The existence of a chaotic region due to the overlap of secular resonances ν5 and ν6

Sidlichovsky, M.

doi:10.1007/bf00050713

Cited by 12 publications

(16 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…27. However, to explain secular chaos in the solar system, one must extend it to include nonzero inclinations, which we did in ref.…”

Section: Mercurymentioning

confidence: 97%

Secular chaos and its application to Mercury, hot Jupiters, and the organization of planetary systems

Lithwick

2013

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

In the inner solar system, the planets' orbits evolve chaotically, driven primarily by secular chaos. Mercury has a particularly chaotic orbit and is in danger of being lost within a few billion years. Just as secular chaos is reorganizing the solar system today, so it has likely helped organize it in the past. We suggest that extrasolar planetary systems are also organized to a large extent by secular chaos. A hot Jupiter could be the end state of a secularly chaotic planetary system reminiscent of the solar system. However, in the case of the hot Jupiter, the innermost planet was Jupiter (rather than Mercury) sized, and its chaotic evolution was terminated when it was tidally captured by its star. In this contribution, we review our recent work elucidating the physics of secular chaos and applying it to Mercury and to hot Jupiters. We also present results comparing the inclinations of hot Jupiters thus produced with observations.planetary dynamics | extrasolar planets T he question of the stability of the solar system has a long and illustrious history (e.g., ref. 1). It was finally answered with the aid of computer simulations (2-4), which have shown that the solar system is "marginally stable": it is chaotically unstable, but on a timescale comparable to its age. In the inner solar system, the planets' eccentricities (e) and inclinations (i) diffuse in billions of years, with the two lightest planets, Mercury ( Fig. 1) and Mars, experiencing particularly large variations. Mercury may even be lost from the solar system on a billion-year timescale (5-7). [Chaos is much weaker in the outer solar system than in the inner (8-10).] However, despite the spectacular success in solving solar system stability, fundamental questions remain: What is the theoretical explanation for orbital chaos of the solar system? What does the chaotic nature of the solar system teach us about its history and organization? Also, how does this relate to extrasolar systems?For well-spaced planets that are not close to strong meanmotion resonances (MMRs), the orbits evolve on timescales much longer than orbital periods. Hence one may often simplify the problem by orbit-averaging the interplanetary interactions. The averaged equations are known as the "secular" equations (e.g., ref. 11). To linear order in masses, secular evolution consists of interactions between rings, which represent the planets after their masses have been smeared out over an orbit. Secular evolution dominates the evolution of the terrestrial planets in the solar system (5), and it is natural to suppose that it dominates in many extrasolar systems as well. This is the type of planetary interaction we focus on in this contribution.One might be tempted by the small eccentricities and inclinations in the solar system to simplify further and linearize the secular equations, i.e., consider only terms to leading order in eccentricity and inclination. Linear secular theory reduces to a simple eigenvalue problem. For N secularly interacting planets, the solution consists of 2N...

show abstract

“…27. However, to explain secular chaos in the solar system, one must extend it to include nonzero inclinations, which we did in ref.…”

Section: Mercurymentioning

confidence: 97%

Secular chaos and its application to Mercury, hot Jupiters, and the organization of planetary systems

Lithwick

2013

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

show abstract

“…That is, much like GJ 876 "e," Mercury is characterized by a Lyapunov time that is orders of magnitude shorter than the Solar Systemʼs lifetime and has only a slim chance of escaping the Solar System within the remaining main-sequence lifetime of the Sun (Batygin & Laughlin 2008;Laskar 2008;Laskar & Gastineau 2009). In a related effort, Lithwick & Wu (2011) have shown that Mercuryʼs secular evolution can be understood within the context of an autonomous Hamiltonian corresponding to a pair of momentum-coupled pendulums 14 (see also Sidlichovsky 1990;Boué et al 2012), much like the case of the resonant evolution of GJ 876 "e." Furthermore, in direct correspondence to the stability of GJ 876, Batygin et al (2014) have recently shown that Mercuryʼs long-term stability also arises from a topological boundary associated with the approximate conservation of the Hamiltonian itself (see Poincaré surfaces of section depicted in Figure 4). …”

