Trajectory of the stellar flyby that shaped the outer Solar System

Planets formed from a circumsolar disk and therefore follow near-coplanar, near-circular orbits, whereas most of the ~3,000 known trans-Neptunian objects (TNOs) beyond Neptune are on eccentric and inclined orbits, implying substantial post-formation excitation. Giant-planet migration and scattering can explain many TNOs, but three observed dynamical groups remain difficult for that scenario alone: (i) cold Kuiper belt objects on nearly circular, low-inclination orbits; (ii) Sedna-like objects with large perihelia (r_p > 60 au) and high eccentricities (e > 0.5); and (iii) highly inclined (i > 60°) and retrograde TNOs. The authors build on an alternative hypothesis: a close stellar flyby of the Solar System’s outer disk excited and redistributed native planetesimals. Recent observations indicate close flybys are not rare, and prior simulations showed flybys can create cold Kuiper belt and Sedna-like populations. The research question is to determine whether a single specific flyby can quantitatively reproduce the full suite of TNO dynamical populations, their locations in a–e–i space, and their relative abundances, without disrupting the planets. The study performs a comprehensive parameter search to identify a near-unique flyby that matches the observations and yields testable predictions for upcoming surveys, highlighting retrograde TNOs as a key diagnostic.

Prior work proposed that giant-planet migration and scattering sculpted the Kuiper belt (e.g., Fernandez & Ip 1984; Hahn & Malhotra 1999; Gomes 2003; Levison et al. 2008), but struggles to reproduce the cold classical belt, Sedna-like objects, and very high inclinations, including retrograde orbits. Flyby-origin models date back to Kobayashi & Ida (2001), Kenyon & Bromley (2004), and Kobayashi et al. (2005), with recent simulations (Punzo et al. 2014; Pfalzner et al. 2018; Moore et al. 2020) showing feasibility for producing key TNO groups. Observations of young systems (e.g., RW Aur, HV/DO Tau, SU Aur, UX Tau) suggest stellar flybys are relatively common. An alternative capture scenario proposed an exchange encounter with a solar sibling to abduct Sedna (Jílková et al. 2015). Planet Nine has been invoked to explain certain high-inclination and retrograde TNOs (Batygin & Brown 2016; Batygin et al. 2024), though very distant, highly inclined retrograde TNOs may remain challenging. Recent work also ties the radial distribution of distant TNOs to Sun’s cluster birth environment (Nesvorný et al. 2023).

- Performed 3,080 simulations of a stellar flyby perturbing a massless tracer particle disk around the Sun, with initial disk radii R_⊥ = 150 au and 300 au (typical of proto-planetary/debris disks). - Parameter scan guided by previous work: perturber mass M_p = 0.3–1.0 M_⊙ (step 0.1 M_⊙), periastron distance r_p = 50–150 au (step 10 au), inclination i = 50°–70° (step 5°), argument of periastron ω = 60°–120° (in 10° variations). Focused on parabolic encounters. - Disk sampled with N = 10^4–10^5 massless tracers. Integrated three-body interactions (Sun, perturber, each tracer) with a Runge–Kutta Cash–Karp scheme. Simulations start/end when the perturber’s force on each particle is <0.1% of the Sun’s. Post-processed tracer weights to mimic realistic surface density distributions. - Selection procedure: (i) reject cases that perturb inside ~30–35 au (using r_a ≈ 0.28 M^0.32 r as a guide; extended for inclined encounters). 490 simulations passed. (ii) require production of cold Kuiper belt and Sedna-like objects in correct regions of a–e–i space and relative abundances; evaluate TNOs largely decoupled from Neptune (Tisserand parameter T_N > 3.05 for comparison; Sedna-like objects have T_N < 3.05 and are less affected by Neptune after flyby). Excluded a > 10,000 au due to long-term galactic/stellar effects. - Among surviving models, constrained to M_p ~0.7–0.9 M_⊙ and r_p ~90–110 au. Higher masses at r_p = 110 au yield too few cold objects; lower masses fail to excite high-eccentricity TNOs. For M_p = 0.8 M_⊙, r_p = 110 au gives the best unperturbed inner region; r_p = 100 au produces ~80% fewer cold TNOs. - Constrained geometry by maximizing cold population and matching i–e distributions: best at i ≈ 70° and ω ≈ 80° (acceptable ω ≈ 60°–90°), relative to the pre-flyby disk plane. - High-resolution runs for best-fit cases (models A–C) with 10^5 particles and both disk sizes (150 au, 300 au) to confirm stability of results. - Long-term evolution: integrated a subset (~20% of particles; those with 35 au < r < 90 au, i < 60°, a < 2,000 au) for 1 Gyr including the four outer giant planets using the GENGA hybrid symplectic integrator. Started from 12,000 yr post-periastron. - Flyby frequency: conducted extensive N-body star cluster simulations with Nbody6++ across a range of cluster environments; recorded close encounters and post-processed to infer expected unperturbed disk sizes and frequency of encounters matching best-fit parameters. - Oort cloud toy model: simulated impact of the best-fit flyby (model A) on a pre-existing Oort cloud modeled as 10,000 particles within a 100,000 au sphere using REBOUND with the IAS15 integrator. - Also cross-checked observability with the OSSOS observation simulator for model A1 (finding ~70 simulated objects should be currently observable), acknowledging sensitivity to selection of comparison space and observational biases.

