The Orbital Eccentricity of Small Planet Systems

We determine the orbital eccentricitiesof individual small Kepler planets, through a combination of asteroseismologyand transit light-curve analysis. We are able to constrain the eccentricitiesof 51 systems with a single transiting planet, which supplement our previous measurements of 66 planetsin multi- planetsystems. Through a Bayesian hierarchical analysis, we find evidence that systems with only one detected transiting planethave a different eccentricitydistribution than systems with multiple detected transiting planets. The eccentricitydistribution of the single- transiting systemsis well described by the positive half of a zero-mean Gaussian distribution with a dispersion $\sigma_e = 0.32 \pm 0.06$, while the multiple- transit systemsare consistent with $\sigma_e = 0.083^{+0.015}_{-0.020}$. A mixture model suggests a fraction of $0.76^{+0.21}_{-0.12}$ of single- transiting systemshave a moderate eccentricity, represented by a Rayleigh distributionthat 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 eccentricitiesare "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 eccentricityand stellar metallicity, as has been seen for giant planets. Neither do we find any evidence that orbital eccentricityis linked to the detection of a companion star. Along with this paper we make available all of the parameters and uncertainties in the eccentricitydistributions, as well as the properties of individual systems, for use in future studies.