Section: Discussionmentioning

confidence: 99%

Dynamical Evolution of Multi-Resonant Systems: The Case of Gj 876

Batygin

Deck

Holman

2015

View full text Add to dashboard Cite

The GJ 876 system was among the earliest multi-planetary detections outside of the Solar System, and has long been known to harbor a resonant pair of giant planets. Subsequent characterization of the system revealed the presence of an additional Neptune mass object on an external orbit, locked in a three body Laplace mean motion resonance with the previously known planets. While this system is currently the only known extrasolar example of a Laplace resonance, it differs from the Galilean satellites in that the orbital motion of the planets is known to be chaotic. In this work, we present a simple perturbative model that illuminates the origins of stochasticity inherent to this system and derive analytic estimates of the Lyapunov time as well as the chaotic diffusion coefficient. We then address the formation of the multi-resonant structure within a protoplanetary disk and show that modest turbulent forcing in addition to dissipative effects is required to reproduce the observed chaotic configuration. Accordingly, this work places important constraints on the typical formation environments of planetary systems and informs the attributes of representative orbital architectures that arise from extended disk-driven evolution.

show abstract

“…One example is the appearance of nonlinear secular resonances, including new fixed points and separatrices that are not present in the linear system (Michtchenko & Malhotra 2004;Michtchenko et al 2006;Migaszewski & Goździewski 2009). A second is the chaotic motion associated with the overlap of neighboring resonances (Sidlichovsky 1990;Michtchenko et al 2006;Lithwick & Wu 2011).…”

Section: Secular Interactionsmentioning

confidence: 99%

Secular Chaos and the Production of Hot Jupiters

Lithwick

2011

ApJ

382

356

View full text Add to dashboard Cite

In a planetary system with two or more well-spaced, eccentric, inclined planets, secular interactions may lead to chaos. The innermost planet may gradually become very eccentric and/or inclined as a result of the secular degrees of freedom drifting toward equipartition of angular momentum deficit. Secular chaos is known to be responsible for the eventual destabilization of Mercury in our own solar system. Here we focus on systems with three giant planets. We characterize the secular chaos and demonstrate the criterion for it to occur, but leave a detailed understanding of secular chaos to a companion paper. After an extended period of eccentricity diffusion, the inner planet's pericenter can approach the star to within a few stellar radii. Strong tidal interactions and ensuing tidal dissipation extract orbital energy from the planet and pull it inward, creating a hot Jupiter. In contrast to other proposed channels for the production of hot Jupiters, such a scenario (which we term "secular migration") explains a range of observations: the pile-up of hot Jupiters at 3 day orbital periods, the fact that hot Jupiters are in general less massive than other radial velocity planets, that they may have misaligned inclinations with respect to stellar spin, and that they have few easily detectable companions (but may have giant companions in distant orbits). Secular migration can also explain close-in planets as low in mass as Neptune; and an aborted secular migration can explain the "warm Jupiters" at intermediate distances. In addition, the frequency of hot Jupiters formed via secular migration increases with stellar age. We further suggest that secular chaos may be responsible for the observed eccentricities of giant planets at larger distances and that these planets could exhibit significant spin-orbit misalignment.

show abstract

The existence of a chaotic region due to the overlap of secular resonances ν5 and ν6

Cited by 12 publications

References 11 publications

Secular chaos and its application to Mercury, hot Jupiters, and the organization of planetary systems

Secular chaos and its application to Mercury, hot Jupiters, and the organization of planetary systems

Dynamical Evolution of Multi-Resonant Systems: The Case of Gj 876

Secular Chaos and the Production of Hot Jupiters

Contact Info

Product

Resources

About