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

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 im-aged 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 pro-toplanet not only during the early formation phase, but also during the gas runaway accretion phase, and during 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. We put special emphasis on the validatio