Influence of viscosity and the adiabatic index on planetary migration

The strength and direction of migration of low mass embedded planets depends on the disk's thermodynamic state, where the internal dissipation is balanced by radiative transport, and the migration can be directed outwards, a process which extends the lifetime of growing embryos. Very important parameters determining the structure of disks, and hence the direction of migration, are the viscosity and the adiabatic index. In this paper we investigate the influence of different viscosity prescriptions (alpha-type and constant) and adiabatic indices on disk structures and how this affects the migration rate of planets embedded in such disks. We perform 3D numerical simulations of accretion disks with embedded planets. We use the explicit/implicit hydrodynamical code NIRVANA that includes full tensor viscosity and radiation transport in the flux-limited diffusion approximation, as well as a proper equation of state for molecular hydrogen. The migration of embedded 20Earthmass planets is studied. Low-viscosity disks have cooler temperatures and the migration rates of embedded planets tend toward the isothermal limit. In these disks, planets migrate inwards even in the fully radiative case. The effect of outward migration can only be sustained if the viscosity in the disk is large. Overall, the differences between the treatments for the equation of state seem to play a more important role in disks with higher viscosity. A change in the adiabatic index and in the viscosity changes the zero-torque radius that separates inward from outward migration. For larger viscosities, temperatures in the disk become higher and the zero-torque radius moves to larger radii, allowing outward migration of a 20 Earth-mass planet to persist over an extended radial range. In combination with large disk masses, this may allow for an extended period of the outward migration of growing protoplanetary cores

Migration of Earth-size planets in 3D radiative discs

In this paper, we address the migration of small mass planets in 3D radiative disks. Indeed, migration of small planets is known to be too fast inwards in locally isothermal conditions. However, thermal effects could reverse its direction, potentially saving planets in the inner, optically thick parts of the protoplanetary disc. This effect has been seen for masses larger than 5 Earth masses, but the minimum mass for this to happen has never been probed numerically, although it is of crucial importance for planet formation scenarios. We have extended the hydro-dynamical code FARGO to 3D, with thermal diffusion. With this code, we perform simulations of embedded planets down to 2 Earth masses. For a set of discs parameters for which outward migration has been shown in the range of $[5, 35]$ Earth masses, we find that the transition to inward migration occurs for masses in the range $[3, 5]$ Earth masses. The transition appears to be due to an unexpected phenomenon: the formation of an asymmetric cold and dense finger of gas driven by circulation and libration streamlines. We recover this phenomenon in 2D simulations where we control the cooling effects of the gas through a simple modeling of the energy equation.Comment: 17 pages, 20 figures, accepted. MNRAS, 201

The great dichotomy of the Solar System: small terrestrial embryos and massive giant planet cores

The basic structure of the solar system is set by the presence of low-mass terrestrial planets in its inner part and giant planets in its outer part. This is the result of the formation of a system of multiple embryos with approximately the mass of Mars in the inner disk and of a few multi-Earth-mass cores in the outer disk, within the lifetime of the gaseous component of the protoplanetary disk. What was the origin of this dichotomy in the mass distribution of embryos/cores? We show in this paper that the classic processes of runaway and oligarchic growth from a disk of planetesimals cannot explain this dichotomy, even if the original surface density of solids increased at the snowline. Instead, the accretion of drifting pebbles by embryos and cores can explain the dichotomy, provided that some assumptions hold true. We propose that the mass-flow of pebbles is two-times lower and the characteristic size of the pebbles is approximately ten times smaller within the snowline than beyond the snowline (respectively at heliocentric distance $r<r_{ice}$ and $r>r_{ice}$, where $r_{ice}$ is the snowline heliocentric distance), due to ice sublimation and the splitting of icy pebbles into a collection of chondrule-size silicate grains. In this case, objects of original sub-lunar mass would grow at drastically different rates in the two regions of the disk. Within the snowline these bodies would reach approximately the mass of Mars while beyond the snowline they would grow to $\sim 20$ Earth masses. The results may change quantitatively with changes to the assumed parameters, but the establishment of a clear dichotomy in the mass distribution of protoplanets appears robust, provided that there is enough turbulence in the disk to prevent the sedimentation of the silicate grains into a very thin layer.Comment: In press in Icaru

Surface waves in protoplanetary disks induced by outbursts: Concentric rings in scattered light

