Clement Baruteau

Rapid inward migration of planets formed by gravitational instability

The observation of massive exoplanets at large separation (10 au) 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. 2D 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 time-scale 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 10 4 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.

HOW NOT TO BUILD TATOOINE: THE DIFFICULTY OF IN SITU FORMATION OF CIRCUMBINARY PLANETS KEPLER 16b, KEPLER 34b, AND KEPLER 35b

We study planetesimal evolution in circumbinary disks, focusing on the three systems Kepler 16, 34, and 35 where planets have been discovered recently. We show that for circumbinary planetesimals, in addition to secular forcing, eccentricities evolve on a dynamical timescale, which leads to orbital crossings even in the presence of gas drag. This makes the current locations of the circumbinary Kepler planets hostile to planetesimal accretion. We then present results from simulations including planetesimal formation and dust accretion, and show that even in the most favorable case of 100% efficient dust accretion, in situ growth starting from planetesimals smaller than ~10 km is difficult for Kepler 16b, Kepler 34b, and Kepler 35b. These planets were likely assembled further out in the disk, and migrated inward to their current location.

Numerical convergence in self-gravitating disc simulations: initial conditions and edge effects

We study the numerical convergence of hydrodynamical simulations of self-gravitating accretion discs, in which a simple cooling law is balanced by shock heating. It is well known that there exists a critical cooling time-scale for which shock heating can no longer compensate for the energy losses, at which point the disc fragments. The numerical convergence of previous results of this critical cooling time-scale was questioned recently using smoothed particle hydrodynamics (SPH). We employ a two-dimensional grid-based code to study this problem and find that for smooth initial conditions, fragmentation is possible for slower cooling as the resolution is increased, in agreement with recent SPH results. We show that this non-convergence is at least partly due to the creation of a special location in the disc, the boundary between the turbulent and the laminar region, when cooling towards a gravito-turbulent state. Converged results appear to be obtained in setups where no such sharp edges appear, and we then find a critical cooling time-scale of ∼4Ω−1, where Ω is the local angular velocity.

Non-linear evolution of tidally forced inertial waves in rotating fluid bodies

We perform one of the first studies into the nonlinear evolution of tidally excited inertial waves in a uniformly rotating fluid body, exploring a simplified model of the fluid envelope of a planet (or the convective envelope of a solar-type star) subject to the gravitational tidal perturbations of an orbiting companion. Our model contains a perfectly rigid spherical core, which is surrounded by an envelope of incompressible uniform density fluid. The corresponding linear problem was studied in previous papers which this work extends into the nonlinear regime, at moderate Ekman numbers (the ratio of viscous to Coriolis accelerations). By performing high-resolution numerical simulations, using a combination of pseudo-spectral and spectral element methods, we investigate the effects of nonlinearities, which lead to time-dependence of the flow and the corresponding dissipation rate. Angular momentum is deposited non-uniformly, leading to the generation of significant differential rotation in the initially uniformly rotating fluid, i.e. the body does not evolve towards synchronism as a simple solid body rotator. This differential rotation modifies the properties of tidally excited inertial waves, changes the dissipative properties of the flow, and eventually becomes unstable to a secondary shear instability provided that the Ekman number is sufficiently small. Our main result is that the inclusion of nonlinearities eventually modifies the flow and the resulting dissipation from what linear calculations would predict, which has important implications for tidal dissipation in fluid bodies. We finally discuss some limitations of our simplified model, and propose avenues for future research to better understand the tidal evolution of rotating planets and stars. ; Comment: 17 pages, 17 figures, accepted for publication in MNRAS

A hot Jupiter orbiting a 2-million-year-old solar-mass T Tauri star

Hot Jupiters are giant Jupiter-like exoplanets that orbit their host stars 100 times more closely than Jupiter orbits the Sun. These planets presumably form in the outer part of the primordial disk from which both the central star and surrounding planets are born, then migrate inwards and yet avoid falling into their host star. It is, however, unclear whether this occurs early in the lives of hot Jupiters, when they are still embedded within protoplanetary disks, or later, once multiple planets are formed and interact. Although numerous hot Jupiters have been detected around mature Sun-like stars, their existence has not yet been firmly demonstrated for young stars, whose magnetic activity is so intense that it overshadows the radial velocity signal that close-in giant planets can induce. Here we report that the radial velocities of the young star V830 Tau exhibit a sine wave of period 4.93 days and semi-amplitude 75 metres per second, detected with a false-alarm probability of less than 0.03 per cent, after filtering out the magnetic activity plaguing the spectra. We find that this signal is unrelated to the 2.741-day rotation period of V830 Tau and we attribute it to the presence of a planet of mass 0.77 times that of Jupiter, orbiting at a distance of 0.057 astronomical units from the host star. Our result demonstrates that hot Jupiters can migrate inwards in less than two million years, probably as a result of planet–disk interactions.

