In this Review, I discuss recent developments on the long-term dynamical evolution of exoplanet systems, focusing on how distinctive dynamical processes may have shaped the orbital architectures of observed populations. I include three applications that highlight part of my own work. First, I examine the high-eccentricity tidal migration of hot Jupiters from a phase of dynamical instability and subsequent secular interactions in two-planet systems. Second, secular chaos as the origin of ultra-short-period planets with extreme period ratios. Third, secular resonance sweeping driven by a dispersing protoplanetary disk as the origin hot Neptunes residing in polar orbits. Finally, I discuss how upcoming observations will allow further constraining the prevalence of these dynamical processes.

HD34445 is a system that consists of a star and six planets. In some previous work, we investigated the dynamical stability of the system by means of numerical simulations. Here, we explore the system further by carrying out additional numerical experiments. A total of 100000 simulations confirm previous findings of the stability status of the system at the 1σ and 99% c.i. level. We find that only 2.7% of the systems with parameters varied within 1σ from the mean were unstable, while that percentage rose to about 28% for systems with parameter values taken within the 99% c.i. These preliminary results are presented and discussed herein.

We present the results of a search for additional exoplanets in all multiplanetary systems discovered to date, employing a logarithmic spacing between planets in our Solar System known as the Titius–Bode (TB) relation. We use the Markov Chain Monte Carlo method and separately analyse 229 multiplanetary systems that house at least three or more confirmed planets. We find that the planets in $\sim 53\%$ of these systems adhere to a logarithmic spacing relation remarkably better than the Solar System planets. Using the TB relation, we predict the presence of 426 additional exoplanets in 229 multiplanetary systems, of which 197 candidates are discovered by interpolation and 229 by extrapolation. Altogether, 47 predicted planets are located within the habitable zone of their host stars, and 5 of the 47 planets have a maximum mass limit of 0.1–2 ${\rm M}_{\oplus}$ and a maximum radius lower than 1.25 ${\rm R}_{\oplus}$ . Our results and prediction of additional planets agree with previous studies’ predictions; however, we improve the uncertainties in the orbital period measurement for the predicted planets significantly.

The Lidov-Kozai (LK) resonance is one of the most widely discussed topics since the discovery of exoplanets in eccentric orbits. It constitutes a secular protection mechanism for systems with high mutual inclinations, although large variations in eccentricity and inclination are observed. This review aims to illustrate how the LK resonance influences the dynamics of the three-body problem at different scales, namely i) for two-planet extrasolar systems where the orbital variations occur in a coherent way such that the system remains stable, ii) for inclined planets in protoplanetary discs where the LK cycles are produced by the gravitational force exerted by the disc on the planet, iii) for migrating planets in binary star systems, whose dynamical evolution is strongly affected by the LK resonance even without experiencing a resonance capture, and iv) for triple-star systems for which the migration through LK cycles combined with tidal friction is a possible explanation for the short-period pile-up observed in the distribution of multiple stars.

The Kepler mission has recently discovered a number of exoplanetary systems, such as Kepler 11, in which ensembles of several planets are found in very closely packed orbits. These systems present a challenge for traditional formation and migration scenarios. We present a dynamical study of the evolution of these systems using an N-body approach, incorporating both smooth and stochastic migration forces and a variety of initial conditions, in order to assess the feasibility of assembling such systems via traditional, disc-driven migration.

Perturbation theory in the three body problem has greatly advanced our ability to understand and model a variety of systems ranging from artificial satellites to stars and from extrasolar planets to asteroid-Jupiter interactions. In a series of papers, we developed an analytical technique for estimating the orbital eccentricity of the inner binary in hierarchical triple systems. The method combined the secular theory with calculations of short period terms. The derivation of the short term component was based on an expansion of the rate of change of the Runge-Lenz vector by using first order perturbation theory, while canonical perturbation theory was used to investigate the secular evolution of the system. In the present work we extend the calculation to the orbit of the outer binary. At the same time, we provide an improved version for some previous results. A post-Newtonian correction is included in our model. Our analytical estimates are compared with numerical and analytical results on the subject and applications to stellar triples and extrasolar planets are discussed.

A large number of observed exoplanets are part of multiple planet systems. Most of these systems are sufficiently close-in to be tidally evolving. In such systems, there is a competition between the excitation caused by planet-planet interactions and tidal damping. Using as an example two multiple planet systems, which host planets in the surface liquid water habitable zone (HZ): Kepler-62 and Kepler-186, we show the importance and effect of both planetary and stellar tides on the dynamical evolution of planets and on the climate of the HZ planets.

One of the first stages of planet formation is the growth of small planetesimals and their accumulation into large planetesimals and planetary embryos. This early stage occurs much before the dispersal of most of the gas from the protoplanetary disk. Due to their different aerodynamic properties, planetesimals of different sizes/shapes experience different drag forces from the gas at these stage. Such differential forces produce a wind-shearing effect between close by, different size planetesimals. For any two planetesimals, a wind-shearing radius can be considered, at which the differential acceleration due to the wind becomes greater than the mutual gravitational pull between the planetesimals. We find that the wind-shearing radius could be much smaller than the gravitational shearing radius by the Sun (the Hill radius), i.e. during the gas-phase of the disk wind-shearing could play a more important role than tidal perturbations by the Sun. Here we study the wind-shearing radii for planetesimal pairs of different sizes and compare it with gravitational shearing (drag force vs. gravitational tidal forces). We then discuss the role of wind-shearing for the stability and survival of binary planetesimals, and provide stability criteria for binary planetesimals embedded in a gaseous disk.

We discuss the effects of close scattering and merging between planets on distributions of mass, semimajor axis and orbital eccentricity, using population synthesis model of planet formation, focusing on the distributions of close-in super-Earths, which are being observed recently. We found that a group of compact embryos emerge interior to the ice line, grow, migrate, and congregate into closely-packed convoys which stall in the proximity of their host stars. After the disk-gas depletion, they undergo orbit crossing, close scattering, and giant impacts to form multiple rocky Earths or super-Earths in non-resonant orbits around ~ 0.1AU with moderate eccentricities of ~ 0.01–0.1. The formation of these planets does not depend on model parameters such as type I migration speed. The fraction of solar-type stars with these super-Earths is anti-correlated with the fraction of stars with gas giants. The newly predicted family of close-in super-Earths makes less clear “planet desert” at intermediate mass range than our previous prediction.

The equilibrium tide model in the weak friction approximation is used by the binary star and exoplanet communities to study the tidal evolution of short-period systems, however, each uses a slightly different approach which potentially leads to different conclusions about the timescales on which various processes occur. Here we present an overview of these two approaches, and show that for short-period planets the circularization timescales they predict differ by at most a factor of a few. A discussion of the timescales for orbital decay, spin-orbit synchronization and spin-orbit alignment is also presented.