Constraining the volatile fraction of planets from transit observations

The determination of the abundance of volatiles in extrasolar planets is very important as it can provide constraints on transport in protoplanetary disks and on the formation location of planets. However, constraining the internal structure of low-mass planets from transit measurements is known to be a degenerate problem. Using planetary structure and evolution models, we show how observations of transiting planets can be used to constrain their internal composition, in particular the amount of volatiles in the planetary interior, and consequently the amount of gas (defined in this paper to be only H and He) that the planet harbors. We show for low-mass gas-poor planets that are located close to their central star that assuming evaporation has efficiently removed the entire gas envelope, it is possible to constrain the volatile fraction of close-in transiting planets. We illustrate this method on the example of 55 Cnc e and show that under the assumption of the absence of gas, the measured mass and radius imply at least 20 % of volatiles in the interior. For planets at larger distances, we show that the observation of transiting planets at different evolutionary ages can be used to set statistical constraints on the volatile content of planets. These results can be used in the context of future missions like PLATO to better understand the internal composition of planets.Comment: accepted in Astronomy and Astrophysic

On the radius of habitable planets

The conditions that a planet must fulfill to be habitable are not precisely known. However, it is comparatively easier to define conditions under which a planet is very likely not habitable. Finding such conditions is important as it can help select, in an ensemble of potentially observable planets, which ones should be observed in greater detail for characterization studies. Assuming, as in the Earth, that the presence of a C-cycle is a necessary condition for long-term habitability, we derive, as a function of the planetary mass, a radius above which a planet is likely not habitable. We compute the maximum radius a planet can have to fulfill two constraints: surface conditions compatible with the existence of liquid water, and no ice layer at the bottom of a putative global ocean. We demonstrate that, above a given radius, these two constraints cannot be met. We compute internal structure models of planets, using a five-layer model (core, inner mantle, outer mantle, ocean, and atmosphere), for different masses and composition of the planets (in particular, the Fe/Si ratio of the planet). Our results show that for planets in the Super-Earth mass range (1-12 Mearth), the maximum that a planet, with a composition similar to that of the Earth, can have varies between 1.7 and 2.2 Rearth. This radius is reduced when considering planets with higher Fe/Si ratios and taking radiation into account when computing the gas envelope structure. These results can be used to infer, from radius and mass determinations using high-precision transit observations like those that will soon be performed by the CHaracterizing ExOPlanet Satellite (CHEOPS), which planets are very likely not habitable, and therefore which ones should be considered as best targets for further habitability studies.}Comment: 8 pages, 5 figures, accepted in Astronomy and Astrophysic

The maximum mass of planetary embryos formed in core-accretion models

We compute the maximum mass a growing planetary embryo can reach depending on the size of accreted planetesimals or pebbles, to infer the possibility of growing the cores of giant planets, and giant planets themselves. We compute the internal structure of the gas envelope of planetary embryos, to determine the core mass that is necessary to bind an envelope large enough to destroy planetesimals or pebbles while they are gravitationally captured. We also consider the effect of the advection wind originating from the protoplanetary disk, following the results of Ormel et al. (2015). We show that for low mass pebbles, once the planetary embryo is larger than ~1 Mearth, the envelope is large enough to destroy and vaporize pebbles completely before they can reach the core. The material constituting pebbles is therefore released in the planetary envelope, and later on dispersed in the protoplanetary disk, if the advection wind is strong enough. As a consequence the growth of the planetary embryo is stopped at a mass that is so small that Kelvin-Helmholtz accretion cannot lead to the accretion of significant amounts of gas. For larger planetesimals, a similar process occurs but at much larger mass, of the order of ten Earth masses, and is followed by rapid accretion of gas. If the effect of the advection is as efficient as described in Ormel al. (2015), the combined effect of the vaporization of accreted solids in the envelope of forming planetary embryos, and of this advection wind, prevents the growth of the planets at masses smaller or similar to the Earth mass in the case of formation by pebble accretion, up to a distance of the order of 10 AU. In the case of formation by accretion of large mass planetesimals, the growth of the planetary core is limited at masses ~10 Mearth but further growth of the planet can proceed by gas accretion.Comment: accepted in Astronomy and Astrophysic