Context: Vertically hydrostatic protoplanetary disk models are based on the assumption that the main heating source, stellar irradiation, does not vary much with time. However, it is known that accreting young stars are variable sources of radiation. This is particularly evident for outbursting sources such as EX Lupi and FU Orionis stars. Aim: We investigate how such outbursts affect the vertical structure of the outer regions of the protoplanetary disk, in particular their appearance in scattered light at optical and near-infrared wavelengths. Methods: We employ the 3D FARGOCA radiation-hydrodynamics code, in polar coordinates, to compute the time-dependent behavior of the axisymmetric disk structure. The outbursting inner disk region is not included explicitly. Instead, its luminosity is added to the stellar luminosity and is thus included in the irradiation of the outer disk regions. For time snapshots of interest we insert the density structure into the RADMC-3D radiative transfer code and compute the appearance of the disk at optical/near-infrared wavelengths. Results: We find that, depending on the amplitude of the outbursts, the vertical structure of the disk can become highly dynamic, featuring circular surface waves of considerable amplitude. These "hills" and "valleys" on the disk's surface show up in the scattered light images as bright and dark concentric rings. Initially these rings are small and act as standing waves, but they subsequently lead to outward propagating waves, like the waves produced by a stone thrown into a pond. These waves continue long after the actual outburst has died out. Conclusions: We propose that some of the multi-ringed structures seen in optical/infrared images of several protoplanetary disks may have their origin in outbursts that occurred decades or centuries ago.Comment: Accepted for publication in A&A Letter

RISK IN HUMAN RESOURCE MANAGEMENT AND IMPLICATIONS FOR EXTENSION PROGRAMMING - RESULTS OF FOCUS GROUP DISCUSSIONS WITH DAIRY AND GREEN INDUSTRY MANAGERS

Employees are both a source of risk and means of addressing risk, and good employee management practices can increase risk resilience. Forty green industry managers and 22 dairy managers discussed personnel issues related to their industry. Influx of Hispanic labor has changed personnel management and the focus of risk management.Teaching/Communication/Extension/Profession,

Forming super-Mercuries: The role of stellar abundances

Super-Mercuries, rocky exoplanets with bulk iron mass fraction of more than 60 per cent, appear to be preferentially hosted by stars with higher iron mass fraction than the Earth. It is unclear whether these iron-rich planets can form in the disc, or if giant impacts are necessary. Here we investigate the formation of super-Mercuries in their natal protoplanetary discs by taking into account their host stars' abundances (Fe, Mg, Si, S). We employ a disc evolution model which includes the growth, drift, evaporation and recondensation of pebbles to compute the pebble iron mass fraction. The recondensation of outward-drifting iron vapour near the iron evaporation front is the key mechanism that facilitates an increase in the pebble iron mass fraction. We also simulate the growth of planetary seeds around the iron evaporation front using a planet formation model which includes pebble accretion and planet migration, and compute the final composition of the planets. Our simulations are able to reproduce the observed iron compositions of the super-Mercuries provided that all the iron in the disc are locked in pure Fe grains and that the disc viscosity is low. The combined effects of slow orbital migration of planets and long retention time of iron vapour in low-viscosity discs makes it easier to form iron-rich planets. Furthermore, we find that decreasing the stellar Mg/Si ratio results in an increase in the iron mass fraction of the planet due to a reduction in the abundance of Mg2SiO4, which has a very similar condensation temperature as iron, in the disc. Our results thus imply that super-Mercuries are more likely to form around stars with low Mg/Si, in agreement with observational data.Comment: 9 pages, 6 figures, accepted for publication in A&

Meridional circulation of gas into gaps opened by giant planets in three-dimensional low-viscosity disks

We examine the gas circulation near a gap opened by a giant planet in a protoplanetary disk. We show with high resolution 3D simulations that the gas flows into the gap at high altitude over the mid-plane, at a rate dependent on viscosity. We explain this observation with a simple conceptual model. From this model we derive an estimate of the amount of gas flowing into a gap opened by a planet with Hill radius comparable to the scale-height of a layered disk (i. e. a disk with viscous upper layer and inviscid midplane). Our estimate agrees with modern MRI simulations(Gressel et al., 2013). We conclude that gap opening in a layered disk can not slow down significantly the runaway gas accretion of Saturn to Jupiter-mass planets.Comment: in press as a Note in Icaru

Close-in ice lines and the super-stellar C/O ratio in discs around very low-mass stars