Influence of the circumbinary disk gravity on planetesimal accumulation in the Kepler-16 system

Context. Recent observations from NASA’s Kepler mission detected the first planets in circumbinary orbits. The question we try to answer is where these planets formed in the circumbinary disk and how far inside they migrated to reach their present location. Aims. We investigate the first and most delicate phase of planet formation when planetesimals accumulate to form planetary embryos. Methods. We use the hydrodynamical code FARGO to study the evolution of the disk and of a test population of planetesimals embedded in it. With this hybrid hydrodynamical-N-body code we can properly account for the gas drag force on the planetesimals and for the gravitational force of the disk on them. Results. The numerical simulations show that the gravity of the eccentric disk on the planetesimal swarm excites their eccentricities to much higher values than those induced by the binary perturbations only within 10 AU from the stars. Moreover, the disk gravity prevents a full alignment of the planetesimal pericenters. Both these effects lead to high impact velocities, beyond the critical value for erosion. Conclusions. Planetesimal accumulation in circumbinary disks appears to be prevented close to the stellar pair by the gravitational perturbations of the circumbinary disk. The observed planets possibly formed in the outer regions of the disk and then migrated inside by tidal interaction with the disk.

Inertial waves in a differentially rotating spherical shell

We investigate the properties of small-amplitude inertial waves propagating in a differentially rotating incompressible fluid contained in a spherical shell. For cylindrical and shellular rotation profiles and in the inviscid limit, inertial waves obey a second-order partial differential equation of mixed type. Two kinds of inertial modes therefore exist, depending on whether the hyperbolic domain where characteristics propagate covers the whole shell or not. The occurrence of these two kinds of inertial modes is examined, and we show that the range of frequencies at which inertial waves may propagate is broader than with solid-body rotation. Using high-resolution calculations based on a spectral method, we show that, as with solid-body rotation, singular modes with thin shear layers following short-period attractors still exist with differential rotation. They exist even in the case of a full sphere. In the limit of vanishing viscosities, the width of the shear layers seems to weakly depend on the global background shear, showing a scaling in E^{1/3} with the Ekman number E, as in the solid-body rotation case. There also exist modes with thin detached layers of width scaling with E^{1/2} as Ekman boundary layers. The behavior of inertial waves with a corotation resonance within the shell is also considered. For cylindrical rotation, waves get dramatically absorbed at corotation. In contrast, for shellular rotation, waves may cross a critical layer without visible absorption, and such modes can be unstable for small enough Ekman numbers.

Corotation torques experienced by planets embedded in weakly magnetized turbulent discs

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.

Gas and dust hydrodynamical simulations of massive lopsided transition discs – II. Dust concentration

We investigate the dynamics of large dust grains in massive lopsided transition discs via 2D hydrodynamical simulations including both gas and dust. Our simulations adopt a ring-like gas density profile that becomes unstable against the Rossby-wave instability and forms a large crescent-shaped vortex. When gas self-gravity is discarded, but the indirect force from the displacement of the star by the vortex is included, we confirm that dust grains with stopping times of order the orbital time, which should be typically a few centimetres in size, are trapped ahead of the vortex in the azimuthal direction, while the smallest and largest grains concentrate towards the vortex centre. We obtain maximum shift angles of about 25 degrees. Gas self-gravity accentuates the concentration differences between small and large grains. At low to moderate disc masses, the larger the grains, the farther they are trapped ahead of the vortex. Shift angles up to 90 degrees are reached for 10 cm-sized grains, and we show that such large offsets can produce a double-peaked continuum emission observable at mm/cm wavelengths. This behaviour comes about because the large grains undergo horseshoe U-turns relative to the vortex due to the vortexs gravity. At large disc masses, since the vortexs pattern frequency becomes increasingly slower than Keplerian, small grains concentrate slightly beyond the vortex and large grains form generally non-axisymmetric ring-like structures around the vortexs radial location. Gas self-gravity therefore imparts distinct trapping locations for small and large dust grains which may be probed by current and future observations, and which suggest that the formation of planetesimals in vortices might be more difficult than previously thought.

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.