driven migration. This migration is very slow and cannot continue indefinitely, because eventually the vortex dissolves. The second migration mode occurs when the gap is deep so that the planets eccentricity grows to a value ~0.2 due to inefficient eccentricity damping by corotation resonances. This second, faster migration mode appears to be typical of 2D models in discs with slower damping of temperatures perturbations.
We study the three-dimensional evolution of a viscous protoplanetary disc which accretes gas material from a second protoplanetary disc during a close encounter in an embedded star cluster. The aim is to investigate the capability of the mass accretion scenario to generate strongly inclined gaseous discs which could later form misaligned planets. We use smoothed particle hydrodynamics to study mass transfer and disc inclination for passing stars and circumstellar discs with different masses. We explore different orbital configurations to find the parameter space which allows significant disc inclination generation. citet{Thi2011} suggested that significant disc inclination and disc or planetary system shrinkage can generally be produced by the accretion of external gas material with a different angular momentum. We found that this condition can be fullfilled for a large range of gas mass and angular momentum. For all encounters, mass accretion from the secondary disc increases with decreasing mass of the secondary proto-star. Thus, higher disc inclinations can be attained for lower secondary stellar masses. Variations of the secondary discs orientation relative to the orbital plane can alter the disc evolution significantly. The results taken together show that mass accretion can change the three-dimensional disc orientation significantly resulting in strongly inclined discs. In combination with the gravitational interaction between the two star-disc systems, this scenario is relevant for explaining the formation of highly inclined discs which could later form misaligned planets.
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