We determine the orbital eccentricities of individual small Kepler planets, through a combination of asteroseismology and transit light-curve analysis. We are able to constrain the eccentricities of 51 systems with a single transiting planet, which supplement our previous measurements of 66 planets in multi-planet systems. Through a Bayesian hierarchical analysis, we find evidence that systems with only one detected transiting planet have a different eccentricity distribution than systems with multiple detected transiting planets. The eccentricity distribution of the single-transiting systems is well described by the positive half of a zero-mean Gaussian distribution with a dispersion σ e = 0.32 ± 0.06, while the multiple-transit systems are consistent with σ e = 0.083 +0.015 −0.020 . A mixture model suggests a fraction of 0.76 +0.21 −0.12 of single-transiting systems have a moderate eccentricity, represented by a Rayleigh distribution that peaks at 0.26 +0.04 −0.06 . This finding may reflect differences in the formation pathways of systems with different numbers of transiting planets. We investigate the possibility that eccentricities are "self-excited" in closely packed planetary systems, as well as the influence of long-period giant companion planets. We find that both mechanisms can qualitatively explain the observations. We do not find any evidence for a correlation between eccentricity and stellar metallicity, as has been seen for giant planets. Neither do we find any evidence that orbital eccentricity is linked to the detection of a companion star. Along with this paper we make available all of the parameters and uncertainties in the eccentricity distributions, as well as the properties of individual systems, for use in future studies.Subject headings: planets and satellites: formation -planets and satellites: dynamical evolution and stability -planets and satellites: fundamental parameters -planets and satellites: terrestrial planets -stars: oscillations (including pulsations) -stars: planetary systems

As of August 2019, among the more than 4000 confirmed exoplanets, only one has been detected in a globular cluster (GC) M4. The scarce of exoplanet detections motivates us to employ direct N -body simulations to investigate the dynamical stability of planets in young massive clusters (YMCs), which are potentially the progenitors of GCs. In an N = 128k cluster of virial radius 1.7 pc (comparable to Westerlund-1), our simulations show that most wide-orbit planets (a ≥ 20 au) will be ejected within a timescale of 10 Myr. Interestingly, more than 70% of planets with a < 5 au survive in the 100 Myr simulations. Ignoring planet-planet scattering and tidal damping, the survivability at t Myr as a function of initial semi-major axis a 0 in au in such a YMC can be described as f surv (a 0 , t) = −0.33 log 10 (a 0 ) 1 − e −0.0482t + 1. Upon ejection, about 28.8% of free-floating planets (FFPs) have sufficient speeds to escape from the host cluster at a crossing timescale. The other FFPs will remain bound to the cluster potential, but the subsequent dynamical evolution of the stellar system can result in the delayed ejection of FFPs from the host cluster. Although a full investigation of planet population in GCs requires extending the simulations to multi-Gyr, our results suggest that wideorbit planets and free-floating planets are unlikely to be found in GCs.

Aims. We perform a simulation using the Astrophysical Multipurpose Software Environment of the Orion Trapezium star cluster in which the evolution of the stars and the dynamics of planetary systems are taken into account. Methods. The initial conditions from earlier simulations were selected in which the size and mass distributions of the observed circumstellar disks in this cluster are satisfactorily reproduced. Four, five, or size planets per star were introduced in orbit around the 500 solar-like stars with a maximum orbital separation of 400 au.Results. Our study focuses on the production of free-floating planets. A total of 357 become unbound from a total of 2522 planets in the initial conditions of the simulation. Of these, 281 leave the cluster within the crossing timescale of the star cluster; the others remain bound to the cluster as free-floating intra-cluster planets. Five of these free-floating intra-cluster planets are captured at a later time by another star.Conclusions. The two main mechanisms by which planets are lost from their host star, ejection upon a strong encounter with another star or internal planetary scattering, drive the evaporation independent of planet mass of orbital separation at birth. The effect of small perturbations due to slow changes in the cluster potential are important for the evolution of planetary systems. In addition, the probability of a star to lose a planet is independent of the planet mass and independent of its initial orbital separation. As a consequence, the mass distribution of free-floating planets is indistinguishable from the mass distribution of planets bound to their host star.Article number, page 3 of 17

Due to the high stellar densities in young clusters, planetary systems formed in these environments are likely to have experienced perturbations from encounters with other stars. We carry out direct N-body simulations of multi-planet systems in star clusters to study the combined effects of stellar encounters and internal planetary dynamics. These planetary systems eventually become part of the Galactic field population the parental cluster dissolves, which is where most presently-known exoplanets are observed. We show that perturbations induced by stellar encounters lead to distinct signatures in the field planetary systems, most prominently, the excited orbital inclinations and eccentricities. Planetary systems that form within the cluster's half-mass radius are more prone to such perturbations. The orbital elements are most strongly excited in the outermost orbit, but the effect propagates to the entire planetary system through secular evolution. Planet ejections may occur long after a stellar encounter. The surviving planets in these reduced systems tend to have, on average, higher inclinations and larger eccentricities compared to systems that were perturbed less strongly. As soon as the parental star cluster dissolves, external perturbations stop affecting the escaped planetary systems, and further evolution proceeds on a relaxation time scale. The outer regions of these ejected planetary systems tend to relax so slowly that their state carries the memory of their last strong encounter in the star cluster. Regardless of the stellar density, we observe a robust anticorrelation between multiplicity and mean inclination/eccentricity. We speculate that the "Kepler dichotomy" observed in field planetary systems is a natural consequence of their early evolution in the parental cluster.

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