A dynamical analysis of the Kepler-11 planetary system

Abstract

The Kepler-11 star hosts at least six transiting super-Earth planets detected through the precise photometric observations of the Kepler mission (Lissauer et al.). In this paper, we re-analyze the available Kepler data, using the direct N-body approach rather than an indirect TTV method in the discovery paper. The orbital modeling in the realm of the direct approach relies on the whole data set, not only on the mid-transits times. Most of the results in the original paper are confirmed and extended. We constrained the mass of the outermost planet g to less than 30 Earth masses. The mutual inclinations between orbits b and c as well as between orbits d and e are determined with a good precision, in the range of [1,5] degrees. Having several solutions to four qualitative orbital models of the Kepler-11 system, we analyze its global dynamics with the help of dynamical maps. They reveal a sophisticated structure of the phase space, with narrow regions of regular motion. The dynamics are governed by a dense net of three- and four-body mean motion resonances, forming the Arnold web. Overlapping of these resonances is a main source of instability. We found that the Kepler-11 system may be long-term stable only in particular multiple resonant configurations with small relative inclinations. The mass-radius data derived for all companions reveal a clear anti-correlation between the mean density of the planets with their distance from the star. This may reflect the formation and early evolution history of the system.Comment: 21 pages, 19 figures, 9 tables, accepted to MNRA

TRADES: A new software to derive orbital parameters from observed transit times and radial velocities

“…The orbital parameters we determined agree with the values of the discovery paper and the recent analysis of 14 quarters by Lissauer et al (2013). Furthermore, our analysis agrees with the results by Migaszewski et al (2012) that used a similar approach. Our best simulation (K11-III) returned a value for the mass of the planet g of about 25 M ⊕ , which agrees within the error bars and the confidence interval proposed by Lissauer et al (2013).…”

“…6 from the analysis of T 0 s from Mazeh et al (2013) for the first 12 quarters of Kepler data. Parameters fitted: M, P, e, ω, and M. A38, page 6 of 13 The resulting masses of the solutions K11-I and K11-II all agree within 2σ with the discovery paper (Lissauer et al 2011a) and with all the best-fit solutions determined by Migaszewski et al (2012). In the latter work, the authors presented different sets of orbital parameters determined with an approach similar to ours (direct N-body simulation with genetic algorithm, Levenberg-Marquardt, and bootstrap), but they directly fit the flux of Kepler light curves (so-called dynamical photometric model) without fitting the transit times.…”

Three body resonances in close orbiting planetary systems: tidal dissipation and orbital evolution

“…From this it is potentially possible to estimate tidal quality factors which are in turn related to the composition and state of the planetary interiors. We remark that systems with observed adjacent pairs of first order resonances may have avoided a form of long term orbital instability, associated with higher order many body resonances, that could cause evolution away from them in other systems ( Migaszewski et al 2012).…”

ON THE RELATIVE SIZES OF PLANETS WITHINKEPLERMULTIPLE-CANDIDATE SYSTEMS

“…Kepler-11 has six transiting planets (Lissauer et al 2011a) with the smallest planets residing preferentially inside the orbits of larger planets. Kepler-11 displays an anti-correlation between the mean density of the planets and the semimajor axis distance from the host star; i.e., the larger and lower density planets are located farther out than the smaller and denser planets, possibly indicative of the formation and/or evolution of the planetary system (Migaszewski et al 2012). Kepler-47, the only known circumbinary multiple-planet system, also displays a size hierarchy with the inner planet (∼3 R ⊕ ) being smaller than the outer planet (∼4.6 R ⊕ ; Orosz et al 2012).…”