Statistical Study of the Early Solar System's Instability With Four, Five, and Six Giant Planets

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 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.

Analytical treatment of planetary resonances

“…Furthermore, it is important to note that lack of co-precessing anti-aligned obits in a given system should not be viewed as evidence for lack of past resonant encounters, since resonant encounters in densely populated planetary systems, can lead to orbital instabilities that act to chaotically erase fossilized remnants of past evolution. The lack of apsidal alignment between Jupiter and Saturn suggests that the solar system is in fact, such an example (Morbidelli et al 2009;Batygin & Brown 2010;Nesvorný & Morbidelli 2012). …”

Modeling the Historical Flux of Planetary Impactors

“…Planetary encounters are also needed to explain the secular structure of the giant planet orbits , Nesvorný & Morbidelli 2012, and the Kuiper belt kernel (Nesvorný 2015b). Moreover, at least some of the terrestrial planets, such as Mars, and perhaps also Mercury, may have been present during the instability, even if t inst < 100 Myr.…”

Capture of planets into mean-motion resonances and the origins of extrasolar orbital architectures

“…Although resonant reversal of orbital decay was initially proposed to account for the retention of Jupiter and Saturn at large orbital radii, such a sequence of events smoothly connects the nebular stage of Solar System evolution to the compact initial conditions of the Nice model Batygin & Brown 2010;Nesvorný & Morbidelli 2012), and provides natural explanations for the comparatively small mass of Mars (Walsh et al 2011), the composition of the Asteroid belt (O'Brien et al 2014), and the nonexistence of otherwise common close-in Super-Earths inside of Mercury's orbit (?). Moreover, it has been proposed that a similar mechanism is ubiquitously responsible for halting large-scale migration of giant exoplanets that reside at wide orbital separations (Morbidelli 2013).…”