Kepler-411: a four-planet system with an active host star

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 ($R=2.4R_\oplus$; Kepler-411b) and one with a period of 7.8 days ($R=4.4R_\oplus$; Kepler-411c), as well as a transiting planetary candidate with a 58-day period ($R=3.3R_\oplus$; 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$\pm$2.6$M_\oplus$ for Kepler-411b and 26.4$\pm$5.9 $M_\oplus$ for Kepler-411c, and we confirm the planetary nature of KOI 1781.03 with a mass of 15.2$\pm$5.1$M_\oplus$, hence the name Kepler-411d. Furthermore, by assuming near-coplanarity of the system (mutual inclination below $30^\circ$), we discover a nontransiting planet, Kepler-411e, with a mass of 10.8$\pm$1.1$M_\oplus$ on a 31.5-day orbit, which has a strong dynamical interaction with Kepler-411d. With densities of $1.71\pm0.39$~g\,cm$^{-3}$ and $2.32\pm0.83$~g\,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.