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

Theory of planet formation and comparison with observation: Formation of the planetary mass-radius relationship

The planetary mass-radius diagram is an observational result of central importance to understand planet formation. We present an updated version of our planet formation model based on the core accretion paradigm which allows to calculate planetary radii and luminosities during the entire formation and evolution of the planets. We first study with it the formation of Jupiter, and compare with previous works. Then we conduct planetary population synthesis calculations to obtain a synthetic mass-radius diagram which we compare with the observed one. Except for bloated Hot Jupiters which can be explained only with additional mechanisms related to their proximity to the star, we find a good agreement of the general shape of the observed and the synthetic mass-radius diagram. This shape can be understood with basic concepts of the core accretion model.Comment: Proceedings Haute Provence Observatory Colloquium: Detection and Dynamics of Transiting Exoplanets (23-27 August 2010). Edited by F. Bouchy, R. F. Diaz & C. Moutou. Extended version: 17 pages, 8 figure

Grain opacity and the bulk composition of extrasolar planets. I. Results from scaling the ISM opacity

The opacity due to grains in the envelope of a protoplanet regulates the accretion rate of gas during formation, thus the final bulk composition of planets with primordial H/He is a function of it. Observationally, for exoplanets with known mass and radius it is possible to estimate the bulk composition via internal structure models. We first determine the reduction factor of the ISM grain opacity f_opa that leads to gas accretion rates consistent with grain evolution models. We then compare the bulk composition of synthetic low-mass and giant planets at different f_opa with observations. For f_opa=1 (full ISM opacity) the synthetic low-mass planets have too small radii, i.e., too low envelope masses compared to observations. At f_opa=0.003, the value calibrated with the grain evolution models, synthetic and actual planets occupy similar mass-radius loci. The mean enrichment of giant planets relative to the host star as a function of planet mass M can be approximated as Z_p/Z_star = beta*(M/M_Jup)^alpha. We find alpha=-0.7 independent of f_opa in synthetic populations in agreement with the observational result (-0.71+-0.10). The absolute enrichment level decreases from beta=8.5 at f_opa=1 to 3.5 at f_opa=0. At f_opa=0.003 one finds beta=7.2 which is similar to the observational result (6.3+-1.0). We thus find observational hints that the opacity in protoplanetary atmospheres is much smaller than in the ISM even if the specific value of the grain opacity cannot be constrained here. The result for the enrichment of giant planets helps to distinguish core accretion and gravitational instability. In the simplest picture of core accretion where first a critical core forms and afterwards only gas is added, alpha=-1. If a core accretes all planetesimals inside the feeding zone, alpha=-2/3. The observational result lies between these values, pointing to core accretion as the formation mechanism.Comment: 21 pages, 15 figures. Accepted for A&

Planet Population Synthesis

With the increasing number of exoplanets discovered, statistical properties of the population as a whole become unique constraints on planet formation models provided a link between the description of the detailed processes playing a role in this formation and the observed population can be established. Planet population synthesis provides such a link. The approach allows to study how different physical models of individual processes (e.g., proto-planetary disc structure and evolution, planetesimal formation, gas accretion, migration, etc.) affect the overall properties of the population of emerging planets. By necessity, planet population synthesis relies on simplified descriptions of complex processes. These descriptions can be obtained from more detailed specialised simulations of these processes. The objective of this chapter is twofold: 1) provide an overview of the physics entering in the two main approaches to planet population synthesis and 2) present some of the results achieved as well as illustrate how it can be used to extract constraints on the models and to help interpret observations.Comment: 23 pages, 8 figures, accepted for publication as a chapter in Protostars and Planets VI, University of Arizona Press (2014), eds. H. Beuther, R. Klessen, C. Dullemond, Th. Henning. Updated references relative to v

