We present a GPU accelerated N-body integrator using the Bulirsch–Stoer method, called GANBISS (GPU accelerated n-body code for binary star systems). It is designed to simulate the dynamical evolution of planetesimal disks in binary star systems which contain some thousand disk objects. However, it can also be used for studies of non-interacting massless bodies where up to 50 million objects can be studied in a simulation. GANBISS shows the energy and angular momentum conservation behavior of non-symplectic integration methods. The code is written in CUDA C and can be run on NVIDIA GPUs of compute capability of at least 3.5. A comparison of GPU and CPU computations indicates a speed-up of the GPU performance of up to 100 times—depending on the number of disk objects.

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.

Recent GAIA observations revealed that the K-type star Gliese 710 will cross the Oort cloud in a distance between approximately 4000 and 12000 au in about 1.3 Myrs. This occurrence motivated us to study the influence of a stellar encounter on comets in the outer region of the solar system. Even if the Oort cloud extends to 100000 au from the sun, we restrict our study to the region between 30 and 25000 au where 25 million objects are distributed randomly. Comets at larger distances are not taken into account as they hardly enter the observable region after a single stellar fly-by. An overview of all objects that are scattered towards the sun for the different fly-by distances at 4000, 8000 and 12000 au shows that only a handful of objects are moving towards the sun immediately after the stellar encounter.However, a subsequent long-term study of all objects that are moved into highly eccentric motion by the stellar fly-by shows a significant increase of comets crossing Jupiter’s orbit and entering into the observable region. In addition, our study shows the first comets crossing the orbit of Earth only about 2.5 Myrs after the stellar fly-by. Thus, the impact risk for the Earth increases only some million years after the stellar fly-by.

Based on observations by Bailer-Jones et al. (2018) who propose a close fly-by of the K-type star Gliese 710 in approximately 1.36 Myr we investigate the immediate influence of the stellar passage on trajectories of Oort cloud objects. Using a newly developed GPU-based N-body code (Zimmermann (2021)) we study the motion of 3.6 million testparticles in the outer Solar system where the comets are distributed in three different “layers” around the Sun and the 4 giant planets. We study the immediate influence of Gliese 710 at three passage distances of 12000, 4300, and 1200 au. Additionally, different inclinations of the approaching star are considered. Depending on the passage distance a small number of comets (mainly from the disk and flared disk) is scattered into the observable region (< 5 au) around the Sun. In addition, a huge number of comets (mainly the ones directly in the path of the passing star) shows significant changes of their perihelia. But, they will enter the inner Solar system a long time after the stellar fly-by depending on their dynamical evolution.

Stars passing close by the Sun experience a change of their trajectory due to gravitational interaction -- which also changes the trajectory of the Sun around the galactic center. In this study we show possible changes for the outer Solar system caused by the future flyby of Gliese 710 considering various inclinations of the passing star.Introduction Most stars are born in clusters. Gravitational interactions between the cluster members can have significant influence on the planet formation process and small body distributions [2]. Even after having left the cluster flybys with other stars can happen. The Sun will experience such a flyby in about 1.36 Myr. Gliese 710 (a K-type star) will probably pass inside of the Oort cloud [1]. This motivated us to investigate the influence of passing stars on the trajectory of the Sun as well as on the orbits of the gas planets [3,5] and Oort cloud objects. The stellar flyby has been carried out for different stellar types (M -- G-type stars) with different encounter velocities [4] as well as different impact parameters and different inclinations of the passing star.Setup and Method The setup uses the outer Solar system including the Sun, the 4 giant planets (Jupiter, Saturn, Uranus, and Neptune), Oort cloud comets, and a passing star. The passing star initially moves on a straight line passing the Sun at a certain distance (i.e., impact parameter d). The ranges for the parameters are summed up as follows:Mass of passing star: 0.21 MSun, 0.6 MSun (i.e., Gliese710), and 1 MSun Impact parameter: d between 4000 and 12000 au (estimated area of Gliese 710 flyby [1] -- see figure 1) and for closer flybys (e.g., 400 to 600 au -- see figure 2) Velocity of the passing star: taken from [4]: v - σv , v , v + σv -- see figure 1 The numerical simulations were carried out using the newly developed N-body package [6], i.e., a parallelized GPU-N-body code designed to handle the gravitational interaction of up to 10000 massive particles. Each stellar flyby was integrated for about 30000 yrs where both the initial and the final position of the passing star were 100000 au away from the Sun.ResultsThe results show a distinct bend in the trajectory of the passing stars at the point of closest approach to the Sun. Vice versa the Sun is diverted from its original trajectory, too. Figure 1 shows how much a passing star influences the Sun's path. The Sun might be diverted by up to 30 au by a K-type star. For impact parameters larger than 12000au the diversion is smaller than 20au even for a passing G-type star. An analysis of the orbits of the 4 giant planets after an inclined flyby shows that for retrograde passages of a K-type star the eccentricity for Saturn is decreased. For Uranus the eccentricity increases for inclinations bigger than 80° -- see figure 2.For a passing G-type star at d = 600 au with 0° inclination the long term changes in the eccentricities of the 4 giant planets are depicted in figure 3.The scattering of Oort cloud objects by a passing star with d=12000au, M=0.6MSun (Gliese 710), and inclination of 0° is depicted in figure 4. Objects in the vicinity of the passage (up to 4000 au distance from the passing star) get scattered the strongest. A change in eccentricty is possible up to 0.6. If Gliese 710 passes at 4000 au, we assume that also Kuiper belt objects can be perturbed. Additionally, we assume that in the inner Oort cloud there are more objects than in the outer cloud (used in our integrations) thus more objects might get scattered inwards.Summary and Conclusions We showed that the orbit of the Sun around the galactic center can be altered depending on the properties of the passing star (mass, velocity, impact parameter). This can slightly change change its orbit in the Milky Way. Our study for the outer Solar system shows only small perturbations of the eccentricities of the planetary orbits. Only inclinations of the passing star larger than 80° show some changes of the orbits of Uranus and Saturn. These small perturbations could influence the orbital behaviour and will be studied in more detail. In this context figure 3 shows slight deviations of the planetary eccentricities after a stellar passage with inclination of 0°. The changes of the orbits are only visible in the long time computation. Short time changes are visible in the orbits of Oort cloud objects which experience the close flyby of a star.Acknowledgements This research was funded in whole by the Austrian Science Fund (FWF) [P33351-N].References [1] Bailer-Jones C.~A.~L.: New stellar encounters discovered in the second Gaia data release; A$\&$A, 616, A37, 2018. [2] Bancelin D., Nordlander T., Pilat-Lohinger E., Loibnegger B.: Dynamics of passing-stars-perturbed binary star systems; MNRAS, 486, 4, 4773-4780, 2019. [3] Innanen K.~A., Zheng J.~Q, Mikkola S., Valtonen M.~J.: The Kozai Mechanism and the Stability of Planetary Orbits in Binary Star Systems; AJ, 113, 1915, 1997. [4] Rickman H., Fouchard M., Froeschl{\'e} C., Valsecchi G.~B.: Injection of Oort Cloud Comets: The Fundamental Role of Stellar Perturbations; Asteroids, Comets, Meteors 2008, LPICo, 1405, 8077, 2008. [5] Tanikawa K., Ito T.: Subsystems in a Stable Planetary System; PASJ, 59, 989, 2007. [6] Zimmermann M.: The influene of binary systems on planetesimal disks. Master thesis, University of Vienna, 2021.

