# Revisiting the dynamics of planets in binaries: evolutionary timescales and the effect of early stellar evolution

## TL;DR

This paper develops advanced models for the long-term dynamics of planets in binary systems, incorporating stellar evolution effects, and demonstrates their importance through specific case studies and an open-source computational tool.

## Contribution

It introduces explicit formulas for the secularized octupolar Hamiltonian with relativistic and non-conservative effects, and applies them to study stellar evolution impacts on planetary dynamics.

## Key findings

- Octupolar expansion is essential for accurate evolution predictions of HD 80606b.
- Stellar radius changes significantly affect planetary dynamical timescales.
- The open-source package SecDev3B enables reproducible and improved dynamical modeling.

## 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 \texttt{SecDev3B}, that can be used to reproduce our results or test improved versions of the models. In order to test it, we study the long-term dynamical evolution of S-type binary planets during the pre-main-sequence phase of stellar evolution. During that phase, stellar radius significantly changes in timescales similar to secular timescales. We hypothesize that when close-encounters between the planet and its host star happens (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 inclinations ($\itot\ge 60^\circ$), moderate eccentricities ($0.2\le e\le 0.4$) and planets located around 1 AU, the evolution of stellar radius during the first few hundreds of Myr, alters significantly the timescales of dynamical evolution.