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Description
We present a detailed characterization of the Kepler-411 system (KOI 1781). This system was previously known to host two transiting planets: one with a period of 3 days (R=2.4R_{Earth}_; Kepler-411b) and one with a period of 7.8days (R=4.4R_{Earth}_; Kepler-411c), as well as a transiting planetary candidate with a 58-day period (R=3.3R_{Earth}_; KOI 1781.03) from Kepler photometry. Here, we combine Kepler photometry data and new transit timing variation (TTV) measurements from all the Kepler quarters with previous adaptive-optics imaging results, and dynamical simulations, in order to constrain the properties of the Kepler-411 system. From our analysis, we obtain masses of 25.6+/-2.6M_{Earth}_ for Kepler-411b and 26.4+/-5.9M_{Earth}_ for Kepler-411c, and we confirm the planetary nature of KOI 1781.03 with a mass of 15.2+/-5.1M_{Earth}_, hence the name Kepler-411d. Furthermore, by assuming near-coplanarity of the system (mutual inclination below 30{deg}), we discover a nontransiting planet, Kepler-411e, with a mass of 10.8+/-1.1M_{Earth}_ on a 31.5-day orbit, which has a strong dynamical interaction with Kepler-411d. With densities of 1.71+/-0.39g/cm^3^ and 2.32+/-0.83g/cm^3^, both Kepler-411c and Kepler-411d belong to the group of planets with a massive core and a significant fraction of volatiles. Although Kepler-411b has a sub-Neptune size, it belongs to the group of rocky planets.
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