Exoplanet orbital eccentricities derived from LAMOST–Kepler analysis

Significance The Kepler satellite has made revolutionary discoveries of thousands of planets down to Earth size. However, the orbital shapes (parameterized by eccentricities) of most Kepler planets remain unknown. We derive the eccentricity distributions of an unprecedented large and homogeneous sample of 698 Kepler planets. We discover a dichotomy in eccentricities: the systems with single transiting planets, which make up half of the sample, have a large mean eccentricity (∼ 0.3), whereas the multiples are on nearly circular orbits. The average eccentricity and inclination of the Kepler multiples and the solar system objects fit into an intriguing common pattern. Our results suggest that the circular and coplanar planetary orbits like those in our solar system are likely typical in the galaxy. The nearly circular (mean eccentricity e¯≈0.06) and coplanar (mean mutual inclination i¯≈3°) orbits of the solar system planets motivated Kant and Laplace to hypothesize that planets are formed in disks, which has developed into the widely accepted theory of planet formation. The first several hundred extrasolar planets (mostly Jovian) discovered using the radial velocity (RV) technique are commonly on eccentric orbits (e¯≈0.3). This raises a fundamental question: Are the solar system and its formation special? The Kepler mission has found thousands of transiting planets dominated by sub-Neptunes, but most of their orbital eccentricities remain unknown. By using the precise spectroscopic host star parameters from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) observations, we measure the eccentricity distributions for a large (698) and homogeneous Kepler planet sample with transit duration statistics. Nearly half of the planets are in systems with single transiting planets (singles), whereas the other half are multiple transiting planets (multiples). We find an eccentricity dichotomy: on average, Kepler singles are on eccentric orbits with e¯≈ 0.3, whereas the multiples are on nearly circular (e¯=0.04−0.04+0.03) and coplanar (i¯=1.4−1.1+0.8 degree) orbits similar to those of the solar system planets. Our results are consistent with previous studies of smaller samples and individual systems. We also show that Kepler multiples and solar system objects follow a common relation [e¯≈(1–2)×i¯] between mean eccentricities and mutual inclinations. The prevalence of circular orbits and the common relation may imply that the solar system is not so atypical in the galaxy after all.

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