Revisiting the dynamics of planets in binaries: Evolutionary time-scales and the effect of early stellar evolution

Abstract

The discovery of planets in binaries is one the most interesting outcomes of planetary research. With the growing number of discoveries has also grown the interest on describing their formation, long-term evolution, and potential habitability. In this work, we revisit the dynamics of planets in S-type binary systems. For that purpose, we develop explicit formulas for the secularized octupolar Hamiltonian, coupled with general relativistic corrections and non-conservative interactions. We implemented those formulas in an open-source package secdev3b, which can be used to reproduce our results or test improved versions of the models. We study the long-term dynamical evolution of S-type binary planets during the pre-main-sequence phase of their host stars. During that phase, stellar radius significantly changes in time-scales similar to that of the secular dynamics. We hypothesize that when close-encounters between the planet and its host star happen (e.g. via Lidov-Kozai effect), particularities in the secular formalism plus changes in stellar radius may alter significantly the dynamical evolution. We study the well-known binary planet HD 80606b and found that an octupolar expansion of the conservative Hamiltonian is required to properly predict its dynamical evolution. We also apply the dynamical model, enriched with results coming from stellar evolutionary models, to demonstrate that in S-type systems around low-mass stars, with relative high mutual inclinations (itot ≥ 60°), moderate eccentricities (0.2 ≤ e1 ≤ 0.4), and planets located around 1 au, the evolution of stellar radius during the first few hundreds of Myr, alters significantly the time-scales of dynamical evolution.