- A single parabolic flyby reproduces the observed TNO dynamical populations and their relative abundances: best-fit perturber mass M_p = 0.8(+0.1/−0.1) M_⊙, periastron distance r_p = 110 ± 10 au, inclination i ≈ 70° (±5–10°), argument of periastron ω ≈ 60°–90° relative to the pre-flyby disk plane. - Three nearly identical best-fit scenarios (Table 1) targeted different TNO subgroups (Sedna-like, cold Kuiper belt, ETNOs), all converging on M_p ≈ 0.8 M_⊙, r_p ≈ 110 au, i ≈ 65°–70°, ω ≈ 60°–90°, and disk sizes R_⊥ = 150–300 au. - The model quantitatively matches the distributions of a, e, and i for cold, hot, and Sedna-like TNOs within the current observational window (e.g., 35 au < r < 100 au, a < 2,000 au, i < 60°, T > 3.05), while leaving planetary orbits effectively unperturbed (Neptune’s orbit remains acceptable depending on its orbital phase; shielding in ~25% of cases). - Long-term (1 Gyr) evolution modestly increases low-inclination TNOs, improving the match to the cold population and filling in previously sparse regions, while preserving clustering patterns induced by the flyby. - The best-fit flyby naturally produces retrograde TNOs, matching known retrograde objects 2008 KV2 (i ≈ 103.4°) and 2011 KT19 (i ≈ 110.2°), and predicting additional distant high-inclination retrogrades (including potential objects with r_p ≥ 30 au and i > 150°). - A correlation between maximum retrograde inclination and primordial disk size implies the Sun’s primordial disk extended to at least R_⊥ ≥ 65 au; discovery of low-inclination retrograde TNOs near the plane would argue for R_⊥ ≥ 150 au. - Predictive shifts with expanded discovery space (Rubin/LSST, 10-year survey): Sedna-like fraction rises from ~0.1% of currently accessible TNOs to ~7%; retrograde fraction rises from ~0.15% to ~5%, with many retrogrades at high inclinations. - Mass and particle outcomes from the flyby (model A1): ~9% of initial disk mass injected inside 30 au on high-eccentricity (e > 0.4), high-inclination (>30°) orbits repeatedly revisiting 60–200 au; ~26% of TNOs become unbound; the perturber captures ~8.3% of initially solar-bound material, with some captured bodies reaching r_min ≈ 0.73 au (well within the perturber’s ice lines). - Frequency estimates: in the first ~10 Myr, 8%–15% of solar-type stars in favorable clusters and ~1% in low-density clusters experience encounters truncating disks to 30–50 au; at least ~140 million solar-type stars in the Milky Way (possibly ×10 more) likely had a similar encounter, and ~10% of these with comparable perturber mass (0.6–1.0 M_⊙) and periastron (90–130 au). Later (post-cluster) encounters are less effective due to high relative velocities (hyperbolic orbits). - Compatibility with other Solar System features: a pre-existing Oort cloud would be affected but not erased (~15% retained), and could be enriched by outer-disk bodies and the perturber’s own cloud; planet migration could still contribute to the hot population without erasing the flyby signatures.

