Abstract. We present a new model of giant planet formation that extends the core-accretion model of Pollack et al. (1996, Icarus, 124, 62) to include migration, disc evolution and gap formation. We show that taking these effects into account can lead to much more rapid formation of giant planets, making it compatible with the typical disc lifetimes inferred from observations of young circumstellar discs. This speed up is due to the fact that migration prevents the severe depletion of the feeding zone as observed in in situ calculations. Hence, the growing planet is never isolated and it can reach cross-over mass on a much shorter timescale. To illustrate the range of planets that can form in our model, we describe a set of simulations in which we have varied some of the initial parameters and compare the final masses and semi-major axes with those inferred from observed extra-solar planets.

International audienc

Context. With the high number of extrasolar planets discovered by now, it has become possible to use the properties of this planetary population to constrain theoretical formation models in a statistical sense. This paper is the first in a series in which we carry out a large number of planet population synthesis calculations within the framework of the core accretion scenario. We begin the series with a paper mainly dedicated to the presentation of our approach, but also the discussion of a representative synthetic planetary population of solar like stars. In the second paper we statistically compare the subset of detectable planets to the actual extrasolar planets. In subsequent papers, we shall extend the range of stellar masses and the properties of protoplanetary disks. Aims. The last decade has seen a large observational progress in characterizing both protoplanetary disks, and extrasolar planets. Concurrently, progress was made in developing complex theoretical formation models. The combination of these three developments allows a new kind of study: the synthesis of a population of planets from a model, which is compared with the actual population. Our aim is to obtain a general overview of the population, to check if we quantitatively reproduce the most important observed properties and correlations, and to make predictions about the planets that are not yet observable. Methods. Based as tightly as possible on observational data, we have derived probability distributions for the most important initial conditions for the planetary formation process. We then draw sets of initial conditions from these distributions and obtain the corresponding synthetic planets with our formation model. By repeating this step many times, we synthesize the populations. Results. Although the main purpose of this paper is the description of our methods, we present some key results: we find that the variation of the initial conditions in the limits occurring in nature leads to the formation of planets of wide diversity. This formation process is best visualized in planetary formation tracks in the mass-semimajor axis diagram, where different phases of concurrent growth and migration can be identified. These phases lead to the emergence of sub-populations of planets distinguishable in a mass-semimajor axis diagram. The most important ones are the "failed cores", a vast group of core-dominated low mass planets, the "horizontal branch", a sub-population of Neptune mass planets extending out to 6 AU, and the "main clump", a concentration of giant gaseous planets at around 0.3−2 AU.

Context. A first characterization of extrasolar planets by the observational determination of the radius has recently been achieved for a large number of planets. For some planets, a measurement of the luminosity has also been possible, with many more directly imaged planets expected in the near future. The statistical characterization of exoplanets through their mass-radius and mass-luminosity diagram is becoming possible. This is for planet formation and evolution theory of similar importance as the mass-distance diagram. Aims. Our aim is to extend our planet-formation model into a coupled formation and evolution model. We want to calculate from one single model in a self-consistent way all basic quantities describing a planet: its mass, semimajor axis, composition, radius, and luminosity. We then want to use this model for population synthesis calculations. Methods. In this and a companion paper, we show how we solve the structure equations describing the gaseous envelope of a protoplanet during the early-formation phase, the gas runaway accretion phase, and the evolutionary phase at constant mass on Gyr timescales. We improve the model further with a new prescription for the disk-limited gas accretion rate, an internal structure model for the planetary core assuming a differentiated interior, and the inclusion of radioactive decay as an additional heat source in the core. Results. We study the in situ formation and evolution of Jupiter, the mass-radius relationship of giant planets, the influence of the core mass on the radius, and the luminosity both in the "hot start" and the "cold start" scenario. Special emphasis is placed on the validation of the model by comparing it with other models of planet formation and evolution. We find that our results agree very well with those of more complex models, despite a number of simplifications we make in our calculations.Conclusions. The upgraded model yields the most important physical quantities describing a planet from its beginning as a tiny seed embryo to a Gyr-old planet. This is the case for all planets in a synthetic planetary population. Therefore, we can now use selfconsistently the observational constraints coming from all major observational techniques. This is important in a time where different techniques yield constraints on very diverse sub-populations of planets, and where it is difficult to put all these constraints together in one coherent picture. Our comprehensive formation and evolution model should be helpful in this situation for the understanding of exoplanets.

