Characterization of exoplanets from their formation - I. Models of combined planet formation and evolution

摘要

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 self-consistently 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.