The formation of mini-Neptunes

Mini-Neptunes seem to be common planets. In this work we investigate the possible formation histories and predicted occurrence rates of mini-Neptunes assuming the planets form beyond the iceline. We consider pebble and planetesimal accretion accounting for envelope enrichment and two different opacity conditions. We find that the formation of mini-Neptunes is a relatively frequent output when envelope enrichment by volatiles is included, and that there is a "sweet spot" for mini-Neptune formation with a relatively low solid accretion rate of ~10^{-6} Earth masses per year. This rate is typical for low/intermediate-mass protoplanetary disks and/or disks with low metallicities. With pebble accretion, envelope enrichment and high opacity favor the formation of mini-Neptunes, with more efficient formation at large semi-major axes (~30 AU) and low disk viscosity. For planetesimal accretion, such planets can form also without enrichment, with the opacity being a key aspect in the growth history and favorable formation location. Finally, we show that the formation of Neptune-like planets remains a challenge for planet formation theories.Comment: Accepted for publication in Ap

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

Jupiter's heavy-element enrichment expected from formation models

The goal of this work is to investigate Jupiter's growth focusing on the amount of heavy elements accreted by the planet, and its comparison with recent structure models. Our model assumes an initial core growth dominated by pebble accretion, and a second growth phase that is characterized by a moderate accretion of both planetesimals and gas. The third phase is dominated by runaway gas accretion during which the planet becomes detached from the disk. The second and third phases are computed in detail, considering two different prescriptions for the planetesimal accretion and fits from hydrodynamical studies to compute the gas accretion in the detached phase. In order for Jupiter to consist of $\sim$20-40 $M_{\oplus}$ of heavy elements as suggested by structure models, we find that Jupiter's formation location is preferably at an orbital distance of $1\lesssim a \lesssim 10$ au once the accretion of planetesimals dominates. We find that Jupiter could accrete between $\sim$1 and $\sim$15 $M_{\oplus}$ of heavy elements during runaway gas accretion, depending on the assumed initial surface density of planetesimals and the prescription used to estimate the heavy-element accretion during the final stage of the planetary formation. This would yield an envelope metallicity of $\sim$0.5 to $\sim$3 times solar. By computing the solid accretion during the detached phase, we infer a planetary mass-metallicity ($M_P$-$M_Z$) relation of $M_Z \sim M_P^{2/5}$ when a gap in the planetesimal disk is created, and of $M_Z \sim M_P^{1/6}$ without a planetesimal gap. Our hybrid pebble-planetesimal model can account for Jupiter's bulk and atmospheric enrichment. The high bulk metallicity inferred for many giant exoplanets is difficult to explain from standard formation models. This might suggest a migration history for such highly enriched giant exoplanets and/or giant impacts after the disk's dispersal.Comment: Accepted for publication in A&

Most super-Earths formed by dry pebble accretion are less massive than 5 Earth masses

We study the formation of rocky planets by dry pebble accretion from self-consistent dust-growth models. In particular, we aim at computing the maximum core mass of a rocky planet that can sustain a thin H-He atmosphere to account for the second peak of the Kepler's size distribution. We simulate planetary growth by pebble accretion inside the ice line. The pebble flux is computed self-consistently from dust growth by solving the advection-diffusion equation for a representative dust size. Dust coagulation, drift, fragmentation and sublimation at the water iceline are included. The disc evolution is computed for $\alpha$-discs with photoevaporation from the central star. The planets grow from a moon-mass embryo by silicate pebble accretion and gas accretion. We analyse the effect of a different initial disc mass, $\alpha$-viscosity, disc metallicity and embryo location. Finally, we compute atmospheric mass-loss due to evaporation. We find that inside the ice line, the fragmentation barrier determines the size of pebbles, which leads to different planetary growth patterns for different disc viscosities. Within the iceline the pebble isolation mass typically decays to values below 5 M$_{\oplus}$ within the first million years of disc evolution, limiting the core masses to that value. After computing atmospheric-mass loss, we find that planets with cores below $\sim$4 M$_{\oplus}$ get their atmospheres completely stripped, and a few 4-5 M$_{\oplus}$ cores retain a thin atmosphere that places them in the gap/second peak of the Kepler size distribution. Overall, we find that rocky planets form only in low-viscosity discs ($\alpha \lesssim 10^{-4}$). When $\alpha \geq 10^{-3}$, rocky objects do not grow beyond Mars-mass. The most typical outcome of dry pebble accretion is terrestrial planets with masses spanning from Mars to $\sim$4 M$_{\oplus}$.Comment: Accepted for publication in A&

BICEPS: An improved characterization model for low- and intermediate-mass exoplanets

Context. The number of exoplanets with precise mass and radius measurements is constantly increasing thanks to novel ground- and space-based facilities such as HARPS, ESPRESSO, CHEOPS, and TESS. The accuracy and robustness of the planetary characterization largely depends on the quality of the data, but also requires a planetary structure model, capable of accurately modeling the interior and atmospheres of exoplanets over a large range of boundary conditions. Aims. Our goal is to provide an improved characterization model for planets with masses between 0.5 and 30 Earth masses, equilibrium temperatures below <2000 K, and a wide range of planetary compositions and physical phases. Methods. In this work, we present the Bayesian Interior Characterization of ExoPlanetS (BICEPS) model, which combines an adaptive Markov chain Monte Carlo sampling method with a state-of-the-art planetary structure model. BICEPS incorporates many recently developed equations of state suited for large ranges of pressures and temperatures, a description for solid and molten planetary cores and mantles, a gaseous envelope composed of hydrogen, helium, and water (with compositional gradients), and a non-gray atmospheric model. Results. We find that the usage of updated equations of state has a significant impact on the interior structure prediction. The impact varies, depending on the planetary composition. For dense rocky planets, BICEPS predicts radii a few percent different to prior internal structure models. For volatile rich planets, we find differences of 10% or even larger. When applying BICEPS to a particular exoplanet, TOI-130 b, we inferred a 25% larger water mass fraction and a 15% smaller core than previous models. Conclusions. The presented exoplanet characterization model is a robust method applicable over a large range of planetary masses, compositions, and thermal boundary conditions. We show the importance of implementing state-of-the-art equations of state for the encountered thermodynamic conditions of exoplanets. Hence, using BICEPS improves the predictive strength of the characterization process compared to previous methods.ISSN:0004-6361ISSN:1432-074

