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

Dynamical rearrangement of super-Earths during disk dispersal II. Assessment of the magnetospheric rebound model for planet formation scenarios

Context.The Kepler mission has provided a large sample to statistically analyze the orbital properties of the super-Earth planets. We hypothesize that these planets formed early and consider the problem of matching planet formation theory to the current observations. Two scenarios, disk migration and in-situ formation, have been proposed to explain their origin. In the migration scenario planets migrate inward due to planet-disk interaction, whereas in the in-situ scenario planets assemble locally. Therefore, planets formed by migration are expected to end up in resonances, whereas those formed in-situ are expected to stay in short period ratios and in non-resonant orbits. Both predictions are at odds with observations. Aims. We investigate whether a preferred formation scenario can be identified through a comparison between the magnetospheric rebound model and the Kepler data. Methods. We conduct N-body simulations of two-planet systems during the disk dispersal phase, and make a statistical comparison between the simulations and the Kepler observations. Results. Comparing the two scenarios, we find that magnetospheric rebound tends to erase the difference in the orbital configuration that was initially presented. After disk dispersal, not all planets are in resonance in the migration scenario, whereas planets do not remain in compact configurations in the in-situ scenario. In both scenarios, the orbits of planets increase with the cavity expansion, and their period ratios have a wider distribution. Conclusions. From a statistical perspective, the magnetospheric rebound model reproduces several observed properties of Kepler planets, such as the significant number of planets are not in resonances and planet pairs can end up at large period ratios. The disparity in orbital configuration between the two formation scenarios is substantially reduced after disk dispersal.Comment: 8 pages, 4 figures, accepted for publication in A&

A Lagrangian Model for Dust Evolution in Protoplanetary Disks: Formation of Wet and Dry Planetesimals at Different Stellar Masses

We introduce a new Lagrangian smooth-particle method to model the growth and drift of pebbles in protoplanetary disks. The Lagrangian nature of the model makes it especially suited to follow characteristics of individual (groups of) particles, such as their composition. In this work we focus on the water content of solid particles. Planetesimal formation via streaming instability is taken into account, partly based on previous results on streaming instability outside the water snowline that were presented in Schoonenberg & Ormel (2017). We validate our model by reproducing earlier results from the literature and apply our model to steady-state viscous gas disks (with constant gas accretion rate) around stars with different masses. We also present various other models where we explore the effects of pebble accretion, the fragmentation velocity threshold, the global metallicity of the disk, and a time-dependent gas accretion rate. We find that planetesimals preferentially form in a local annulus outside the water snowline, at early times in the lifetime of the disk ($\lesssim$$10^{5} \: \rm{yr}$), when the pebble mass fluxes are high enough to trigger the streaming instability. During this first phase in the planet formation process, the snowline location hardly changes due to slow viscous evolution, and we conclude that assuming a constant gas accretion rate is justified in this first stage. The efficiency of converting the solids reservoir of the disk to planetesimals depends on the location of the water snowline. Cooler disks with a closer-in water snowline are more efficient at producing planetesimals than hotter disks where the water snowline is located further away from the star. Therefore, low-mass stars tend to form planetesimals more efficiently, but any correlation may be overshadowed by the spread in disk properties.Comment: 18 pages, 15 figures, 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

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

Effect of Core Cooling on the Radius of Sub-Neptune Planets

Sub-Neptune planets are very common in our galaxy and show a large diversity in their mass-radius relation. In sub-Neptunes most of the planet mass is in the rocky part (hereafter core) which is surrounded by a modest hydrogen-helium envelope. As a result, the total initial heat content of such a planet is dominated by that of the core. Nonetheless, most studies contend that the core cooling will only have a minor effect on the radius evolution of the gaseous envelope, because the core's cooling is in sync with the envelope, i.e., most of the initial heat is released early on timescales of about 10-100 Myr. In this Letter we examine the importance of the core cooling rate for the thermal evolution of the envelope. Thus, we relax the early core cooling assumption and present a model where the core is characterized by two parameters: the initial temperature and the cooling time. We find that core cooling can significantly enhance the radius of the planet when it operates on a timescale similar to the observed age, i.e. several Gyr. Consequently, the interpretation of sub-Neptunes' mass-radius observations depends on the assumed core thermal properties and the uncertainty therein. The degeneracy of composition and core thermal properties can be reduced by obtaining better estimates of the planet ages (in addition to their radii and masses) as envisioned by future observations.Comment: Accepted for publication in A&A Letter