The Solar System's planets orbit the Sun on near-circular orbits within a common plane, a consequence of their formation from a protoplanetary disk. However, thousands of smaller bodies beyond Neptune (trans-Neptunian objects or TNOs) exhibit surprisingly eccentric and inclined orbits. This discrepancy suggests a significant perturbing force acted on these objects after their formation. One prevalent hypothesis attributes this to the migration of the giant planets during the early Solar System, causing scattering of the TNOs. However, this model struggles to explain three distinct TNO populations: (i) the cold Kuiper belt objects with near-circular orbits close to the plane, (ii) Sedna-like objects at large distances with highly eccentric orbits, and (iii) TNOs with high inclinations. The existence of these populations, particularly their clustering, challenges the planet-scattering hypothesis. This research explores an alternative hypothesis: a close passage of another star during the early Solar System. While initially deemed too infrequent, recent observations suggest such encounters are more common than previously thought. Previous simulations have indicated the potential for a stellar flyby to generate populations similar to the cold Kuiper belt and Sedna-like objects, but the parameter space remains vast and the predictions lack precision. This study aims to identify the specific parameters of a stellar flyby that can reproduce all observed TNO populations, their locations, and abundances, providing precise predictions to distinguish between competing formation scenarios.

Previous research has explored the influence of giant planet migration on the scattering of TNOs, showing how gravitational interactions between the planets could have ejected objects to more eccentric and inclined orbits. However, this model doesn't fully account for the observed characteristics of the cold Kuiper belt, Sedna-like objects, and high-inclination TNOs. These objects are located far beyond the gravitational reach of the giant planets, suggesting alternative mechanisms were involved. The stellar flyby hypothesis proposes that a close passage of another star could have drastically altered the orbits of TNOs. Early work in this area focused on the feasibility of such encounters and their possible consequences. More recent studies have used numerical simulations to demonstrate the potential of flybys to produce the observed TNO populations, but these works often had limitations in the scope of the parameter space explored or lacked detailed quantitative comparisons with observed TNO properties. The lack of precision in these predictions hindered the ability to decisively compare the flyby hypothesis to other models, creating a need for more comprehensive modeling and analysis.

This study conducted an extensive numerical parameter study comprising over 3,000 individual simulations. Each simulation modeled the effects of a stellar flyby on a planetesimal disk around the Sun, extending to 150 au and 300 au to reflect typical protoplanetary and debris disk sizes. Key parameters varied included the mass of the perturbing star (M_p), its perihelion distance (r_⊥), the inclination (i), and the argument of perihelion (ω) of its orbit. The simulations utilized 10⁴–10⁵ massless tracer particles to represent the planetesimal disk. The simulations tracked gravitational three-body interactions between the Sun, the perturbing star, and each tracer particle. Self-gravity and viscosity were deemed negligible due to the short interaction time and relatively low disk mass. A Runge-Kutta Cash-Karp scheme was used to integrate the equations of motion. Simulations were carefully evaluated to meet stringent criteria for matching observations, requiring them to accurately reproduce the observed location and relative population sizes of the cold Kuiper belt, Sedna-like, and high-inclination TNOs. The comparison focused on TNOs not strongly coupled to Neptune (T_N > 3.05, where T_N is the Tisserand parameter). Furthermore, the study ensured that the giant planet orbits remained largely unperturbed. A decision-tree approach was used to systematically eliminate simulations that failed to meet the strict matching criteria, ultimately identifying a set of flybys that yielded a near-perfect match to the observed TNO distributions. Long-term simulations (1 Gyr) were performed for a subset of these best-fit models to assess the effects of secular evolution on the TNO populations. The frequency of close stellar flybys was determined using N-body simulations to model the evolution of different stellar clusters. A toy model was also employed to assess the potential impact of the flyby on a primordial Oort cloud.

The study identified a stellar flyby scenario that exceptionally well matches the observed TNO population. The best-fit parameters indicate a 0.8^+0.1_−0.1 *M*_⊙ star passing at a perihelion distance of r_⊥ = 110 ± 10 au, with an inclination of i = 70° ± 10° and an argument of perihelion between 60° and 90°. This flyby successfully reproduced the relative abundances and orbital characteristics of the cold Kuiper belt, Sedna-like, and high-inclination TNOs. Unexpectedly, this scenario also accounted for the retrograde TNO population, which had been challenging to explain by previous models. The analysis of the long-term evolution (1 Gyr) of the TNO population after the flyby demonstrated that the overall agreement with observations improved over time. The simulation indicated a distinct clustering in the a, e, i parameter space, and a notable increase in the fraction of Sedna-like and retrograde TNOs. The maximum inclination of retrograde TNOs correlates with the size of the primordial solar system disk, suggesting that the disk extended to at least 65 au, and possibly much further. Analysis of the flyby frequency revealed that such encounters are relatively common, particularly in young, dense stellar clusters. At least 140 million solar-type stars in the Milky Way are estimated to have experienced a similar flyby during their first 10 million years. The simulation also revealed that the flyby injected a significant number of TNOs into the inner Solar System (within 30 au) and ejected a considerable portion of the disk material into unbound orbits, with approximately 8% of the initial disk mass being captured by the perturbing star.

The findings strongly support the hypothesis that a close stellar flyby significantly shaped the outer Solar System. The identified flyby parameters quantitatively reproduce the diverse characteristics of the observed TNO populations, including the previously unexplained retrograde objects. The close match between simulations and observations suggests this event was a primary driver of the observed TNO orbital architecture. The predictions generated by the model, such as the predicted clustering of TNOs in a, e, i space and the increased relative fraction of retrograde and Sedna-like TNOs with expanding observational capabilities, are testable with future surveys. The correlation between the maximum inclination of retrograde TNOs and the size of the primordial disk provides a powerful constraint on early Solar System conditions. The relatively high frequency of such flybys suggests that this type of shaping event could be a common feature in planetary system formation. While the model assumes the planets were at their current positions during the flyby, the results are consistent with various scenarios of early Solar System evolution, including planet migration and the presence of a primordial Oort cloud. The study's limitations should be considered when interpreting the results. The current TNO sample is incomplete and subject to selection biases, and the exact size and structure of the primordial disk are unknown.

This study demonstrates that a close stellar flyby provides a compelling explanation for the observed structure of the outer Solar System. The best-fit parameters for this flyby quantitatively reproduce the orbital properties of various TNO populations, including retrograde objects, which had been particularly challenging to account for using other models. The model makes specific, testable predictions about future TNO discoveries, including clustering patterns and changes in the relative abundances of different TNO groups. Further observations, especially with the Vera Rubin Observatory, will be crucial in validating these predictions and refining our understanding of early Solar System evolution. Future research could investigate the detailed dynamics of the flyby's interaction with a primordial Oort cloud and how this event might have affected the potential for life to develop on the perturbing star.

The study's findings are subject to limitations. The current observational sample of TNOs is incomplete and affected by selection biases, potentially influencing the interpretation of the results. The exact size and structure of the primordial protoplanetary disk are not definitively known, which could introduce uncertainty in the model's predictions. Long-term simulations were computationally expensive, limiting the duration and resolution of the analysis. The model simplifies certain aspects of the problem, such as neglecting self-gravity and viscosity effects in the planetesimal disk. The impact of potential additional perturbing factors, such as interactions with the galactic potential, was also limited in this study.