Gas and dust hydrodynamical simulations of massive lopsided transition discs - I. Gas distribution

Motivated by lopsided structures observed in some massive transition discs, we have carried out 2D numerical simulations to study vortex structure in massive discs, including the effects of disc self-gravity and the indirect force which is due to the displacement of the central star from the barycenter of the system by the lopsided structure. When only the indirect force is included, we confirm the finding by Mittal & Chiang (2015) that the vortex becomes stronger and can be more than two pressure scale heights wide, as long as the disc-to-star mass ratio is >1%. Such wide vortices can excite strong density waves in the disc and therefore migrate inwards rapidly. However, when disc self-gravity is also considered in simulations, self-gravity plays a more prominent role on the vortex structure. We confirm that when the disc Toomre Q parameter is smaller than pi/(2h), where h is the disc's aspect ratio, the vortices are significantly weakened and their inward migration slows down dramatically. Most importantly, when the disc is massive enough (e.g. Q~3), we find that the lopsided gas structure orbits around the star at a speed significantly slower than the local Keplerian speed. This sub-Keplerian pattern speed can lead to the concentration of dust particles at a radius beyond the lopsided gas structure (as shown in Paper II). Overall, disc self-gravity regulates the vortex structure in massive discs and the radial shift between the gas and dust distributions in vortices within massive discs may be probed by future observations.Comment: 10 pages, 7 figures, accepted for publication in MNRA

Formation, Orbital and Internal Evolutions of Young Planetary Systems

The growing body of observational data on extrasolar planets and protoplanetary disks has stimulated intense research on planet formation and evolution in the past few years. The extremely diverse, sometimes unexpected physical and orbital characteristics of exoplanets lead to frequent updates on the mainstream scenarios for planet formation and evolution, but also to the exploration of alternative avenues. The aim of this review is to bring together classical pictures and new ideas on the formation, orbital and internal evolutions of planets, highlighting the key role of the protoplanetary disk in the various parts of the theory. We begin by briefly reviewing the conventional mechanism of core accretion by the growth of planetesimals, and discuss a relatively recent model of core growth through the accretion of pebbles. We review the basic physics of planet-disk interactions, recent progress in this area, and discuss their role in observed planetary systems. We address the most important effects of planets internal evolution, like cooling and contraction, the mass-luminosity relation, and the bulk composition expressed in the mass-radius and mass-mean density relations.Comment: 49 pages, 12 figures, accepted for publication in Space Science Reviews. Chapter in International Space Science Institute (ISSI) Book on "The Disk in Relation to the Formation of Planets and their Proto-atmospheres" to be published in Space Science Reviews by Springe

Gravito-inertial waves in a differentially rotating spherical shell

The gravito-inertial waves propagating over a shellular baroclinic flow inside a rotating spherical shell are analysed using the Boussinesq approximation. The wave properties are examined by computing paths of characteristics in the non-dissipative limit, and by solving the full dissipative eigenvalue problem using a high-resolution spectral method. Gravito-inertial waves are found to obey a mixed-type second-order operator and to be often focused around short-period attractors of characteristics or trapped in a wedge formed by turning surfaces and boundaries. We also find eigenmodes that show a weak dependence with respect to viscosity and heat diffusion just like truly regular modes. Some axisymmetric modes are found unstable and likely destabilized by baroclinic instabilities. Similarly, some non-axisymmetric modes that meet a critical layer (or corotation resonance) can turn unstable at sufficiently low diffusivities. In all cases, the instability is driven by the differential rotation. For many modes of the spectrum, neat power laws are found for the dependence of the damping rates with diffusion coefficients, but the theoretical explanation for the exponent values remains elusive in general. The eigenvalue spectrum turns out to be very rich and complex, which lets us suppose an even richer and more complex spectrum for rotating stars or planets that own a differential rotation driven by baroclinicity.Comment: 33 pages, 14 figures, accepted for publication in Journal of Fluid Mechanic

Using planet migration and dust drift to weigh protoplanetary discs

ALMA has spatially resolved over 200 annular structures in protoplanetary discs, many of which are suggestive of the presence of planets. Constraining the mass of these putative planets is quite degenerate for it depends on the disc physical properties, and for simplicity a steady-state is often assumed whereby the planet position is kept fixed and there is a constant source of dust at the outer edge of the disc. Here we argue against this approach by demonstrating how the planet and dust dynamics can lift degeneracies of such steady-state models. We take main disc parameters from the well-known protoplanetary disc HD 163296 with a suspected planet at $R\approx 86$~au as an example. By running gas and dust hydrodynamical simulations post-processed with dust radiative transfer calculations, we first find steady-state disc and planet parameters that reproduce ALMA continuum observations fairly well. For the same disc mass, but now allowing the planet to migrate in the simulation, we find that the planet undergoes runaway migration and reaches the inner disc in $\sim 0.2$ Myr. Further, decreasing the disc mass slows down planet migration, but it then also increases the dust's radial drift, thereby depleting the disc dust faster. We find that the opposing constraints of planet migration and dust drift require the disc mass to be at most 0.025~\msun, must less massive than previously estimated, and for the dust to be porous rather than compact. We propose that similar analysis should be extended to other sources with suspected planetary companions.Comment: 15 pages, 9 figures, resubmitted to MNRAS, version addressing referee's comment

The complex interplay between tidal inertial waves and zonal flows in differentially rotating stellar and planetary convective regions:I. Free waves