Formation and composition of planets around very low mass stars

The recent detection of planets around very low mass stars raises the question of the formation, composition and potential habitability of these objects. We use planetary system formation models to infer the properties, in particular their radius distribution and water content, of planets that may form around stars ten times less massive than the Sun. Our planetary system formation and composition models take into account the structure and evolution of the protoplanetary disk, the planetary mass growth by accretion of solids and gas, as well as planet-planet, planet-star and planet-disk interactions. We show that planets can form at small orbital period in orbit about low mass stars. We show that the radius of the planets is peaked at about 1 rearth and that they are, in general, volatile rich especially if proto-planetary discs orbiting this type of stars are long-lived. Close-in planets orbiting low-mass stars similar in terms of mass and radius to the ones recently detected can be formed within the framework of the core accretion paradigm as modeled here. The properties of protoplanetary disks, and their correlation with the stellar type, are key to understand their composition.Comment: to appear in Astronomy and Astrophysics Letter

Modeling the Jovian subnebula: II - Composition of regular satellites ices

We use the evolutionary turbulent model of Jupiter's subnebula described by Alibert et al. (2005a) to constrain the composition of ices incorporated in its regular icy satellites. We consider CO2, CO, CH4, N2, NH3, H2S, Ar, Kr, and Xe as the major volatile species existing in the gas-phase of the solar nebula. All these volatile species, except CO2 which crystallized as a pure condensate, are assumed to be trapped by H2O to form hydrates or clathrate hydrates in the solar nebula. Once condensed, these ices were incorporated into the growing planetesimals produced in the feeding zone of proto-Jupiter. Some of these solids then flowed from the solar nebula to the subnebula, and may have been accreted by the forming Jovian regular satellites. We show that ices embedded in solids entering at early epochs into the Jovian subdisk were all vaporized. This leads us to consider two different scenarios of regular icy satellites formation in order to estimate the composition of the ices they contain. In the first scenario, icy satellites were accreted from planetesimals that have been produced in Jupiter's feeding zone without further vaporization, whereas, in the second scenario, icy satellites were accreted from planetesimals produced in the Jovian subnebula. In this latter case, we study the evolution of carbon and nitrogen gas-phase chemistries in the Jovian subnebula and we show that the conversions of N2 to NH3, of CO to CO2, and of CO to CH4 were all inhibited in the major part of the subdisk. Finally, we assess the mass abundances of the major volatile species with respect to H2O in the interiors of the Jovian regular icy satellites. Our results are then compatible with the detection of CO2 on the surfaces of Callisto and Ganymede and with the presence of NH3 envisaged in subsurface oceans within Ganymede and Callisto.Comment: 9 pages, A&A, in pres

Planetesimal formation starts at the snow line

Planetesimal formation stage represents a major gap in our understanding of the planet formation process. The late-stage planet accretion models typically make arbitrary assumptions about planetesimals and pebbles distribution while the dust evolution models predict that planetesimal formation is only possible at some orbital distances. We want to test the importance of water snow line for triggering formation of the first planetesimals during the gas-rich phase of protoplanetary disk, when cores of giant planets have to form. We connect prescriptions for gas disk evolution, dust growth and fragmentation, water ice evaporation and recondensation, as well as transport of both solids and water vapor, and planetesimal formation via streaming instability into a single, one-dimensional model for protoplanetary disk evolution. We find that processes taking place around the snow line facilitate planetesimal formation in two ways. First, due to the change of sticking properties between wet and dry aggregates, there is a "traffic jam" inside of the snow line that slows down the fall of solids onto the star. Second, ice evaporation and outward diffusion of water followed by its recondensation increases the abundance of icy pebbles that trigger planetesimal formation via streaming instability just outside of the snow line. Planetesimal formation is hindered by growth barriers and radial drift and thus requires particular conditions to take place. Snow line is a favorable location where planetesimal formation is possible for a wide range of conditions, but still not in every protoplanetary disk model. This process is particularly promoted in large, cool disks with low intrinsic turbulence and increased initial dust-to-gas ratio.Comment: Accepted for publication in Astronomy & Astrophysic

