We present two new Lagrangian methods for hydrodynamics, in a systematic comparison with moving-mesh, smoothed particle hydrodynamics (SPH), and stationary (non-moving) grid methods. The new methods are designed to simultaneously capture advantages of both SPH and grid-based/adaptive mesh refinement (AMR) schemes. They are based on a kernel discretization of the volume coupled to a high-order matrix gradient estimator and a Riemann solver acting over the volume ‘overlap’. We implement and test a parallel, second-order version of the method with self-gravity and cosmological integration, in the code gizmo:1 this maintains exact mass, energy and momentum conservation; exhibits superior angular momentum conservation compared to all other methods we study; does not require ‘artificial diffusion’ terms; and allows the fluid elements to move with the flow, so resolution is automatically adaptive. We consider a large suite of test problems, and find that on all problems the new methods appear competitive with moving-mesh schemes, with some advantages (particularly in angular momentum conservation), at the cost of enhanced noise. The new methods have many advantages versus SPH: proper convergence, good capturing of fluid-mixing instabilities, dramatically reduced ‘particle noise’ and numerical viscosity, more accurate sub-sonic flow evolution, and sharp shock-capturing. Advantages versus non-moving meshes include: automatic adaptivity, dramatically reduced advection errors and numerical overmixing, velocity-independent errors, accurate coupling to gravity, good angular momentum conservation and elimination of ‘grid alignment’ effects. We can, for example, follow hundreds of orbits of gaseous discs, while AMR and SPH methods break down in a few orbits. However, fixed meshes minimize ‘grid noise’. These differences are important for a range of astrophysical problems.

A new class of accurate, mesh-free hydrodynamic simulation methods

As planets form and grow within gaseous protoplanetary disks, the mutual gravitational interaction between the disk and planet leads to the exchange of angular momentum and migration of the planet. We review current understanding of disk-planet interactions, focusing in particular on physical processes that determine the speed and direction of migration. We describe the evolution of low-mass planets embedded in protoplanetary disks and examine the influence of Lindblad and corotation torques as a function of the disk properties. The role of the disk in causing the evolution of eccentricities and inclinations is also discussed. We describe the rapid migration of intermediate-mass planets that may occur as a runaway process and examine the transition to gap formation and slower migration driven by the viscous evolution of the disk for massive planets. The roles and influence of disk self-gravity and magnetohydrodynamic turbulence are discussed in detail, as a function of the planet mass, as is the evolution...

/pdf/planet-disk-interaction-and-orbital-evolution-30h99z7v4g.pdf

Planet-Disk Interaction and Orbital Evolution

Planets are built from planetesimals: solids larger than a kilometer that grow by colliding in pairs. Planetesimals themselves are unlikely to form by twobody collisions alone; subkilometer objects have gravitational fields individually too weak, and electrostatic attraction is too feeble for growth beyond a few centimeters. We review the possibility that planetesimals form when self-gravity brings together vast ensembles of small particles. Even when self-gravity is weak, aerodynamic processes can accumulate solids relative to gas, paving the way for gravitational collapse. Particles pile up as they drift radially inward. Gas turbulence stirs particles but can also seed collapse by clumping them. Whereas the feedback of solids on gas triggers vertical-shear instabilities that obstruct self-gravity, this same feedback triggers streaming instabilities that strongly concentrate particles. Numerical simulations find that solids ∼10–100 cm in size gravitationally collapse in turbulent disks. We outline areas for progress, including the possibility that still smaller objects self-gravitate.

Forming Planetesimals in Solar and Extrasolar Nebulae

We study the torque on low-mass planets embedded in protoplanetary discs in the two-dimensional approximation, incorporating non-isothermal eects. We couple linear estimates of the Lindblad (or wave) torque to a simple, but non-linear, model of adiabatic corotation torques (or horseshoe drag), resulting in a simple formula that governs Type I migration in non-isothermal discs. This formula should apply in optically thick regions of the disc, where viscous and thermal diusion act to keep the horseshoe drag unsaturated. We check this formula against numerical hydrodynamical simulations, using three independent numerical methods, and nd good agreement.

A torque formula for non-isothermal type I planetary migration – I. Unsaturated horseshoe drag

Context. Transition disks are believed to be the final stages of protoplanetary disks, during which a forming planetary system or photoevaporation processes open a gap in the inner disk, drastically changing the disk structure. From theoretical arguments it is expected that dust growth, fragmentation and radial drift are strongly influenced by gas disk structure, and pressure bumps in disks have been suggested as key features that may allow grains to converge and grow efficiently.Aims. We want to study how the presence of a large planet in a disk influences the growth and radial distribution of dust grains, and how observable properties are linked to the mass of the planet.Methods. We combined two-dimensional hydrodynamical disk simulations of disk-planet interactions with state-of-the-art coagulation/fragmentation models to simulate the evolution of dust in a disk, which has a gap created by a massive planet. We computed images at different wavelengths and illustrated our results using the example of the transition disk LkCa15.Results. The gap opened by a planet and the long-range interaction between the planet and the outer disk create a single large pressure bump outside the planetary orbit. Millimeter-sized particles form and accumulate at the pressure maximum and naturally produce ring-shaped sub-millimeter emission that is long-lived because radial drift no longer depletes the large grain population of the disk. For large planet masses around 9 M Jup , the pressure maximum and, therefore, the ring of millimeter particles is located at distances that can be more than twice the star-planet separation, creating a large spatial separation between the gas inner edge of the outer disk and the peak millimeter emission. Smaller grains do get closer to the gap and we predict how the surface brightness varies at different wavelengths.

