Gas disk interactions, tides and relativistic effects in the rocky planet formation at the sub-stellar mass limit

Abstract

Context. The confirmed exoplanet population around very low mass stars is increasing considerable through data from the latest space missions and improvements in ground-based observations, particularly with the detection of Earth-like planets in the habitable zones. However, theoretical models need to improve in the study of planet formation and evolution around low-mass hosts. Aims. Our main goal is to study the formation of rocky planets and the first 100 Myr of their dynamical evolution around a star with a mass of 0.08 M·, which is close to the substellar mass limit. Methods. We developed two sets of N-body simulations assuming an embryo population affected by tidal and general relativistic effects, refined by the inclusion of the spin-up and contraction of the central star. This population is immersed in a gas disk during the first 10 Myr. Each set of simulations incorporated a different prescription from the literature to calculate the interaction between the gas-disk and the embryos: one widely used prescription which is based on results from hydrodynamics simulations, and a recent prescription that is based on the analytic treatment of dynamical friction. Results. We found that in a standard disk model, the dynamical evolution and the final architectures of the resulting rocky planets are strongly related with the prescription used to treat the interaction within the gas and the embryos. Its impact on the resulting close-in planet population and particularly on those planets that are located inside the habitable zone is particularly strong. Conclusions. The distribution of the period ratio of adjacent confirmed exoplanets observed around very low mass stars and brown dwarfs and the exoplanets that we obtained from our simulations agrees well only when the prescription based on dynamical friction for gas-embryo interaction was used. Our results also reproduce a close-in planet population of interest that is located inside the habitable zone. A fraction of these planets will be exposed for a long period of time to the stellar irradiation inside the inner edge of the evolving habitable zone until the zone reaches them.