Statistical Study of the Early Solar System's Instability with 4, 5 and 6 Giant Planets (1208.2957v1)

Abstract: Several properties of the Solar System, including the wide radial spacing and orbital eccentricities of giant planets, can be explained if the early Solar System evolved through a dynamical instability followed by migration of planets in the planetesimal disk. Here we report the results of a statistical study, in which we performed nearly 10^4 numerical simulations of planetary instability starting from hundreds of different initial conditions. We found that the dynamical evolution is typically too violent, if Jupiter and Saturn start in the 3:2 resonance, leading to ejection of at least one ice giant from the Solar System. Planet ejection can be avoided if the mass of the transplanetary disk of planetesimals was large (M_disk>50 M_Earth), but we found that a massive disk would lead to excessive dynamical damping (e.g., final e_55 < 0.01 compared to present e_55=0.044, where e_55 is the amplitude of the fifth eccentric mode in the Jupiter's orbit), and to smooth migration that violates constraints from the survival of the terrestrial planets. Better results were obtained when the Solar System was assumed to have five giant planets initially and one ice giant, with the mass comparable to that of Uranus and Neptune, was ejected into interstellar space by Jupiter. The best results were obtained when the ejected planet was placed into the external 3:2 or 4:3 resonance with Saturn and M_disk ~ 20 M_Earth. The range of possible outcomes is rather broad in this case, indicating that the present Solar System is neither a typical nor expected result for a given initial state, and occurs, in best cases, with only a ~5% probability (as defined by the success criteria described in the main text). The case with six giant planets shows interesting dynamics but does offer significant advantages relative to the five planet case.

• The paper shows that resonant configurations among giant planets can trigger dynamical instabilities, often ejecting ice giants without a massive planetesimal disk.
• The paper employs nearly 10,000 numerical simulations to compare four-, five-, and six-planet scenarios against current orbital characteristics.
• The paper finds that a five-planet configuration—with one ice giant ejected—most closely reproduces the observed solar system architecture, achieving a 5% success probability.

A Statistical Study of Early Solar System Instability

This paper explores a crucial aspect of solar system dynamics by investigating the early evolution of giant planets in the solar system through statistical analysis. Using nearly 10,000 numerical simulations, Nesvorný et al. paper how the dynamical instability of the early solar system could lead to the current configuration and characteristics of the giant planets. The research primarily addresses different initial scenarios involving four, five, and six giant planets, including scenarios with possible ejections of ice giants.

Key Findings

1. Initial Resontant Configurations: The paper investigates various initial resonant configurations among early Solar System's giant planets. The simulations show that starting Jupiter and Saturn in a resonant 3:2 configuration frequently leads to violent dynamical instabilities. Such instabilities often result in the ejection of ice giants unless the system is surrounded by a sufficiently massive transplanetary planetesimal disk (greater than 50 Earth masses).
2. Massive Disk Challenges: While a massive planetesimal disk helps avoid planet ejections, it dampens dynamical excitations excessively and leads to a smooth migration that conflicts with the survival of terrestrial planets. The final systems often display eccentricities and inclinations that don't align with current observations.
3. Five Planet Systems: A promising configuration emerges with five initial giant planets, where one ice giant is ejected in the instability phase. Notably, configurations with an additional ice giant located between Saturn and what are now Uranus/Neptune orbits, combine to match several constraints necessary to produce a configuration similar to the current solar system within a 5% success probability.
4. Six Planet Systems: While involving intriguing dynamics with two sequential ejections, six-planet configurations do not provide significant advantages in stabilizing the system compared to five-planet scenarios.

Simulation Criteria

Success in replication of present solar characteristics is rigorously defined with four constraints:

• Four surviving planets with current mean semimajor axis.
• Planetary orbital eccentricities and inclinations match observations.
• Excitation of Jupiter's eccentricity mode $e_{55}$ should reflect current mea- surements.
• Avoidance of secular resonances with terrestrial planets during the giant planet instability.

Implications and Future Investigations

The scenarios with five giant planets offer a potential solution to the Solar System's early evolution while indicating that achieving the present-day configuration is a highly non-deterministic process. The simulations supporting the existence of a now-ejected ice giant indicate the role complex scattering dynamics may play in determining final planetary orbits.

Future studies are invited to incorporate constraints from small body populations such as the Kuiper belt and Asteroid belt to further validate these scenarios. The introduction of more precise initial conditions, extending observational constraints, could also provide deeper insights into planetary migrations and interactions during the instability phase.

The comparative paper between four, five, and six-planet initial conditions underscores the nuanced nature of planetary evolution within our solar system, providing a valuable framework for ongoing investigations into planetary system formation across the galaxy.