The origin of the elevated C/O ratios in discs around late M dwarfs compared to discs around solar-type stars is not well understood. Here we endeavour to reproduce the observed differences in the disc C/O ratios as a function of stellar mass using a viscosity-driven disc evolution model and study the corresponding atmospheric composition of planets that grow inside the water-ice line in these discs. We carried out simulations using a coupled disc evolution and planet formation code that includes pebble drift and evaporation. We used a chemical partitioning model for the dust composition in the disc midplane. Inside the water-ice line, the disc's C/O ratio initially decreases to sub-stellar due to the inward drift and evaporation of water-ice-rich pebbles before increasing again to super-stellar values due to the inward diffusion of carbon-rich vapour. We show that this process is more efficient for very low-mass stars compared to solar-type stars due to the closer-in ice lines and shorter disc viscous timescales. In high-viscosity discs, the transition from sub-stellar to super-stellar takes place faster due to the fast inward advection of carbon-rich gas. Our results suggest that planets accreting their atmospheres early (when the disc C/O is still sub-stellar) will have low atmospheric C/O ratios, while planets that accrete their atmospheres late (when the disc C/O has become super-stellar) can obtain high C/O ratios. Our model predictions are consistent with observations, under the assumption that all stars have the same metallicity and chemical composition, and that the vertical mixing timescales in the inner disc are much shorter than the radial advection timescales. This further strengthens the case for considering stellar abundances alongside disc evolution in future studies that aim to link planet (atmospheric) composition to disc composition.Comment: Accepted for publication in A&

The solar abundance problem and eMSTOs in clusters

We study the impact of accretion from protoplanetary discs on stellar evolution of AFG-type stars. We use a simplified disc model computed using the Two-Pop-Py code that contains the growth and drift of dust particles in the protoplanetary disc. It is used to model the accretion scenarios for a range of physical conditions of protoplanetary discs. Two limiting cases are combined with the evolution of stellar convective envelopes computed using the Garstec stellar evolution code. We find that the accretion of metal-poor (gas) or metal-rich (dust) material has a significant impact on the chemical composition of the stellar convective envelope. As a consequence, the evolutionary track of the star diverts from the standard scenario predicted by canonical stellar evolution models, which assume a constant and homogeneous chemical composition after the assembly of the star has finished. In the case of the Sun, we find a modest impact on the solar chemical composition. Accretion of metal-poor material indeed reduces the overall metallicity of the solar atmosphere, and it is consistent, within the uncertainty, with the solar Z reported by Caffau et al. (2011), but our model is not consistent with the measurement by Asplund et al. (2009). Another effect is the change of the position of the star in the colour-magnitude diagram. We compare our predictions to a set of open clusters from the Gaia DR2 and show that it is possible to produce a scatter close to the turn-off of young clusters that could contribute to explain the observed scatter in CMDs. Detailed measurements of metallicities and abundances in the nearby open clusters will provide a stringent observational test of our proposed scenario.Comment: 10 pages, 7 figures, 1 table. Accepted for publication in A&

Evolution of inclined planets in three-dimensional radiative discs

While planets in the solar system only have a low inclination with respect to the ecliptic there is mounting evidence that in extrasolar systems the inclination can be very high, at least for close-in planets. One process to alter the inclination of a planet is through planet-disc interactions. Recent simulations considering radiative transport have shown that the evolution of migration and eccentricity can strongly depend on the thermodynamic state of the disc. We extend previous studies to investigate the planet-disc interactions of fixed and moving planets on inclined and eccentric orbits. We also analyse the effect of the disc's thermodynamic properties on the orbital evolution of embedded planets in detail. The protoplanetary disc is modelled as a viscous gas where the internally produced dissipation is transported by radiation. For locally isothermal discs, we confirm previous results and find inclination damping and inward migration for planetary cores. For low inclinations i < 2 H/r, the damping is exponential, while di/dt is proportional to i^-2 for larger i. For radiative discs, the planetary migration is very limited, as long as their inclination exceeds a certain threshold. If the inclination is damped below this threshold, planetary cores with a mass up to approximately 33 Earth masses start to migrate outwards, while larger cores migrate inwards right from the start. The inclination is damped for all analysed planet masses. In a viscous disc an initial inclination of embedded planets will be damped for all planet masses. This damping occurs on timescales that are shorter than the migration time. If the inclination lies beneath a certain threshold, the outward migration in radiative discs is not handicapped. Outward migration is strongest for circular and non-inclined orbits