The study addresses whether a single, well-characterized stellar flyby can account for multiple challenging features of the outer Solar System. By exhaustively scanning parameter space and enforcing strict matching criteria, the authors identify a narrow set of flyby parameters that reproduces the cold classical belt, Sedna-like objects, high-inclination and retrograde TNOs, and their relative abundances, while preserving the planetary architecture. The flyby explains observed clustering in multidimensional orbital space and predicts that these patterns will persist, though blur slightly, over Gyr timescales. Retrograde TNOs emerge as a decisive diagnostic: their distribution and maximum inclination provide constraints on the primordial disk size, offering an avenue to reconstruct early Solar System structure as surveys expand. The model offers clear, falsifiable predictions—e.g., increased fractions of Sedna-like and retrograde TNOs and specific distributions in a–e–i—which near-future observations with the Vera C. Rubin Observatory can test. Compared with alternatives, Planet Nine can explain some retrogrades (r_p < 30 au, i < 150°) but may struggle with distant, very high-inclination retrogrades; hybrid models (planet scattering plus flybys) remain possible but their predictive power is unclear. Timing considerations favor an early cluster-phase encounter, though a later flyby cannot be fully excluded and warrants further study. The scenario remains compatible with planet migration and a primordial Oort cloud, and even suggests potential exchange and capture processes enriching both systems.

A parabolic stellar flyby by a M_p = 0.8(+0.1/−0.1) M_⊙ star at r_p = 110 ± 10 au and inclination i ≈ 70° (±5°) offers a simple, unified explanation for the outer Solar System’s key unexplained features. It quantitatively reproduces the cold Kuiper belt, Sedna-like objects, high-inclination and retrograde TNOs, and yields distinct, testable predictions: persistent clustering in a–e–i space and rising fractions of retrograde and Sedna-like TNOs as the observable volume grows. The model also links retrograde inclinations to the primordial disk size, enabling constraints on the early Solar System architecture from future discoveries. Given the estimated frequency of such encounters, this flyby scenario is astrophysically plausible and falsifiable with upcoming survey data.

- Observational biases: The known TNO sample is highly incomplete and biased (<1%–10% of the total population), especially against distant, high-eccentricity, and high-inclination objects, complicating quantitative comparisons. - Primordial disk unknowns: The size and structure (e.g., possible rings) of the pre-flyby solar disk are uncertain; different initial conditions could produce gaps or features not captured here. - Simulation scope: Long-term evolution was modeled for only ~20% of particles (those likely observable) over 1 Gyr; longer integrations could alter resonant populations and secular evolution details. - Dynamical simplifications: Tracers are massless; self-gravity and gas/viscosity were neglected (reasonable for short encounter times and low disk mass but still an approximation). - Selection criteria: Comparisons excluded most resonant TNOs (T_N ≤ 3.05) and very distant objects (a > 10,000 au), potentially omitting populations influenced by later dynamics. - Sensitivity to planetary phases: Planet perturbations depend on giant planets’ orbital phases during the flyby; while acceptable ranges exist, precise historical configurations are unknown. - Automated statistics: The team used a decision-tree inspection due to multi-modal clustering and biases; lack of a unified automated metric introduces some subjectivity, though extensive sampling and strict rejection were applied. - Later hyperbolic flybys: The efficacy of late, high-velocity encounters remains to be fully assessed and could affect conclusions about timing.