Using Deep Neural Networks to compute the mass of forming planets

Computing the mass of planetary envelopes and the critical mass beyond which planets accrete gas in a runaway fashion is important when studying planet formation, in particular for planets up to the Neptune mass range. This computation requires in principle solving a set of differential equations, the internal structure equations, for some boundary conditions (pressure, temperature in the protoplanetary disk where a planet forms, core mass and accretion rate of solids by the planet). Solving these equations in turn proves being time consuming and sometimes numerically unstable. We developed a method to approximate the result of integrating the internal structure equations for a variety of boundary conditions. We compute a set of planet internal structures for a very large number (millions) of boundary conditions, considering two opacities,(ISM and reduced). This database is then used to train Deep Neural Networks in order to predict the critical core mass as well as the mass of planetary envelopes as a function of the boundary conditions. We show that our neural networks provide a very good approximation (at the level of percents) of the result obtained by solving interior structure equations, but with a much smaller required computer time. The difference with the real solution is much smaller than the one obtained using some analytical formulas available in the literature which at best only provide the correct order of magnitude. We compare the results of the DNN with other popular machine learning methods (Random Forest, Gradient Boost, Support Vector Regression) and show that the DNN outperforms these methods by a factor of at least two. We show that some analytical formulas that can be found in various papers can severely overestimate the mass of planets, therefore predicting the formation of planets in the Jupiter-mass regime instead of the Neptune-mass regime.Comment: accepted in A&A. Animations visible at http://nccr-planets.ch/research/phase2/domain2/project5/machine-learning-and-advanced-statistical-analysis/ and code available at https://github.com/yalibert/DNN_internal_structur

Nebular water depletion as the cause of Jupiter's low oxygen abundance

Motivated by recent spectroscopic observations suggesting that atmospheres of some extrasolar giant-planets are carbon-rich, i.e. carbon/oxygen ratio (C/O) $\ge$ 1, we find that the whole set of compositional data for Jupiter is consistent with the hypothesis that it be a carbon-rich giant planet. We show that the formation of Jupiter in the cold outer part of an oxygen-depleted disk (C/O $\sim$1) reproduces the measured Jovian elemental abundances at least as well as the hitherto canonical model of Jupiter formed in a disk of solar composition (C/O = 0.54). The resulting O abundance in Jupiter's envelope is then moderately enriched by a factor of $\sim$2 $\times$ solar (instead of $\sim$7 $\times$ solar) and is found to be consistent with values predicted by thermochemical models of the atmosphere. That Jupiter formed in a disk with C/O $\sim$1 implies that water ice was heterogeneously distributed over several AU beyond the snow line in the primordial nebula and that the fraction of water contained in icy planetesimals was a strong function of their formation location and time. The Jovian oxygen abundance to be measured by NASA's Juno mission en route to Jupiter will provide a direct and strict test of our predictions.Comment: Accepted for publication in Astrophysical Journal Letter

Modeling the Jovian subnebula: I - Thermodynamical conditions and migration of proto-satellites

We have developed an evolutionary turbulent model of the Jovian subnebula consistent with the extended core accretion formation models of Jupiter described by Alibert et al. (2005b) and derived from Alibert et al. (2004,2005a). This model takes into account the vertical structure of the subnebula, as well as the evolution of the surface density as given by an $\alpha$-disk model and is used to calculate the thermodynamical conditions in the subdisk, for different values of the viscosity parameter. We show that the Jovian subnebula evolves in two different phases during its lifetime. In the first phase, the subnebula is fed through its outer edge by the solar nebula as long as it has not been dissipated. In the second phase, the solar nebula has disappeared and the Jovian subdisk expands and gradually clears with time as Jupiter accretes the remaining material. We also demonstrate that early generations of satellites formed during the beginning of the first phase of the subnebula cannot survive in this environment and fall onto the proto-Jupiter. As a result, these bodies may contribute to the enrichment of Jupiter in heavy elements. Moreover, migration calculations in the Jovian subnebula allow us to follow the evolution of the ices/rocks ratios in the proto-satellites as a function of their migration pathways. By a tempting to reproduce the distance distribution of the Galilean satellites, as well as their ices/rocks ratios, we obtain some constraints on the viscosity parameter of the Jovian subnebula.Comment: Accepted in Astronomy and Astrohpysic

Migration and giant planet formation

We extend the core-accretion model of giant gaseous planets by Pollack et al. (\cite{P96}) to include migration, disc evolution and gap formation. Starting with a core of a fraction of an Earth's mass located at 8 AU, we end our simulation with the onset of runaway gas accretion when the planet is at 5.5 AU 1 Myr later. This timescale is about a factor ten shorter than the one found by Pollack et al. (\cite{P96}) even though the disc was less massive initially and viscously evolving. Other initial conditions can lead to even shorter timescales. The reason for this speed-up is found to result from the fact that a moving planet does not deplete its feeding zone to the extend of a static planet. Thus, the uncomfortably long formation timescale associated with the core-accretion scenario can be considerably reduced and brought in much better agreement with the typical disc lifetimes inferred from observations of young circumstellar discs.Comment: 9 pages, 2 figures, published in A&A Letter