We have analysed radial velocity measurements for known transiting exoplanets to study the empirical signature of tidal orbital evolution for close-in planets. Compared to standard eccentricity determination, our approach is modified to focus on the rejection of the null hypothesis of a circular orbit. We are using a Markov Chain Monte Carlo analysis of radial velocity measurements and photometric constraints, including a component of correlated noise, as well as Bayesian model selection to check if the data justify the additional complexity of an eccentric orbit. We find that among planets with non-zero eccentricity values quoted in the literature, there is no evidence for an eccentricity detection for the seven planets CoRoT-5b, WASP-5b, WASP-6b, WASP-10b, WASP-12b, WASP-17b and WASP-18b. In contrast, we confirm the eccentricity of HAT-P-16b, e= 0.034 ± 0.003, the smallest eccentricity that is reliably measured so far for an exoplanet as well as that of WASP-14b, which is the planet at the shortest period (P= 2.24 d), with a confirmed eccentricity, e= 0.088 ± 0.003. As part of the study, we present new radial velocity data using the HARPS spectrograph for CoRoT-1, CoRoT-3, WASP-2, WASP-4, WASP-5 and WASP-7 as well as the SOPHIE spectrograph for HAT-P-4, HAT-P-7, TrES-2 and XO-2.
We show that the dissipative effect of tides raised in the planet by the star and vice versa explain all the eccentricity and spin–orbit alignment measurements available for transiting planets. We revisit the mass–period relation and consider its relation to the stopping mechanism of orbital migration for hot Jupiters. In addition to CoRoT-2 and HD 189733, we find evidence for excess rotation of the star in the systems CoRoT-18, HAT-P-20, WASP-19 and WASP-43.