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SOPHIE velocimetry of Kepler transit candidates: X KOI-142c: first radial velocity confirmation of a non-transiting exoplanet discovered by transit timing

The exoplanet KOI-142b (Kepler-88b) shows transit timing variations (TTVs) with a semi-amplitude of $\sim 12\,$ hours, earning the nickname of "king of transit variations". Only the transit of the planet b was detected in the Kepler data with an orbital period of $\sim 10.92\,$ days and a radius of $\sim 0.36$ R$_{\mathrm{Jup}}$. The TTVs together with the transit duration variations (TDVs) of KOI-142b were analysed by Nesvorny et al. (2013) who found a unique solution for a companion perturbing planet. The authors predicted an outer non-transiting companion, KOI-142c, with a mass of $0.626\pm 0.03$ M$_{\mathrm{Jup}}$ and a period of $22.3397^{+0.0021}_{-0.0018}\,$days, and hence close to the 2:1 mean-motion resonance with the inner transiting planet. We report independent confirmation of KOI-142c using radial velocity observations with the SOPHIE spectrograph at the Observatoire de Haute-Provence. We derive an orbital period of $22.10 \pm 0.25\,$days and a minimum planetary mass of $0.76^{+0.32}_{0.16}\,$ M$_{\mathrm{Jup}}$, both in good agreement with the predictions by previous transit timing analysis. Therefore, this is the first radial velocity confirmation of a non-transiting planet discovered with transit timing variations, providing an independent validation of the TTVs technique.