Planetary Population Synthesis: the importance of the solids accretion rate

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In the framework of the nucleated instability model, the formation time-scale of giant planets is very sensitive to the time it takes to build the solid core. The accretion of solids can be described by two different, consecutive regimes: it first proceeds in a very fast fashion, known as runaway growth, and later on in a much slower regime, the so-called oligarchic growth. The transition between the runaway and the oligarchic growth depends on many parameters (e.g. the isolation mass and the size of the accreted planetesimals), but as a general rule we can assume that an embryo of a Lunar mass is already an oligarch. Then, the timescale to build a 10 Earth masses (M ) core is regulated by the oligarchic regime, as the previous runaway stage proceeds in a negligible amount of time compared to the oligarchic timescale. In this work we show the results of adopting the oligarchic growth for the core in planetary population synthesis calculations. In previous works (see [1], [2]) a fast solids accretion rate was prescribed, leading to a very fast formation of massive solid embryos. Here we show that when considering the oligarchic growth, the formation of giant planets is more difficult, especially in the outer parts of the disk, where the formation of big planets is almost impossible under these hypothesis. On the other hand, many Earth to Super- Earth sized planets are found in the very innermost parts of the disk. However, if the size of the accreted planetesimals is reduced, the formation of giant planets is more likely, preserving also a large amount of smaller planets. We also consider the formation of planetary systems, including the N-body interaction between the forming planets and the collisions that may occur among them during their migration. In the case of many planets forming in the same disk, we find that the final masses of the planets are smaller (but not too small) than in the case of a single planet per star.

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