Introduction:Gaia observations (DR1-DR3) confirmed that the solar system will experience a close flyby of the K-type star Gliese 710 in about 1.3 Myrs. This 0.6 solar mass star will pass through the Oort cloud at a velocity of ~14.4 km/s, an inclination of ~150° with respect to the ecliptic and approach the Sun up to approximately 10,000 au (according to Gaia DR3 release). Earlier studies predicted flyby distances between 12000 and 4300 au (see e.g. Berski and Dybczynski 2016; Bailer-Jones et al. 2018; De la Fuente Marcos and De la Fuente Marcos 2018). The stellar passage will perturb the comets outside Neptune’s orbit, especiallyobjects entering the sphere of influence of Gliese 710.Assuming that there are 10¹² Oort cloud objects between 100 to 100000 au from the Sun (resulting in a mean object density of 0.0002 comets/au³), it is obvious that numerical calculations of such a system are not within the realms of possibility even if a numerical code allows orbit calculation of tens of millions of (non-interacting) objects.Numerical study:Using our recently developed GPU based N-body code GANBISS (Zimmermann & Pilat-Lohinger 2023) we studied the orbits of some hundred million test-comets in the outer solar system for the time of the flyby of Gliese 710 which takes about 64000 years. 50 million comets were distributed in each of the six zones around the hyperbolic trajectory of the passing star. The cross section of this (red) tube is defined by the sphere of influence of Gliese 710. Figure 1 shows the six zones of the Oort cloud: a flat disk (purple) from 50 to 5000 au (i < 1°), a flared disk (green) from 5000 to 10000 au (i < 45°) and a spherical cloud between 10000 and 100000 au (0° < i < 180°) which has been divided into four zones.Results:When looking at the changes in the orbital parameters of the comets due to the stellar flyby in the individual zones, the (a,e) diagrams show V-structures (see Pilat-Lohinger et al. 2022a, 2022b) that disappear when the entire area of the Oort cloud is considered at once.The passage of a star thus produces two branches of comets: an inward-facing branch that can transport comets towards the inner solar system, and an outward-facing branch that might scatter objects into the interstellar region. Moreover, the inward-facing branch shows higher eccentricities than the outward-facing branch, particularly in case of comets of the outer spherical cloud.Assuming that the radius of Gliese 710's sphere of influence is about 2000 au -- resulting in an average object density of 0.00017 obj/au3 in the tube around the trajectory -- our calculations show that after the stellar flyby more than 4500 comets have their pericenter within 5 au and more than 108 million comets were scattered into interstellar space.Conclusion:Our numerical study shows that the star Gliese 710 -- which will pass through the Oort Cloud up to a distance of 10000 au from the Sun in about 1.3 million years -- will scatter several thousand comets towards the inner solar system, increasing the number of comets crossing Earth’s orbit and the risk of encounters with planet Earth.Figure 1: Sketch of Gliese 710's flybyFigure 2: Semi-major axis – eccentricity map of the comets after the stellar flyby. The different colors denote the different zone (see Fig.1). Note that the map shows a reduced number of comets.