The ARCiS framework for Exoplanet Atmospheres: The Cloud Transport Model

Understanding of clouds is instrumental in interpreting current and future spectroscopic observations of exoplanets. Modelling clouds consistently is complex, since it involves many facets of chemistry, nucleation theory, condensation physics, coagulation, and particle transport. We develop a simple physical model for cloud formation and transport, efficient and versatile enough that it can be used in modular fashion for parameter optimization searches of exoplanet atmosphere spectra. The transport equations are formulated in 1D, accounting for sedimentation and diffusion. The grain size is obtained through a moment method. For simplicity, only one cloud species is considered and the nucleation rate is parametrized. From the resulting physical profiles we simulate transmission spectra covering the visual to mid-IR wavelength range. We apply our models towards KCl clouds in the atmosphere of GJ1214 b and towards MgSiO3 clouds of a canonical hot-Jupiter. We find that larger cloud diffusivity $K_{zz}$ increases the thickness of the cloud, pushing the $\tau=1$ surface to a lower pressure layer higher in the atmosphere. A larger nucleation rate also increases the cloud thickness while it suppresses the grain size. Coagulation is most important at high nuclei injection rates ($\dot\Sigma_n$) and low $K_{zz}$. We find that the investigated combinations of $K_{zz}$ and $\dot\Sigma_n$ greatly affect the transmission spectra in terms of the slope at near-IR wavelength (a proxy for grain size), the molecular features seen at ~1\micr (which disappear for thick clouds, high in the atmosphere), and the 10\micr silicate feature, which becomes prominent for small grains high in the atmosphere. The result of our hybrid approach -- aimed to provide a good balance between physical consistency and computational efficiency -- is ideal towards interpreting (future) spectroscopic observations of exoplanets.Comment: language and other tiny correction

Rapid Formation of Saturn after Jupiter Completion

We have investigated Saturn's core formation at a radial pressure maximum in a protoplanetary disk, which is created by gap opening by Jupiter. A core formed via planetesimal accretion induces the fragmentation of surrounding planetesimals, which generally inhibits further growth of the core by removal of the resulting fragments due to radial drift caused by gas drag. However, the emergence of the pressure maximum halts the drift of the fragments, while their orbital eccentricities and inclinations are efficiently damped by gas drag. As a result, the core of Saturn rapidly grows via accretion of the fragments near the pressure maximum. We have found that in the minimum-mass solar nebula, kilometer sized planetesimals can produce a core exceeding 10 Earth masses within two million years. Since Jupiter may not have undergone significant type II inward migration, it is likely that Jupiter's formation was completed when the local disk mass has already decayed to a value comparable to or less than Jovian mass. The expected rapid growth of Saturn's core on a timescale comparable to or shorter than observationally inferred disk lifetime enables Saturn to acquire the current amount of envelope gas before the disk gas is completely depleted. The high heat energy release rate onto the core surface due to the rapid accretion of the fragments delays onset of runaway gas accretion until the core mass becomes somewhat larger than that of Jupiter, which is consistent with the estimate based on interior modeling. Therefore, the rapid formation of Saturn induced by gap opening of Jupiter can account for the formation of multiple gas giants (Jupiter and Saturn) without significant inward migration and larger core mass of Saturn than that of Jupiter.Comment: Accepted for publication in Ap

Formation of TRAPPIST-1 and other compact systems

TRAPPIST-1 is a nearby 0.08 M M-star, which was recently found to harbor a planetary system of at least seven Earth-mass planets, all within 0.1 au. The configuration confounds theorists as the planets are not easily explained by either in situ or migration models. In this Paper we present a scenario for the formation and orbital architecture of the TRAPPIST-1 system. In our model, planet formation starts at the H2O iceline, where pebble-size particles -- whose origin is the outer disk -- concentrate to trigger streaming instabilities. After their formation, planetary embryos quickly mature by pebble accretion. Planet growth stalls at Earth masses, where the planet's gravitational feedback on the disk keeps pebbles at bay. Planets are transported by Type I migration to the inner disk, where they stall at the magnetospheric cavity and end up in mean motion resonances. During disk dispersal, the cavity radius expands and the inner-most planets escape resonance. We argue that the model outlined here can also be applied to other compact systems and that the many close-in super-Earth systems are a scaled-up version of TRAPPIST-1. We also hypothesize that few close-in compact systems harbor giant planets at large distances, since they would have stopped the pebble flux from the outer disk.Comment: 8 pages, accepted for publication in A&

What pebbles are made of: Interpretation of the V883 Ori disk

Recently, an Atacama Large Millimeter/submillimeter Array (ALMA) observation of the water snow line in the protoplanetary disk around the FU Orionis star V883 Ori was reported. The radial variation of the spectral index at mm-wavelengths around the snow line was interpreted as being due to a pileup of particles interior to the snow line. However, radial transport of solids in the outer disk operates on timescales much longer than the typical timescale of an FU Ori outburst ($10^{1}$--$10^{2}$ yr). Consequently, a steady-state pileup is unlikely. We argue that it is only necessary to consider water evaporation and re-coagulation of silicates to explain the recent ALMA observation of V883 Ori because these processes are short enough to have had their impact since the outburst. Our model requires the inner disk to have already been optically thick before the outburst, and our results suggest that the carbon content of pebbles is low.Comment: Accepted to A&A Letter

