SOPHIE velocimetry of Kepler transit candidates

XVIII. Radial velocity confirmation, absolute masses and radii, and origin of the Kepler-419 multiplanetary system^★,★★

¹ Observatoire de Genève, Département d’Astronomie, Université de Genève, Chemin des Maillettes 51, 1290 Versoix, Switzerland
e-mail: jose.almenara@unige.ch
² Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Buenos Aires, Argentina
³ CONICET – Universidad de Buenos Aires, Instituto de Astronomía y Física del Espacio (IAFE), Buenos Aires, Argentina
⁴ Institut d’Astrophysique de Paris, UMR7095 CNRS, Université Pierre & Marie Curie, 98bis boulevard Arago, 75014 Paris, France
⁵ Observatoire de Haute Provence, 04670 Saint-Michel-l’Observatoire, France
⁶ School of Physics & Astronomy, Monash University, Victoria 3800, Australia
⁷ Université Paris-Sud, CNRS, Institut d’Astrophysique Spatiale, UMR8617, 91405 Orsay Cedex, France
⁸ Aix-Marseille Université, CNRS, LAM, Laboratoire d’Astrophysique de Marseille, Marseille, France
⁹ Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762 Porto, Portugal
¹⁰ Université Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
¹¹ INAF – Osservatorio Astrofisico di Torino, via Osservatorio 20, 10025 Pino Torinese, Italy
¹² Leiden Observatory, Leiden University, Postbus 9513, 2300 RA Leiden, The Netherlands

Received: 20 December 2017
Accepted: 24 March 2018

Abstract

Kepler-419 is a planetary system discovered by the Kepler photometry which is known to harbour two massive giant planets: an inner 3 M_J transiting planet with a 69.8-day period, highly eccentric orbit, and an outer 7.5 M_J non-transiting planet predicted from the transit-timing variations (TTVs) of the inner planet b to have a 675-day period, moderately eccentric orbit. Here we present new radial velocity (RV) measurements secured over more than two years with the SOPHIE spectrograph, where both planets are clearly detected. The RV data is modelled together with the Kepler photometry using a photodynamical model. The inclusion of velocity information breaks the MR⁻³ degeneracy inherent in timing data alone, allowing us to measure the absolute stellar and planetary radii and masses. With uncertainties of 12 and 13% for the stellar and inner planet radii, and 35, 24, and 35% for the masses of the star, planet b, and planet c, respectively, these measurements are the most precise to date for a single host star system using this technique. The transiting planet mass is determined at better precision than the star mass. This shows that modelling the radial velocities and the light curve together in systems of dynamically interacting planets provides a way of characterising both the star and the planets without being limited by knowledge of the star. On the other hand, the period ratio and eccentricities place the Kepler-419 system in a sweet spot; had around twice as many transits been observed, the mass of the transiting planet could have been measured using its own TTVs. Finally, the origin of the Kepler-419 system is discussed. We show that the system is near a coplanar high-eccentricity secular fixed point, related to the alignment of the orbits, which has prevented the inner orbit from circularising. For most other relative apsidal orientations, planet b’s orbit would be circular with a semi-major axis of 0.03 au. This suggests a mechanism for forming hot Jupiters in multiplanetary systems without the need of high mutual inclinations.