In-depth characterization of the Kepler-10 three-planet system with HARPS-N radial velocities and Kepler transit timing variations

The old G3V star Kepler-10 is known to host two transiting planets, the ultra-short-period super-Earth Kepler-10b ($P=0.837$ d; $R_{\rm p}=1.47~\rm R_\oplus$) and the long-period sub-Neptune Kepler-10c ($P=45.294$ d; $R_{\rm p}=2.35~\rm R_\oplus$), and a non-transiting planet that causes variations in the Kepler-10c transit times. Measurements of the mass of Kepler-10c in the literature have shown disagreement, depending on the radial-velocity dataset and/or the modeling technique used. Here we report on the analysis of almost 300 high-precision radial velocities gathered with the HARPS-N spectrograph at the Telescopio Nazionale Galileo over $\sim11$~years, and extracted with the YARARA-v2 tool, which corrects for possible systematics and/or low-level activity variations at the spectrum level. To model these radial velocities, we used three different noise models and various numerical techniques, which all converged to the solution: $M_{\rm p, b}=3.24 \pm 0.32~\rm M_\oplus$ (10$σ$) and $ρ_{\rm p, b}=5.54 \pm 0.64~\rm g\;cm^{-3}$ for planet b; $M_{\rm p, c}=11.29 \pm 1.24~\rm M_\oplus$ (9$σ$) and $ρ_{\rm p, c}=4.75 \pm 0.53~\rm g\;cm^{-3}$ for planet c; and $M_{\rm p, d}\sin{i}=12.00 \pm 2.15~\rm M_\oplus$ (6$σ$) and $P=151.06 \pm 0.48$ d for the non-transiting planet Kepler-10d. This solution is further supported by the analysis of the Kepler-10c transit timing variations and their simultaneous modeling with the HARPS-N radial velocities. While Kepler-10b is consistent with a rocky composition and a small or no iron core, Kepler-10c may be a water world that formed beyond the water snowline and subsequently migrated inward.