Wind-shearing in gaseous protoplanetary disks

One of the first stages of planet formation is the growth of small planetesimals and their accumulation into large planetesimals and planetary embryos. This early stage occurs much before the dispersal of most of the gas from the protoplanetary disk. Due to their different aerodynamic properties, planetesimals of different sizes/shapes experience different drag forces from the gas at these stage. Such differential forces produce a wind-shearing effect between close by, different size planetesimals. For any two planetesimals, a wind-shearing radius can be considered, at which the differential acceleration due to the wind becomes greater than the mutual gravitational pull between the planetesimals. We find that the wind-shearing radius could be much smaller than the gravitational shearing radius by the Sun (the Hill radius), i.e. during the gas-phase of the disk wind-shearing could play a more important role than tidal perturbations by the Sun. Here we study the wind-shearing radii for planetesimal pairs of different sizes and compare it with gravitational shearing (drag force vs. gravitational tidal forces). We then discuss the role of wind-shearing for the stability and survival of binary planetesimals, and provide stability criteria for binary planetesimals embedded in a gaseous disk.Comment: To be published in the proceedings of IAU 276: The Astrophysics of planetary systems - formation, structure, and dynamical evolutio

On the filtering and processing of dust by planetesimals 1. Derivation of collision probabilities for non-drifting planetesimals

Context. Circumstellar disks are known to contain a significant mass in dust ranging from micron to centimeter size. Meteorites are evidence that individual grains of those sizes were collected and assembled into planetesimals in the young solar system. Aims. We assess the efficiency of dust collection of a swarm of non-drifting planetesimals {\rev with radii ranging from 1 to $10^3$\,km and beyond. Methods. We calculate the collision probability of dust drifting in the disk due to gas drag by planetesimal accounting for several regimes depending on the size of the planetesimal, dust, and orbital distance: the geometric, Safronov, settling, and three-body regimes. We also include a hydrodynamical regime to account for the fact that small grains tend to be carried by the gas flow around planetesimals. Results. We provide expressions for the collision probability of dust by planetesimals and for the filtering efficiency by a swarm of planetesimals. For standard turbulence conditions (i.e., a turbulence parameter $\alpha=10^{-2}$), filtering is found to be inefficient, meaning that when crossing a minimum-mass solar nebula (MMSN) belt of planetesimals extending between 0.1 AU and 35 AU most dust particles are eventually accreted by the central star rather than colliding with planetesimals. However, if the disk is weakly turbulent ($\alpha=10^{-4}$) filtering becomes efficient in two regimes: (i) when planetesimals are all smaller than about 10 km in size, in which case collisions mostly take place in the geometric regime; and (ii) when planetary embryos larger than about 1000 km in size dominate the distribution, have a scale height smaller than one tenth of the gas scale height, and dust is of millimeter size or larger in which case most collisions take place in the settling regime. These two regimes have very different properties: we find that the local filtering efficiency $x_{filter,MMSN}$ scales with $r^{-7/4}$ (where $r$ is the orbital distance) in the geometric regime, but with $r^{-1/4}$ to $r^{1/4}$ in the settling regime. This implies that the filtering of dust by small planetesimals should occur close to the central star and with a short spread in orbital distances. On the other hand, the filtering by embryos in the settling regime is expected to be more gradual and determined by the extent of the disk of embryos. Dust particles much smaller than millimeter size tend only to be captured by the smallest planetesimals because they otherwise move on gas streamlines and their collisions take place in the hydrodynamical regime. Conclusions. Our results hint at an inside-out formation of planetesimals in the infant solar system because small planetesimals in the geometrical limit can filter dust much more efficiently close to the central star. However, even a fully-formed belt of planetesimals such as the MMSN only marginally captures inward-drifting dust and this seems to imply that dust in the protosolar disk has been filtered by planetesimals even smaller than 1 km (not included in this study) or that it has been assembled into planetesimals by other mechanisms (e.g., orderly growth, capture into vortexes). Further refinement of our work concerns, among other things: a quantitative description of the transition region between the hydro and settling regimes; an assessment of the role of disk turbulence for collisions, in particular in the hydro regime; and the coupling of our model to a planetesimal formation model.Comment: Accepted for publication in A\&A. 31 pages, 29 figures. (Version corrected by the A\&A Language Editor

A new condition for the transition from runaway to oligarchic growth

Accretion among macroscopic bodies of ~km size or larger is enhanced significantly due to gravitational focusing. Two regimes can be distinguished. Initially, the system experiences runaway growth, in which the gravitational focusing factors increase, and bodies at the high-mass tail of the distribution grow fastest. However, at some point the runaway body dynamically heats its environment, gravitational focusing factors decrease, and runaway growth passes into oligarchic growth. Based on the results of recent simulations, we reconsider the runaway growth-oligarchy transition. In contrast to oligarchy, we find that runaway growth cannot be approximated with a two component model (of small and large bodies) and that the criterion of Ida & Makino (1993), which is frequently adopted as the start of oligarchy, is not a sufficient condition to signify the transition. Instead, we propose a new criterion based on timescale arguments. We then find a larger value for the runaway growth-oligarchy transition: from several hundreds of km in the inner disk regions up to ~10^3 km for the outer disk. These findings are consistent with the view that runaway growth has been responsible for the size distribution of the present day Kuiper belt objects. Our finding furthermore outlines the proper initial conditions at the start of the oligarchy stage.Comment: 5 pages, 5 figures, accepted for publication in the Astrophysical Journal Letter