Context. This is the fourth paper in a series showing the results of planet population synthesis calculations. In Paper I, we presented our methods. In Paper II, we compared the synthetic and the observed planetary population statistically. Paper III addressed the influences of the stellar mass on the population. Aims. Our goal in this fourth paper is to systematically study the effects of important disk properties, namely disk metallicity, mass, and lifetime on fundamental properties of planets like mass and semimajor axis. Methods. For a large number of protoplanetary disks that have properties following distributions derived from observations, we calculated a population of planets with our formation model. The model is based on the classical core accretion paradigm but selfconsistently includes planet migration and disk evolution. Results. We find a very large number of correlations. Regarding the planetary initial mass function, metallicity, M disk , and τ disk play different roles. For high metallicities, giant planets are more frequent. For high M disk , giant planets are more massive. For long τ disk , giant planets are both more frequent and massive. At low metallicities, very massive giant planets cannot form, but otherwise giant planet mass and metallicity are nearly uncorrelated. In contrast, (maximum) planet masses and disk gas masses are correlated. The formation of giant planets is possible for initial planetesimal surface densities Σ S of at least 6 g/cm 2 at 5.2 AU. The best spot for giant planet formation is at ∼5 AU. In-and outside this distance, higher Σ S are necessary. Low metallicities can be compensated for by high M disk , and vice versa, but not ad infinitum. At low metallicities, giant planets only form outside the ice line, while giant planet formation occurs throughout the disk at high metallicities. The extent of migration increases with M disk and τ disk and usually decreases with metallicity. No clear correlation of metallicity and the semimajor axis distribution of giant planets exists because in low-metallicity disks, planets start farther out, but migrate more, while the contrary applies to high metallicities. The final semimajor axis distribution contains an imprint of the ice line. Close-in low mass planets have a lower mean metallicity than hot Jupiters. The frequency of giant planets varies approximately as M Conclusions. The properties of protoplanetary disks -the initial and boundary conditions for planet formation -are decisive for the properties of planets, and leave many imprints on the population.

Context. This is the second paper in a series of papers showing the results of extrasolar planet population synthesis calculations using our extended core accretion model. In the companion paper (Paper I), we presented in detail the methods we use. In subsequent papers, we shall discuss the effect of the host star's mass on the planetary population and the influence of various properties of protoplanetary disks. Aims. In this second paper, we focus on planets orbiting solar-like stars. The goal is to use the main characteristics of the actually observed extrasolar planet population to derive in a statistical manner constraints on the planet formation models. Methods. Drawing initial conditions for our models at random from probability distributions derived as closely as possible from observations, we synthesize a number of planetary populations. By applying an observational detection bias appropriate for radial velocity surveys, we identify the potentially detectable synthetic planets. The properties of these planets are compared in quantitative statistical tests with the properties of a carefully selected sub-population of actually observed extrasolar planets. Results. We use a two dimensional Kolmogorov-Smirnov test to compare the mass-distance distributions of synthetic and observed planets, as well as the one dimensional version of the test to compare the M sin i, the semimajor axis and the [Fe/H] distribution. We find that while many combinations of parameters lead to unacceptable distributions, a number of models can account to a reasonable degree of statistical significance for most of the properties of the observed sample. We concurrently account for many other observed features, e.g. the "metallicity effect". This gives us confidence that our model captures several essential features of giant planet formation. In addition, the fact that many parameter combinations could be rejected indicates that planet population synthesis is indeed a promising approach to constrain formation models. Our simulations allow us also to extract a number of properties of the underlying exoplanet population that are not yet directly detectable. For example, we have derived the planetary initial mass function (PIMF) and have been led to conclude that the planets detected so far represent only the tip of the iceberg (9%) of all the existing planets. The PIMF can also be used to predict how the detectable extrasolar planet population will change as the instrumental precision of radial velocity surveys improves from ∼10 m/s to ∼1 m/s, or even to an extreme precision of 0.1 m/s.

Over the past two years, the search for low-mass extrasolar planets has led to the detection of seven so-called 'hot Neptunes' or 'super-Earths' around Sun-like stars. These planets have masses 5-20 times larger than the Earth and are mainly found on close-in orbits with periods of 2-15 days. Here we report a system of three Neptune-mass planets with periods of 8.67, 31.6 and 197 days, orbiting the nearby star HD 69830. This star was already known to show an infrared excess possibly caused by an asteroid belt within 1 au (the Sun-Earth distance). Simulations show that the system is in a dynamically stable configuration. Theoretical calculations favour a mainly rocky composition for both inner planets, while the outer planet probably has a significant gaseous envelope surrounding its rocky/icy core; the outer planet orbits within the habitable zone of this star.

Aims. We present an inversion method based on Bayesian analysis to constrain the interior structure of terrestrial exoplanets, in the form of chemical composition of the mantle and core size. Specifically, we identify what parts of the interior structure of terrestrial exoplanets can be determined from observations of mass, radius, and stellar elemental abundances. Methods. We perform a full probabilistic inverse analysis to formally account for observational and model uncertainties and obtain confidence regions of interior structure models. This enables us to characterize how model variability depends on data and associated uncertainties. Results. We test our method on terrestrial solar system planets and find that our model predictions are consistent with independent estimates. Furthermore, we apply our method to synthetic exoplanets up to 10 Earth masses and up to 1.7 Earth radii, and to exoplanet Kepler-36b. Importantly, the inversion strategy proposed here provides a framework for understanding the level of precision required to characterize the interior of exoplanets. Conclusions. Our main conclusions are (1) observations of mass and radius are sufficient to constrain core size; (2) stellar elemental abundances (Fe, Si, Mg) are principal constraints to reduce degeneracy in interior structure models and to constrain mantle composition; (3) the inherent degeneracy in determining interior structure from mass and radius observations does not only depend on measurement accuracies, but also on the actual size and density of the exoplanet. We argue that precise observations of stellar elemental abundances are central in order to place constraints on planetary bulk composition and to reduce model degeneracy. We provide a general methodology of analyzing interior structures of exoplanets that may help to understand how interior models are distributed among star systems. The methodology we propose is sufficiently general to allow its future extension to more complex internal structures including hydrogen-and water-rich exoplanets.