Dynamical corotation torques on low-mass planets

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.Comment: 14 pages, 13 figures, accepted for publication in MNRA

Growing and moving planets in disks

Planets form in disks that are commonly found around young stars. The intimate relationship that exists between planet and disk can account for a lot of the exotic extrasolar planetary systems known today. In this thesis we explore disk-planet interaction using numerical hydrodynamical simulations. We study the growth and migration of embedded planets, as well as the condition for gap formation in the disk. These planetary gaps provide an important link to future observations of circumstellar disks.UBL - phd migration 201

The formation of systems with closely spaced low-mass planets and the application to Kepler-36

The Kepler-36 system consists of two planets that are spaced unusually close together, near the 7:6 mean motion resonance. While it is known that mean motion resonances can easily form by convergent migration, Kepler-36 is an extreme case due to the close spacing and the relatively high planet masses of 4 and 8 times that of the Earth. In this paper, we investigate whether such a system can be obtained by interactions with the protoplanetary disc. These discs are thought to be turbulent and exhibit density fluctuations which might originate from the magneto-rotational instability. We adopt a realistic description for stochastic forces due to these density fluctuations and perform both long term hydrodynamical and N-body simulations. Our results show that planets in the Kepler-36 mass range can be naturally assembled into a closely spaced planetary system for a wide range of migration parameters in a turbulent disc similar to the minimum mass solar nebula. The final orbits of our formation scenarios tend to be Lagrange stable, even though large parts of the parameter space are chaotic and unstable.Comment: 13 pages, 8 figures, accepted for publication in MNRA

Buoyancy response of a disk to an embedded planet: a cross-code comparison at high resolution

In radiatively inefficient, laminar protoplanetary disks, embedded planets can excite a buoyancy response as gas gets deflected vertically near the planet. This results in vertical oscillations that drive a vortensity growth in the planet's corotating region, speeding up inward migration in the type-I regime. We present a comparison between PLUTO/IDEFIX and FARGO3D using 3D, inviscid, adiabatic numerical simulations of planet-disk interaction that feature the buoyancy response of the disk, and show that PLUTO/IDEFIX struggle to resolve higher-order modes of the buoyancy-related oscillations, weakening vortensity growth and the associated torque. We interpret this as a drawback of total-energy-conserving, finite-volume schemes. Our results indicate that a very high resolution or high-order scheme is required in shock-capturing codes in order to adequately capture this effect.Comment: 13 pages, 17 figures, 1 table; accepted by MNRA

Forming Circumbinary Planets: N-body Simulations of Kepler-34

Observations of circumbinary planets orbiting very close to the central stars have shown that planet formation may occur in a very hostile environment, where the gravitational pull from the binary should be very strong on the primordial protoplanetary disk. Elevated impact velocities and orbit crossings from eccentricity oscillations are the primary contributors towards high energy, potentially destructive collisions that inhibit the growth of aspiring planets. In this work, we conduct high resolution, inter-particle gravity enabled N-body simulations to investigate the feasibility of planetesimal growth in the Kepler-34 system. We improve upon previous work by including planetesimal disk self-gravity and an extensive collision model to accurately handle inter-planetesimal interactions. We find that super-catastrophic erosion events are the dominant mechanism up to and including the orbital radius of Kepler-34(AB)b, making in-situ growth unlikely. It is more plausible that Kepler-34(AB)b migrated from a region beyond 1.5 AU. Based on the conclusions that we have made for Kepler-34 it seems likely that all of the currently known circumbinary planets have also migrated significantly from their formation location with the possible exception of Kepler-47(AB)c.Comment: 6 pages, 5 figures, accepted for publication in ApJ

Vortex migration in protoplanetary disks

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.Comment: 13 pages, 13 figures, accepted for publication in Ap

Rapid inward migration of planets formed by gravitational instability

The observation of massive exoplanets at large separation from their host star, like in the HR 8799 system, challenges theories of planet formation. A possible formation mechanism involves the fragmentation of massive self-gravitating discs into clumps. While the conditions for fragmentation have been extensively studied, little is known of the subsequent evolution of these giant planet embryos, in particular their expected orbital migration. Assuming a single planet has formed by fragmentation, we investigate its interaction with the gravitoturbulent disc it is embedded in. Two-dimensional hydrodynamical simulations are used with a simple prescription for the disc cooling. A steady gravitoturbulent disc is first set up, after which simulations are restarted including a planet with a range of masses approximately equal to the clump's initial mass expected in fragmenting discs. Planets rapidly migrate inwards, despite the stochastic kicks due to the turbulent density fluctuations. We show that the migration timescale is essentially that of type I migration, with the planets having no time to open a gap. In discs with aspect ratio ~ 0.1 at their forming location, planets with a mass comparable to, or larger than Jupiter's can migrate in as short as 10000 years, that is, about 10 orbits at 100 AU. Massive planets formed at large separation from their star by gravitational instability are thus unlikely to stay in place, and should rapidly migrate towards the inner parts of protoplanetary discs, regardless of the planet mass.Comment: 13 pages, 10 figures, accepted for publication in MNRA

Numerical convergence in self-gravitating shearing sheet simulations and the stochastic nature of disc fragmentation

We study numerical convergence in local two-dimensional hydrodynamical simulations of self-gravitating accretion discs with a simple cooling law. It is well-known that there exists a steady gravito-turbulent state, in which cooling is balanced by dissipation of weak shocks, with a net outward transport of angular momentum. Previous results indicated that if cooling is too fast (typical time scale 3/Omega, where Omega is the local angular velocity), this steady state can not be maintained and the disc will fragment into gravitationally bound clumps. We show that, in the two-dimensional local approximation, this result is in fact not converged with respect to numerical resolution and longer time integration. Irrespective of the cooling time scale, gravito-turbulence consists of density waves as well as transient clumps. These clumps will contract because of the imposed cooling, and collapse into bound objects if they can survive for long enough. Since heating by shocks is very local, the destruction of clumps is a stochastic process. High numerical resolution and long integration times are needed to capture this behaviour. We have observed fragmentation for cooling times up to 20/Omega, almost a factor 7 higher than in previous simulations. Fully three-dimensional simulations with a more realistic cooling prescription are necessary to determine the effects of the use of the two-dimensional approximation and a simple cooling law.Comment: 15 pages, 10 figures, accepted for publication in MNRA

Planet-Disc Interactions and Early Evolution of Planetary Systems

The great diversity of extrasolar planetary systems has challenged our understanding of how planets form, and how their orbits evolve as they form. Among the various processes that may account for this diversity, the gravitational interaction between planets and their parent protoplanetary disc plays a prominent role in shaping young planetary systems. Planet-disc forces are large, and the characteristic times for the evolution of planets orbital elements are much shorter than the lifetime of protoplanetary discs. The determination of such forces is challenging, because it involves many physical mechanisms and it requires a detailed knowledge of the disc structure. Yet, the intense research of the past few years, with the exploration of many new avenues, represents a very significant improvement on the state of the discipline. This chapter reviews current understanding of planet-disc interactions, and highlights their role in setting the properties and architecture of observed planetary systems