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

Abstract: Our main goal is to study the formation of rocky planets and the first $100~\textrm{Myr}$ of their dynamical evolution around a star with mass $0.08 M_\odot$ close to the substellar mass limit. 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, and immerse in a gas disk during the first 10 Myr. Each set of simulations incorporates a different prescription from literature to calculate the interaction between the gas-disk and the embryos: one widely used prescription based on results from hydrodynamics simulations, and a recent prescription based on the analytic treatment of dynamical friction. We found that given a standard disk model, the dynamical evolution and the final architectures of the resulting rocky planets is strongly related with the prescription used to treat the interaction within the gas and the embryos, having a big impact on the resulting close-in planet population and particularly on those located inside the habitable zone. We found a good agreement within the distribution of period ratio of adjacent confirmed exoplanets observed around very low mass stars and brown dwarfs and those obtained from our simulations only when the prescription based on dynamical friction for gas-embryo interaction is used. Our results also reproduce a close-in planet population of interest located inside the habitable zone. A fraction of those 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.