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

Abstract

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; $R_{\mathrm{p}}=1.47{\mathrm{R}}_{\oplus }$) and the long-period sub-Neptune Kepler-10c ($P=45.294$ d; $R_{\mathrm{p}}=2.35{\mathrm{R}}_{\oplus }$), 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 $\sim 11$~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: $M_{\mathrm{p},\mathrm{b}}=3.24\pm 0.32{\mathrm{M}}_{\oplus }$ (10$\sigma$) and ${\rho }_{\mathrm{p},\mathrm{b}}=5.54\pm 0.64\mathrm{g}\mathrm{c}{\mathrm{m}}^{-3}$ for planet b; $M_{\mathrm{p},\mathrm{c}}=11.29\pm 1.24{\mathrm{M}}_{\oplus }$ (9$\sigma$) and ${\rho }_{\mathrm{p},\mathrm{c}}=4.75\pm 0.53\mathrm{g}\mathrm{c}{\mathrm{m}}^{-3}$ for planet c; and $M_{\mathrm{p},\mathrm{d}}\sin i=12.00\pm 2.15{\mathrm{M}}_{\oplus }$ (6$\sigma$) 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.

15 pages, 11 figures, 5 tables, Astronomy and Astrophysics, in press

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