Tidal and general relativistic effects in rocky planet formation at the substellar mass limit using N-body simulations

Context. Recent observational results show that very low mass stars and brown dwarfs are able to host close-in rocky planets. Low-mass stars are the most abundant stars in the Galaxy, and the formation efficiency of their planetary systems is relevant in the computation of a global probability of finding Earth-like planets inside habitable zones. Tidal forces and relativistic effects are relevant in the latest dynamical evolution of planets around low-mass stars, and their effect on the planetary formation efficiency still needs to be addressed. Aims. Our goal is to evaluate the impact of tidal forces and relativistic effects on the formation of rocky planets around a star close to the substellar mass limit in terms of the resulting planetary architectures and its distribution according to the corresponding evolving habitable zone. Methods. We performed a set of N-body simulations spanning the first 100 Myr of the evolution of two systems composed of 224 embryos with a total mass 0.25 M⊕ and 74 embryos with a total mass 3 M⊕ around a central object of 0.08 M⊙. For these two scenarios we compared the planetary architectures that result from simulations that are purely gravitational with those from simulations that include the early contraction and spin-up of the central object, the distortions and dissipation tidal terms, and general relativistic effects. Results. We found that including these effects allows the formation and survival of a close-in (r < 0.07 au) population of rocky planets with masses in the range 0.001 < m∕M⊕ < 0.02 in all the simulations of the less massive scenario, and a close-in population with masses m ~ 0.35 M⊕ in just a few of the simulations of the more massive scenario. The surviving close-in bodies suffered more collisions during the integration time of the simulations. These collisions play an important role in their final masses. However, all of these bodies conserved their initial amount of water in mass throughout the integration time. Conclusions. The incorporation of tidal and general relativistic effects allows the formation of an in situ close-in population located in the habitable zone of the system. This means that both effects are relevant during the formation of rocky planets and their early evolution around stars close to the substellar mass limit, in particular when low-mass planetary embryos are involved.