Origin and sustainability of the population of asteroids captured in the exterior resonance 1:2 with Mars

At present, approximately 1500 asteroids are known to evolve inside or sticked to the exterior 1:2 resonance with Mars at a ≃ 2.418 AU, being (142) Polana the largest member of this group. The effect of the forced secular modes superposed to the resonance gives rise to a complex dynamical evolution. Chaotic diffusion, collisions, close encounters with massive asteroids and mainly orbital migration due to the Yarkovsky effect generate continuous captures to and losses from the resonance, with a fraction of asteroids remaining captured over long time scales and generating a concentration in the semimajor axis distribution that exceeds by 20% the population of background asteroids. The Yarkovsky effect induces different dynamics according to the asteroid size, producing an excess of small asteroids inside the resonance. The evolution in the resonance generates a signature on the orbits, mainly in eccentricity, that depends on the time the asteroid remains captured inside the resonance and on the magnitude of the Yarkovsky effect. The greater the asteroids, the larger the time they remain captured in the resonance, allowing greater diffusion in eccentricity and inclination. The resonance generates a discontinuity and mixing in the space of proper elements producing misidentification of dynamical family members, mainly for Vesta and Nysa-Polana families. The half-life of resonant asteroids large enough for not being affected by the Yarkovsky effect is about 1 Gyr. From the point of view of taxonomic classes, the resonant population does not differ from the background population and the excess of small asteroids is confirmed.Fil: Tabaré Gallardo, Carlos. Universidad de la República; UruguayFil: Venturini, Julia. Universidad de la República; UruguayFil: Roig, Fernando Virgilio. Ministério de Ciencia, Tecnologia e Innovacao. Observatorio Nacional; BrasilFil: Gil Hutton, Ricardo Alfredo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan. Complejo Astronómico "el Leoncito". Universidad Nacional de Córdoba. Complejo Astronómico ; Argentin

The formation of Jupiter by hybrid pebble-planetesimal accretion

The standard model for giant planet formation is based on the accretion of solids by a growing planetary embryo, followed by rapid gas accretion once the planet exceeds a so-called critical mass. The dominant size of the accreted solids (cm-size particles named pebbles or km to hundred km-size bodies named planetesimals) is, however, unknown. Recently, high-precision measurements of isotopes in meteorites provided evidence for the existence of two reservoirs in the early Solar System. These reservoirs remained separated from ~1 until ~ 3 Myr after the beginning of the Solar System's formation. This separation is interpreted as resulting from Jupiter growing and becoming a barrier for material transport. In this framework, Jupiter reached ~20 Earth masses within ~1 Myr and slowly grew to ~50 Earth masses in the subsequent 2 Myr before reaching its present-day mass. The evidence that Jupiter slowed down its growth after reaching 20 Earth masses for at least 2 Myr is puzzling because a planet of this mass is expected to trigger fast runaway gas accretion. Here, we use theoretical models to describe the conditions allowing for such a slow accretion and show that Jupiter grew in three distinct phases. First, rapid pebble accretion brought the major part of Jupiter's core mass. Second, slow planetesimal accretion provided the energy required to hinder runaway gas accretion during 2 Myr. Third, runaway gas accretion proceeded. Both pebbles and planetesimals therefore have an important role in Jupiter's formation.Comment: Published in Nature Astronomy on August 27, 201

The importance of thermal torques on the migration of planets growing by pebble accretion

A key process in planet formation is the exchange of angular momentum between a growing planet and the protoplanetary disc, which makes the planet migrate through the disc. Several works show that in general low-mass and intermediate-mass planets migrate towards the central star, unless corotation torques become dominant. Recently, a new kind of torque, called the thermal torque, was proposed as a new source that can generate outward migration of low-mass planets. While the Lindblad and corotation torques depend mostly on the properties of the protoplanetary disc and on the planet mass, the thermal torque depends also on the luminosity of the planet, arising mainly from the accretion of solids. Thus, the accretion of solids plays an important role not only in the formation of the planet but also in its migration process. In a previous work, we evaluated the thermal torque effects on planetary growth and migration mainly in the planetesimal accretion paradigm. In this new work, we study the role of the thermal torque within the pebble accretion paradigm. Computations are carried out consistently in the framework of a global model of planet formation that includes disc evolution, dust growth and evolution, and pebble formation. We also incorporate updated prescriptions of the thermal torque derived from high-resolution hydrodynamical simulations. Our simulations show that the thermal torque generates extended regions of outward migration in low-viscosity discs. This has a significant impact in the formation of the planets.Fil: Guilera, Octavio Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; ArgentinaFil: Miller Bertolami, Marcelo Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; ArgentinaFil: Masset, Frederic. Universidad Nacional Autónoma de México; MéxicoFil: Cuadra, Jorge. Pontificia Universidad Católica de Chile; ChileFil: Venturini, Julia Elisa. International Space Science Institute; SuizaFil: Ronco, María Paula. Pontificia Universidad Católica de Chile; Chil