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-10 b (P$_b$ = 0.837 d; R$_b$ = 1.47 R$_{\bigoplus}$) and the long-period sub-Neptune Kepler-10 c (P$_c$ = 45.294 d; R$_c$ = 2.35 R$_{\bigoplus}$), and a non-transiting planet that causes variations in the Kepler-10 c transit times. Measurements of the mass of Kepler-10 c 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 ~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$_b$ = 3.24 $\pm$ 0.32 M$_{\bigoplus}$ (10σ) and ρ$_b$ = 5.54 $\pm$ 0.64 g cm$^{-3}$ for planet b; M$_c$ = 11.29 $\pm$ 1.24 M$_{\bigoplus}$ (9σ) and ρ$_c$ = 4.75 $\pm$ 0.53 g cm$^{-3}$ for planet c; and M$_d$ sin i = 12.00 $\pm$ 2.15 M$_{\bigoplus}$ (6σ) and P$_d$ = 151.06 $\pm$ 0.48 d for the non-transiting planet Kepler-10 d. This solution is further supported by the analysis of the Kepler-10 c transit timing variations and their simultaneous modeling with the HARPS-N radial velocities. While Kepler-10 b is consistent with a rocky composition and a small or no iron core, Kepler-10 c may be a water world that formed beyond the water snowline and subsequently migrated inward.