Exoplanet orbital eccentricities derived from LAMOST–Kepler analysis

Abstract

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 MultiObject 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 +0.03 −0.04 ) and coplanar ( i = 1.4 +0.8 −1.1 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.orbital eccentricities | exoplanets | transit | solar system | planetary dynamics O ur knowledge of orbital shapes (parameterized with eccentricities) of planetary systems has been drastically advanced in the last 2 decades largely thanks to the radial velocity (RV) planet surveys, but there remain some major puzzles. For example, the majority of RV planets are found on eccentric orbits ( e ≈ 0.3) (1) in contrast to the solar system planets, raising a fundamental question: Is the solar system an atypical member of the planetary system population in the galaxy (2)? Furthermore, the RV method has some key limitations. For example, several notable biases and degeneracies can introduce considerable systematical uncertainties into the eccentricity distributions derived from the RV technique (3-5). In addition, the majority of eccentricities measured using the RV method are for giant planets (e.g., Jupiter size), whereas the eccentricity distributions of smaller planets (e.g., Earth to Neptune size) remain poorly understood.Complementary to the RV technique, the Kepler mission has discovered thousands of planet candidates down to about Earth radius using the transit technique (6). About half of the Kepler planets are in systems with multiple transiting planets, and on average, they are on nearly coplanar orbits sim...

Dynamically Hot Super-Earths from Outer Giant Planet Scattering

“…The mean, median and their 1-σ uncertainties is determined by bootstrapping the single planet population for 1000 realizations. This is slightly higher than the estimated value by Xie et al (2016), which it might be expected, since the observed single transit planet systems are likely to be a mixture between the single super-Earths and the multiple superEarths systems with relatively high mutual inclinations, which have lower eccentricities.…”

“…The bulk of these low mutual inclination systems have similar properties as the Kepler multiple systems, which are much more circular and coplanar, with an upper limit to the mean eccentricity of ∼ 0.07 (Xie et al 2016).…”

“…First, Xie et al (2016) find that the best fit to the transit durations of single transiting planets is a single Rayleigh distribution withē 0.3. Second, by combining measurements of the star's rotation period, radius, and projected rotational velocity, Morton & Winn (2014) found statistically significant evidence that multiple transiting systems to have lower stellar obliquity angles than their single transiting counterparts.…”

“…In particular, the eccentricities derived from transit timing variations (TTVs) are typically ∼ 0.01 (Wu & Lithwick 2013), while the transit durations of ensembles of multiple transiting planets can be well-fitted with a Rayleigh distribution (Equation 3) with mean values ofē ∼ 0.04 (Van Eylen & Albrecht 2015;Xie et al 2016) andī m 1 − 2…”

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“…Assuming a moderate eccentricity e=0.1 of ProximaCen-taurib (Xie et al 2016;Brown 2017), we simulate the strengths of its TTVs perturbed by an outer planet with varying masses and orbital periods in coplanar orbits. The mass and orbital period of the outer planet are constrained by the requirement that the Doppler reflex stellar RV should be <3 m s −1 to keep the planet undetectable in the high-precision observation of Anglada-Escudé et al (2016).…”