Global Models of Planet Formation and Evolution

Despite the increase in observational data on exoplanets, the processes that lead to the formation of planets are still not well understood. But thanks to the high number of known exoplanets, it is now possible to look at them as a population that puts statistical constraints on theoretical models. A method that uses these constraints is planetary population synthesis. Its key element is a global model of planet formation and evolution that directly predicts observable planetary properties based on properties of the natal protoplanetary disk. To do so, global models build on many specialized models that address one specific physical process. We thoroughly review the physics of the sub-models included in global formation models. The sub-models can be classified as models describing the protoplanetary disk (gas and solids), the (proto)planet (solid core, gaseous envelope, and atmosphere), and finally the interactions (migration and N-body interaction). We compare the approaches in different global models and identify physical processes that require improved descriptions in future. We then address important results of population synthesis like the planetary mass function or the mass-radius relation. In these results, the global effects of physical mechanisms occurring during planet formation and evolution become apparent, and specialized models describing them can be put to the observational test. Due to their nature as meta models, global models depend on the development of the field of planet formation theory as a whole. Because there are important uncertainties in this theory, it is likely that global models will in future undergo significant modifications. Despite this, they can already now yield many testable predictions. With future global models addressing the geophysical characteristics, it should eventually become possible to make predictions about the habitability of planets.Comment: 30 pages, 16 figures. Accepted for publication in the International Journal of Astrobiology (Cambridge University Press

Impacts of planet migration models on planetary populations. Effects of saturation, cooling and stellar irradiation

Context: Several recent studies have found that planet migration in adiabatic discs differs significantly from migration in isothermal discs. Depending on the thermodynamic conditions, i.e., the effectiveness of radiative cooling, and the radial surface density profile, planets migrate inward or outward. Clearly, this will influence the semimajor axis - mass distribution of planets as predicted by population synthesis simulations. Aims: Our goal is to study the global effects of radiative cooling, viscous torque desaturation and gap opening as well as stellar irradiation on the tidal migration of a synthetic planet population. Methods: We combine results from several analytical studies and 3D hydrodynamic simulations in a new semi-analytical migration model for the application in our planet population synthesis calculations. Results: We find a good agreement of our model with torques obtained in a 3D radiative hydrodynamic simulations. We find three convergence zones in a typical disc, towards which planets migrate from the in- and outside, affecting strongly the migration behavior of low-mass planets. Interestingly, this leads to slow type II like migration behavior for low-mass planets captured in those zones even without an ad hoc migration rate reduction factor or a yet to be defined halting mechanism. This means that the new prescription of migration including non-isothermal effects makes the preciously widely used artificial migration rate reduction factor obsolete. Conclusions: Outward migration in parts of a disc makes some planets survive long enough to become massive. The convergence zones lead to a potentially observable accumulations of low-mass planets at certain semimajor axes. Our results indicate that further studies of the mass where the corotation torque saturates will be needed since its value has a major impact on the properties of planet populations.Comment: 18 pages, 15 figures. Accepted for A&

Formation and structure of the three Neptune-mass planets system around HD69830

Since the discovery of the first giant planet outside the solar system in 1995 (Mayor & Queloz 1995), more than 180 extrasolar planets have been discovered. With improving detection capabilities, a new class of planets with masses 5-20 times larger than the Earth, at close distance from their parent star is rapidly emerging. Recently, the first system of three Neptune-mass planets has been discovered around the solar type star HD69830 (Lovis et al. 2006). Here, we present and discuss a possible formation scenario for this planetary system based on a consistent coupling between the extended core accretion model and evolutionary models (Alibert et al. 2005a, Baraffe et al. 2004,2006). We show that the innermost planet formed from an embryo having started inside the iceline is composed essentially of a rocky core surrounded by a tiny gaseous envelope. The two outermost planets started their formation beyond the iceline and, as a consequence, accrete a substantial amount of water ice during their formation. We calculate the present day thermodynamical conditions inside these two latter planets and show that they are made of a rocky core surrounded by a shell of fluid water and a gaseous envelope.Comment: Accepted in AA Letter

Elemental abundances and minimum mass of heavy elements in the envelope of HD 189733b