/pdf/ring-shaped-dust-accumulation-in-transition-disks-1i8fvrl1er.pdf

Ring shaped dust accumulation in transition disks

We perform numerical simulations of a disc-planet system using various grid-based and smoothed particle hydrodynamics (SPH) codes. The tests are run for a simple setup where Jupiter and Neptune mass planets on a circular orbit open a gap in a protoplanetary disc during a few hundred orbital periods. We compare the surface density contours, potential vorticity and smoothed radial profiles at several times. The disc mass and gravitational torque time evolution are analyzed with high temporal resolution. There is overall consistency between the codes. The density profiles agree within about 5% for the Eulerian simulations while the SPH results predict the correct shape of the gap although have less resolution in the low density regions and weaker planetary wakes. The disc masses after 200 orbital periods agree within 10%. The spread is larger in the tidal torques acting on the planet which agree within a factor 2 at the end of the simulation. In the Neptune case the dispersion in the torques is greater than for Jupiter, possibly owing to the contribution from the not completely cleared region close to the planet.

A comparative study of disc-planet interaction

Many planets orbit within an AU of their stars, raising questions about their origins. Particularly puzzling are the planets found near the silicate sublimation front. We investigate conditions near the front in the protostellar disk around a young intermediate-mass star, using the first global 3-D radiation non-ideal MHD simulations in this context. We treat the starlight heating; the silicate grains sublimation and deposition at the local, time-varying temperature and density; temperature-dependent Ohmic dissipation; and various initial magnetic fields. The results show magnetorotational turbulence around the sublimation front at 0.5 AU. The disk interior to 0.8 AU is turbulent, with velocities exceeding 10% of the sound speed. Beyond 0.8 AU is the dead zone, cooler than 1000 K and with turbulence orders of magnitude weaker. A local pressure maximum just inside the dead zone concentrates solid particles, favoring their growth. Over many orbits, a vortex develops at the dead zones inner edge, increasing the disks thickness locally by around 10%. We synthetically observe the results using Monte Carlo transfer calculations, finding the sublimation front is near-infrared bright. The models with net vertical magnetic fields develop extended, magnetically-supported atmospheres that reprocess extra starlight, raising the near-infrared flux 20%.The vortex throws a nonaxisymmetric shadow on the outer disk. At wavelengths > 2 micron, the flux varies several percent on monthly timescales. The variations are more regular when the vortex is present. The vortex is directly visible as an arc at ultraviolet through near-infrared wavelengths, given sub-AU spatial resolution.

https://iopscience.iop.org/article/10.3847/1538-4357/835/2/230/pdf

3D Radiation Nonideal Magnetohydrodynamical Simulations of the Inner Rim in Protoplanetary Disks

3D Radiation Non-ideal Magnetohydrodynamical Simulations Of The Inner Rim In Protoplanetary Disks

On the aerodynamic redistribution of chondrite components in protoplanetary disks

Our aim is to study the thermal and dynamical evolution of protoplanetary disks in global simulations, including the physics of radiation transfer and magneto-hydrodynamic (MHD) turbulence caused by the magneto-rotational instability. We develop a radiative transfer method based on the flux-limited diffusion approximation that includes frequency dependent irradiation by the central star. This hybrid scheme is implemented in the PLUTO code. The focus of our implementation is on the performance of the radiative transfer method. Using an optimized Jacobi preconditioned BiCGSTAB solver, the radiative module is three times faster than the MHD step for the disk setup we consider. We obtain weak scaling efficiencies of 70% up to 1024 cores. We present the first global 3D radiation MHD simulations of a stratified protoplanetary disk. The disk model parameters are chosen to approximate those of the system AS 209 in the star-forming region Ophiuchus. Starting the simulation from a disk in radiative and hydrostatic equilibrium, the magnetorotational instability quickly causes MHD turbulence and heating in the disk. For the disk parameters we use, turbulent dissipation heats the disk midplane and raises the temperature by about 15% compared to passive disk models. A roughly flat vertical temperature profile establishes in the disk optically thick region close to the midplane. We reproduce the vertical temperature profile with a viscous disk models for which the stress tensor vertical profile is flat in the bulk of the disk and vanishes in the disk corona. The present paper demonstrates for the first time that global radiation MHD simulations of turbulent protoplanetary disks are feasible with current computational facilities. This opens up the windows to a wide range of studies of the dynamics of protoplanetary disks inner parts, for which there are significant observational constraints.

/pdf/radiation-magnetohydrodynamics-in-global-simulations-of-4pp4238nlf.pdf

S. Fromang

Papers

A comparative study of disc-planet interaction

3D Radiation Nonideal Magnetohydrodynamical Simulations of the Inner Rim in Protoplanetary Disks

3D Radiation Non-ideal Magnetohydrodynamical Simulations Of The Inner Rim In Protoplanetary Disks

On the aerodynamic redistribution of chondrite components in protoplanetary disks

Radiation Magnetohydrodynamics In Global Simulations Of Protoplanetary Disks