Quantifying tidal interactions in close-in two-body systems is of prime interest since they have a crucial impact on the architecture and on the rotational history of the bodies. Various studies have shown that the dissipation of tides in either body is very sensitive to its structure and to its dynamics, like differential rotation which exists in the outer convective enveloppe of solar-like stars and giant gaseous planets. In particular, tidal waves may strongly interact with zonal flows at the so-called corotation resonances, where the wave's Doppler-shifted frequency cancels out. We aim to provide a deep physical understanding of the dynamics of tidal inertial waves at corotation resonances, in the presence of differential rotation profiles typical of low-mass stars and giant planets. By developping an inclined shearing box, we investigate the propagation and the transmission of free inertial waves at corotation, and more generally at critical levels, which are singularities in the governing wave differential equation. Through the construction of an invariant called the wave action flux, we identify different regimes of wave transmission at critical levels, which are confirmed with a one-dimensional three-layer numerical model. We find that inertial waves can be either fully transmitted, strongly damped, or even amplified after crossing a critical level. The occurrence of these regimes depends on the assumed profile of differential rotation, on the nature as well as the latitude of the critical level, and on wave parameters such as the inertial frequency and the longitudinal and vertical wavenumbers. Waves can thus either deposit their action flux to the fluid when damped at critical levels, or they can extract action flux to the fluid when amplified at critical levels. Both situations could lead to significant angular momentum exchange between the tidally interacting bodies.Comment: 25 pages, 12 figures, 4 tables, accepted for publication in Astronomy & Astrophysic

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

No snow-plough mechanism during the rapid hardening of supermassive black hole binaries

We present two-dimensional hydrodynamical simulations of the tidal interaction between a supermassive black hole binary with moderate mass ratio, and the fossil gas disc where it is embedded. Our study extends previous one-dimensional height-integrated disc models, which predicted that the density of the gas disc between the primary and the secondary black holes should rise significantly during the ultimate stages of the binary's hardening driven by the gravitational radiation torque. This snow-plough mechanism, as we call it, would lead to an increase in the bolometric luminosity of the system prior to the binary merger, which could be detected in conjunction with the gravitational wave signal. We argue here that the snow-plough mechanism is unlikely to occur. In two-dimensions, when the binary's hardening timescale driven by gravitational radiation becomes shorter than the disc's viscous drift timescale, fluid elements in the inner disc get funneled to the outer disc through horseshoe trajectories with respect to the secondary. Mass leakage across the secondary's gap is thus found to be effective and, as a result, the predicted accretion disc luminosity will remain at roughly the same level prior to merger.Comment: 5 pages, 5 figures, accepted for publication in MNRA

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 ~ 4 $\Omega^{-1}$, where $\Omega$ is the local angular velocity.Comment: 5 pages, 5 figures, accepted for publication in MNRA

The Disk Substructures at High Angular Resolution Project (DSHARP). VII. The Planet–Disk Interactions Interpretation

The Disk Substructures at High Angular Resolution Project (DSHARP) provides a large sample of protoplanetary disks with substructures that could be induced by young forming planets. To explore the properties of planets that may be responsible for these substructures, we systematically carry out a grid of 2D hydrodynamical simulations, including both gas and dust components. We present the resulting gas structures, including the relationship between the planet mass, as well as (1) the gaseous gap depth/width and (2) the sub/super-Keplerian motion across the gap. We then compute dust continuum intensity maps at the frequency of the DSHARP observations. We provide the relationship between the planet mass, as well as (1) the depth/width of the gaps at millimeter intensity maps, (2) the gap edge ellipticity and asymmetry, and (3) the position of secondary gaps induced by the planet. With these relationships, we lay out the procedure to constrain the planet mass using gap properties, and study the potential planets in the DSHARP disks. We highlight the excellent agreement between observations and simulations for AS 209 and the detectability of the young solar system analog. Finally, under the assumption that the detected gaps are induced by young planets, we characterize the young planet population in the planet mass–semimajor axis diagram. We find that the occurrence rate for \u3e5 M J planets beyond 5–10 au is consistent with direct imaging constraints. Disk substructures allow us to probe a wide-orbit planet population (Neptune to Jupiter mass planets beyond 10 au) that is not accessible to other planet searching techniques

Dust traps in the protoplanetary disc MWC 758: two vortices produced by two giant planets?

Resolved ALMA and VLA observations indicate the existence of two dust traps in the protoplanetary disc MWC 758. By means of 2D gas+dust hydrodynamical simulations post-processed with 3D dust radiative transfer calculations, we show that the spirals in scattered light, the eccentric, asymmetric ring and the crescent-shaped structure in the (sub)millimetre can all be caused by two giant planets: a 1.5-Jupiter mass planet at 35 au (inside the spirals) and a 5-Jupiter mass planet at 140 au (outside the spirals). The outer planet forms a dust-trapping vortex at the inner edge of its gap (at ~85 au), and the continuum emission of this dust trap reproduces the ALMA and VLA observations well. The outer planet triggers several spiral arms which are similar to those observed in polarised scattered light. The inner planet also forms a vortex at the outer edge of its gap (at ~50 au), but it decays faster than the vortex induced by the outer planet, as a result of the disc's turbulent viscosity. The vortex decay can explain the eccentric inner ring seen with ALMA as well as the low signal and larger azimuthal spread of this dust trap in VLA observations. Finding the thermal and kinematic signatures of both giant planets could verify the proposed scenario.Comment: 18 pages, 8 figures, accepted for publication in MNRA