<i>N</i> -body interactions and collisions in circumstellar discs for planar and inclined binary star configurations

ABSTRACT The discovery of exoplanets in binary star systems – now numbering about 850 of the nearly 4600 known exoplanet systems – raises questions about whether observational bias or stellar companions inhibit planet formation. While most studies on terrestrial planet formation assume planar configurations, wide binaries likely feature random inclinations, potentially disrupting planet-forming discs. This study explores the evolution of embryo–planetesimal discs in S-type motion in misaligned binary systems, focusing on the stage after the gas phase when terrestrial planet formation begins and gravitational interactions dominate. Using our GPU-accelerated N-body code GANBISS, we simulate discs with 2000 planetesimals and 25 planetary embryos, studying the influence of the planetesimals on the evolution of the embryos and tracking their growth through collisions. After the simulations, we analyse collision outcomes with an analytical model. Moreover, for certain inclined binary configurations, we compare dynamically excited (perturbed by the secondary star) with cold discs in inclined configurations, as the distribution after the gas phase in misaligned binaries remains unclear. Our simulations reveal two key outcomes: (i) embryos migrate slightly inwards in misaligned systems, and (ii) the initial large oscillations in embryos’ inclinations and nodes around the respective values of the secondary star dampen over time. Collision analysis shows distinct differences: planar systems favour accretive collisions, while inclined configurations exhibit more destructive events. These findings underscore the sensitivity of planet formation dynamics to binary star alignment and initial disc conditions.