The PAIRS project: a global formation model for planets in binaries. II. Gravitational perturbation effects from secondary stars

Roughly half of Sun-like stars have at least one stellar companion, whereas it is widely assumed that most known exoplanets orbit single stars, largely due to observational biases. However, astrometric surveys, direct imaging, and speckle interferometry are steadily increasing the number of confirmed exoplanets in binaries. A stellar companion introduces additional effects, such as circumstellar disk truncation and gravitational perturbations, which can strongly impact planet formation. While global planet formation models (e.g., Bern model) have been broadly applied to single stars, modeling S-type binaries requires key modifications to capture these effects. This study extends the Bern model by incorporating the gravitational influence of a stellar companion into its N-body integrator, allowing us to quantify how this perturbation affects planetary formation and final system architecture across a range of binary configurations. By comparing binary and single-star systems under identical initial conditions, we can assess the specific impact of binary-induced dynamics. We modified the Bern model’s N-body integrator to include secondary star perturbations and ran three sets of simulations: (i) a grid of in situ single-embryo cases to quantify gravitational effects; (ii) formation simulations with and without migration to compare outcomes with single-star analogs; and (iii) multi-embryo runs to evaluate impacts on multi-planetary systems. Planets forming beyond half the host star’s Hill radius are much more likely to become unbound (i.e., in about six out of seven cases), especially in systems with high binary eccentricity. Even within stable zones, growth is suppressed by both reduced material availability (due to disk truncation) and increased eccentricity from stellar perturbations. Multi-embryo simulations have shown that these perturbations tend to reshape architectures even in dynamically stable regions. Both disk truncation and stellar perturbations must be included to model planet formation in S-type binaries accurately. Neglecting either one will end up misrepresenting planetary growth and survival. Finally, population synthesis studies will be key in making statistical comparisons with observed systems.