Oxygen (O) and carbon (C) have been inferred recently to be subsolar in abundance from spectra of the atmosphere of the transiting hot Jupiter HD 189733b. Yet, the mass and radius of the planet coupled with structure models indicate a strongly supersolar abundance of heavy elements in the interior of this object. Here we explore the discrepancy between the large amount of heavy elements suspected in the planet's interior and the paucity of volatiles measured in its atmosphere. We describe the formation sequence of the icy planetesimals formed beyond the snow line of the protoplanetary disk and calculate the composition of ices ultimately accreted in the envelope of HD 189733b on its migration pathway. This allows us to reproduce the observed volatile abundances by adjusting the mass of ices vaporized in the envelope. The predicted elemental mixing ratios should be 0.15--0.3 times solar in the envelope of HD 189733b if they are fitted to the recent O and C determinations. However, our fit to the minimum mass of heavy elements predicted by internal structure models gives elemental abundances that are 1.2--2.4 times oversolar in the envelope of HD189733b. We propose that the most likely cause of this discrepancy is irradiation from the central star leading to development of a radiative zone in the planet's outer envelope which would induce gravitational settling of elements. Hence, all strongly irradiated extrasolar planets should present subsolar abundances of volatiles. We finally predict that the abundances of nitrogen (N), sulfur (S) and phosphorus (P) are of $\sim$ $2.8 \times 10^{-5}$, $5.3 \times 10^{-6}$ and $1.8 \times 10^{-7}$ relative to H$_2$, respectively in the atmosphere of HD 189733b.Comment: Accepted for publication in Astronomy & Astrophysic

Application of recent results on the orbital migration of low mass planets: convergence zones

Previous models of the combined growth and migration of protoplanets needed large ad hoc reduction factors for the type I migration rate as found in the isothermal approximation. In order to eliminate these factors, a simple semi-analytical model is presented that incorporates recent results on the migration of low mass planets in non-isothermal disks. It allows for outward migration. The model is used to conduct planetary populations synthesis calculations. Two points with zero torque are found in the disks. Planets migrate both in- and outward towards these convergence zones. They could be important for accelerating planetary growth by concentrating matter in one point. We also find that the updated type I migration models allow the formation of both close-in low mass planets, but also of giant planets at large semimajor axes. The problem of too rapid migration is significantly mitigated.Comment: 4 pages, 3 figures. Proceedings of the IAU Symposium 276, 2010: The Astrophysics of Planetary Systems: Formation, Structure, and Dynamical Evolution, ed. A. Sozzetti, M. G. Lattanzi, and A. P. Bos

Theoretical models of planetary system formation: mass vs semi-major axis

Planet formation models have been developed during the last years in order to try to reproduce the observations of both the solar system, and the extrasolar planets. Some of these models have partially succeeded, focussing however on massive planets, and for the sake of simplicity excluding planets belonging to planetary systems. However, more and more planets are now found in planetary systems. This tendency, which is a result of both radial velocity, transit and direct imaging surveys, seems to be even more pronounced for low mass planets. These new observations require the improvement of planet formation models, including new physics, and considering the formation of systems. In a recent series of papers, we have presented some improvements in the physics of our models, focussing in particular on the internal structure of forming planets, and on the computation of the excitation state of planetesimals, and their resulting accretion rate. In this paper, we focus on the concurrent effect of the formation of more than one planet in the same protoplanetary disc, and show the effect, in terms of global architecture and composition of this multiplicity. We use a N-body calculation including collision detection to compute the orbital evolution of a planetary system. Moreover, we describe the effect of competition for accretion of gas and solids, as well as the effect of gravitational interactions between planets. We show that the masses and semi-major axis of planets are modified by both the effect of competition and gravitational interactions. We also present the effect of the assumed number of forming planets in the same system (a free parameter of the model), as well as the effect of the inclination and eccentricity damping.Comment: accepted in Astronomy and Astrophysic