On the long-term stability of the Solar System in the presence of weak perturbations from stellar flybys (2206.14240v1)

Abstract: The architecture and evolution of planetary systems are shaped in part by stellar flybys. Within this context, we look at stellar encounters which are too weak to immediately destabilize a planetary system but are nevertheless strong enough to measurably perturb the system's dynamical state. We estimate the strength of such perturbations on secularly evolving systems using a simple analytic model and confirm those estimates with direct N-body simulations. We then run long-term integrations and show that even small perturbations from stellar flybys can influence the stability of planetary systems over their lifetime. We find that small perturbations to the outer planets' orbits are transferred between planets, increasing the likelihood that the inner planetary system will destabilize. Specifically, our results for the Solar System show that relative perturbations to Neptune's semi-major axis of order 0.1% are strong enough to increase the probability of destabilizing the Solar System within 5 Gyrs by one order of magnitude.

• The paper demonstrates that weak stellar flybys, even with a 0.1% perturbation to Neptune’s orbit, can significantly elevate the risk of long-term instability.
• Analytical models combined with direct N-body simulations reveal how minor perturbations propagate inward to disrupt secular resonances.
• Exploring diverse stellar environments, the study shows that denser regions can markedly increase both the frequency and impact of destabilizing encounters.

An Analysis of the Long-Term Stability of the Solar System Under Weak Stellar Flyby Perturbations

In the paper "On the long-term stability of the Solar System in the presence of weak perturbations from stellar flybys," the authors investigate the impact of weak perturbations from stellar flybys on the long-term stability of planetary systems, particularly focusing on the Solar System. This paper combines both analytical models and direct N-body simulations to assess how small yet non-negligible perturbations can influence the evolution of planetary systems over billions of years.

This research builds on a rich historical foundation where the long-term stability of the Solar System has been scrutinized since the time of Newton. The chaotic nature of the Solar System, first highlighted by Laskar (1989), implies that predictions are reliable only over a limited temporal scope, extending to several Lyapunov timescales (approximately 100 million years). Consequently, the probability of destabilization events, such as Mercury's orbit destabilizing within 5 billion years, has been estimated at about 1% in earlier studies.

Numerical and Analytical Approaches

The paper's primary contribution is its focus on weak perturbations, typically overlooked in models concentrating on more immediate destabilizing flybys. Through analytic methods, it estimates the perturbative effects on a secularly evolving system and then corroborates these findings using N-body simulations. Key to these simulations is demonstrating that perturbations, though faint, can have substantial cumulative impacts on the system's stability if they occur within specific thresholds.

For instance, the Solar System simulations suggest that a mere 0.1% relative perturbation to Neptune's semi-major axis could increase the probability of the Solar System entering a dynamically unstable state by a factor of ten within 5 billion years. The paper emphasizes that even small changes in the outer planets' orbits can propagate inward, affecting the entire system's long-term dynamics.

Implications of Stellar Environments

The paper provides an in-depth analysis of different stellar environments and their propensity to effectuate perturbing flybys. These environments range from the local stellar neighborhood, open and globular clusters, to the dense cores of galaxies, each characterized by varying stellar densities, velocities, and masses. The results suggest that while the local neighborhood may subject the Solar System to potentially destabilizing flybys infrequently (once every 100 billion years), denser environments could significantly accelerate the frequency and intensity of such events.

Successive Flybys and Accumulating Effects

An interesting aspect of the paper is the examination of successive flybys, where the aggregate effects of multiple encounters over billions of years mimic a Levy flight pattern rather than a simple random walk. This indicates that the largest perturbations tend to dominate the system's evolution, making these rare yet significant encounters crucial in assessing the Solar System’s long-term stability.

Discussion on Secular Dynamics and Resonances

The paper dives into the changes in secular frequencies due to perturbations, asserting that all secular modes experience shifts proportional to perturbations in Neptune’s semi-major axis. These dynamics can disrupt existing secular resonances, such as the $g_1-g_5$ Mercury-Jupiter resonance and the $g_3-g_4$ Earth-Mars resonance, which are closely tied to the system's stability. By altering these resonances, flybys can lead to eccentricity pumping and destabilization of planetary orbits.

Conclusion and Future Directions

The findings of this research underline the significance of weak perturbations from stellar flybys in potentially altering the Solar System's stability over geologic timescales. While direct destabilizations from such events are rare in the present-day Solar System's environment, they become increasingly probable in denser star clusters. This work sets the stage for further exploration into how these minor perturbations might shape the architecture of exoplanetary systems, contributing to our broader understanding of cosmic dynamical processes. Future investigations could focus on the effects of binary stars and hypothetical distant planets within the Solar System, which were not within this paper’s scope but could offer additional insights into the dynamics of planetary systems under similar perturbative forces.