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

Abstract

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...

Ultra-short-period Planets from Secular Chaos

“…The inclinations reached by USP planets in these experiments are generally lower than previous experiments of secular chaos in hot Jupiter systems by Hamers et al (2017) where planets reach a broad range in 0 − 140 • with ∼ 10% being retrograde (similar results were found by Lithwick & Wu 2014). We believe that the main difference between the hot Jupiter set-up and ours is that the USP planets start migration much closer in, so these only need to reach e 1 ∼ 0.9 in order to migrate.…”

Formation of hot Jupiters through secular chaos and dynamical tides

“…In this paper, we perform the first systematic study of HJ formation via the secular chaos mechanism. Our work goes beyond that of and Lithwick & Wu (2014) in several ways: (i) We use a secular Gaussian ring code (Murray & Dermott 1999;Touma et al 2009) to compute the long-term evolution of 3-planet systems and explore the conditions for the onset of secular chaos; (ii) Using the ring code we carry out a large suite of calculations (population synthesis) for various initial conditions and parameters; (iii) We incorporate dynamical tides (using the method developed in , which can significantly affect the outcomes of high-e migration; (iv) We include all relevant physical effects (tidal disruption, shortrange forces, spin-orbit coupling and magnetic braking of host stars) to determine the properties of HJs formed in the secular chaos scenario. This paper is organized as follows.…”

“…This makes direct N -body integrations impractical to survey the large parameter space covered by a system of three planets. The work by Lithwick & Wu (2014) represents so far the only attempt at exploring the outcome of secular chaos, using at limited set of 100 simulations. In addition, tidal disruption of the planet, which severely limits the efficiency of Lidov-Kozai migration of giant planets (Petrovich 2015a;Anderson et al 2016;Muñoz et al 2016), has not been systematically explored in the secular chaos scenario.…”

On the formation of hot and warm Jupiters via secular high-eccentricity migration in stellar triples

“…24 of Anderson et al (2016) for m 1 = 1M J and χ = 100 are shown with black open circles. Additionally, we show with black stars observational data adopted from Lithwick & Wu (2014). The initial obliquities in the simulations were assumed to be zero.…”