Was the Solar System's dynamical instability triggered by a (sub)stellar flyby?

TL;DR

The study investigates whether a flyby during the Sun's birth cluster could trigger the giant-planet dynamical instability. Using 3000 N-body simulations with a multi-resonant four-planet system and an outer planetesimal disk, it explores a wide range of flyby masses, velocities, and periastra. A Solar System–like outcome requires a close substellar flyby (3–30 M_Jup) passing within ~20 au, capable of exciting the giant planets while preserving the cold classical Kuiper belt, though only a small fraction of runs achieve this. Monte Carlo cluster modeling then estimates the likelihood of such a flyby given cluster parameters, yielding a ~1% probability under standard assumptions, rising to ~5% if free-floating planets are more common, with results broadly consistent with constraints from the Oort cloud and Kuiper belt.

Abstract

An instability among the giant planets' orbits can match many aspects of the Solar System's current orbital architecture. We explore the possibility that this dynamical instability was triggered by the close passage of a star or substellar object during the Sun's embedded cluster phase. We run N-body simulations starting with the giant planets in a resonant chain and an outer planetesimal disk, with a wide-enough planet-disk separation to preserve the planets' orbital stability for $>$100 Myr. We subject the system to a single flyby, testing a wide range in flyby mass, velocity and closest approach distance. We find a variety of outcomes, from flybys that over-excite the system (or strip the planets entirely) to flybys too weak to perturb the planets at all. An intermediate range of flybys triggers a dynamical instability that matches the present-day Solar System. Successful simulations -- that match the giant planets' orbits without over-exciting the cold classical Kuiper belt -- are characterized by the flyby of a substellar object ($3-30 M_{Jup}$) passing within 20 au of the Sun. We performed Monte Carlo simulations of the Sun's birth cluster phase, parameterized by the product of the stellar density $η$ and the cluster lifetime $T$. The balance between under- and over-excitation of the young Solar System is at $ηT \approx 5 \times 10^4$~Myr pc$^{-3}$, in a range consistent with previous work. We find a probability of $\sim$1% that the Solar System's dynamical instability was triggered by a substellar flyby. The probability increases to $\sim$5% if the occurrence rate of free-floating planets and low-mass brown dwarfs is modestly higher than predicted by standard stellar initial mass functions.

Figures (14)

• Figure 1: Outcomes of our 3000 simulations in the parameter space of stellar flybys. Each symbol corresponds to a single simulation. The black filled circles are simulations in which four giant planets survived. The large black triangles are cases where the four giant planets survived in the correct order and with an $AMD$ value within a factor of three of the present-day giant planet system. The red crosses are systems that matched the giant planets' $AMD$ and also retained at least 40% of their cold classical Kuiper belt particles, with a contamination rate in the hot Kuiper belt population below 40% (see Section 3.3).
• Figure 2: Final orbits of the giant planets in 75 simulations with four surviving giant planets and $AMD$ values within a factor of three of the present-day system, as compared with the actual (time-averaged) orbits of the giant planets nesvorny12. The blue symbols are a sample from kaib16 in which the giant planets started in the same orbital configuration and four planets survived, with no flyby.
• Figure 3: Evolution of nine simulations that produced a good match to the giant planets' orbits while also retaining at least 40% of their cold classical Kuiper belt particles. Each panel shows the evolution of the orbital semimajor axis of each giant planet, with the thickness of each curve representing the eccentricity (via the perihelion to aphelion range), labeled with the flyby parameters (the closest approach of the flyby star is shown, which is a combination of the impact parameter and velocity at infinity). These examples are ordered by the time of the onset of instability. The two panels with stars (top center and bottom center) are featured in Fig. \ref{['fig:examples']}.
• Figure 4: Snapshots in the evolution of two simulations that both provided a good match to the present-day Solar System yet had very different instability times. The early instability (left panel) was triggered less than $10^5$ years after the flyby of a $5.4 {\rm\,M_{Jup}}$ free-floating planet (${v_{\infty}} =2.7$ km/s, impact parameter of 64.5 au, closest approach of 16.6 au). In contrast, the late instability (right panel) was only triggered 22.5 Myr after the flyby of a $17.5 {\rm\,M_{Jup}}$ brown dwarf (${v_{\infty}} =2$ km/s, impact parameter of 63.2 au, closest approach of 8.5 au). The evolution of the giant planets in these systems is also shown in Fig. \ref{['fig:evol']} (top center and bottom center panels).
• Figure 5: Final orbital configurations of the giant planets and outer planetesimals in simulations with four surviving giant planets interior to 35 au and an $AMD$ within a factor of three of the present-day Solar System value. Here, the semimajor axes of all particles have been rescaled such that Neptune's orbital radius matches its present-day one, of 30.1 au. Detached planetesimals are defined as those with perihelion distances larger than 40.1 au, inclinations below 25 degrees (to filter out particles in Kozai oscillation), and semimajor axes larger than 50 au. The cold classical Kuiper belt region is shaded. Note that the clump of particles with low-eccentricity orbits past 50 au are an artefact -- they are cold classical particles in simulations in which Neptune finished interior to 30.1 au, so in this plot their orbits were widened to calibrate and compare between simulations. In our full analysis, each simulation was considered separately.