Strong scatterings of cold jupiters and their influence on inner low-mass planet systems: theory and simulations

Recent observations have indicated a strong connection between compact (a ≲ 0.5 au) super-Earth and mini-Neptune systems and their outer (a ≳ a few au) giant planet companions. We study the dynamical evolution of such inner systems subject to the gravitational effect of an unstable system of outer giant planets, focussing on systems whose end configurations feature only a single remaining outer giant. In contrast to similar studies which used on N-body simulations with specific (and limited) parameters or scenarios, we implement a novel hybrid algorithm which combines N-body simulations with secular dynamics with aims of obtaining analytical understanding and scaling relations. We find that the dynamical evolution of the inner planet system depends crucially on Nej, the number of mutual close encounters between the outer planets prior to eventual ejection/merger. When Nej is small, the eventual evolution of the inner planets can be well described by secular dynamics. For larger values of Nej, the inner planets gain orbital inclination and eccentricity in a stochastic fashion analogous to Brownian motion. We develop a theoretical model, and compute scaling laws for the final orbital parameters of the inner system. We show that our model can account for the observed eccentric super-Earths/mini-Neptunes with inclined cold Jupiter companions, such as HAT-P-11, Gliese 777 and π Men.

Laplace surface dynamics, revisited: satellites, exo-planets and debris with distant, eccentric companions

To date, studies of Laplace Surface dynamics have concerned themselves with test particle orbits of fixed shape and orientation in the combined field of an oblate central body (to which the particle is bound) and a distant, inclined, companion which is captured to quadrupolar order. While amply sufficient for satellites around planets on near-circular orbits, the quadrupolar approximation fails to capture essential dynamical features induced by a wide binary companion (be it a star, a planet or a black hole) on a fairly eccentric orbit. With similar such astronomical settings in mind, we extend the classical Laplace framework to higher multipoles, and map out the backbone of stationary orbits, now complexified by the broken axial symmetry. Eccentric and inclined Laplace equilibria, which had been presaged in systems of large enough mutual inclination, are here delineated over a broad range of mutually inclined perturbations. We recover them for test particles in the field of a hot Jupiter and a wide eccentric stellar binary, highlighting their relevance for the architecture of multi-planet systems in binaries. We then extend and deploy our machinery closer to home, as we consider the secular dynamics of Trans-Neptunian Objects (TNOs) in the presence of a putative ninth planet. We show how generalized Laplace equilibria seed islands for Trans-Neptunian objects to be sheltered around, islands within chaotic seas which we capture via Poincaré sections, while highlighting a beautiful interplay between Laplace and Kozai-Lidov secular dynamical structures. An eminently classical tale revived for the exo-planetary 21st century!

Secular dynamics of hierarchical multiple systems composed of nested binaries, with an arbitrary number of bodies and arbitrary hierarchical structure – III. Suborbital effects: hybrid integration techniques and orbit-averaging corrections

ABSTRACT The secularmultiple code, presented in two previous papers of this series, integrates the long-term dynamical evolution of multiple systems with any number of bodies and hierarchical structure, provided that the system is composed of nested binaries. In the formalism underlying secularmultiple, we previously averaged over all orbits in the system. This approximation significantly speeds up numerical integration of the equations of motion, making large population synthesis studies possible. However, the orbit averaging approximation can break down when the secular evolution time-scale of the system is comparable to or shorter than any of the orbital periods in the system. Here, we present an update to secularmultiple in which we incorporate hybrid integration techniques, and orbit-averaging corrections. With this update, the user can specify which orbits should be integrated directly (without averaging), or assuming averaged orbits. For orbits that are integrated directly, we implemented two integration techniques, one which is based on the regularized Kustaanheimo–Stiefel equations of motion in element form. We also implemented analytical orbit-averaging corrections for pairwise interactions to quadrupole order. The updates presented here provide more flexibility for integrating the long-term dynamical evolution of hierarchical multiple systems. By effectively combining direct integration and orbit averaging the long-term evolution can be accurately computed, but with significantly lower computational cost compared to existing direct N-body codes. We give a number of examples in which the new features are beneficial. Our updated code, which is written in c++ supplemented with a user-friendly interface in python, is freely available.

Orbital dynamics of circumbinary planets

ABSTRACT We investigate the dynamics of a non-zero mass, circular orbit planet around an eccentric orbit binary for various values of the binary eccentricity, binary mass fraction, planet mass, and planet semimajor axis by means of numerical simulations. Previous studies investigated the secular dynamics mainly by approximate analytic methods. In the stationary inclination state, the planet and binary precess together with no change in relative tilt. For both prograde and retrograde planetary orbits, we explore the conditions for planetary orbital libration versus circulation and the conditions for stationary inclination. As was predicted by analytic models, for sufficiently high initial inclination, a prograde planet’s orbit librates about the stationary tilted state. For a fixed binary eccentricity, the stationary angle is a monotonically decreasing function of the ratio of the planet-to-binary angular momentum j. The larger j, the stronger the evolutionary changes in the binary eccentricity and inclination. We also calculate the critical tilt angle that separates the circulating from the librating orbits for both prograde and retrograde planet orbits. The properties of the librating orbits and stationary angles are quite different for prograde versus retrograde orbits. The results of the numerical simulations are in very good quantitative agreement with the analytic models. Our results have implications for circumbinary planet formation and evolution.