Comparison of gyrochronological and isochronal age estimates for transiting exoplanet host stars

Context. Tidal interactions between planets and their host stars are not well understood, but may be an important factor in their formation, structure, and evolution. Previous studies suggest that these tidal interactions may be responsible for discrepancies between the ages of exoplanet host stars estimated using stellar models (isochronal age estimates) and age estimates based on the stars’ rotation periods (gyrochronological age estimates). Recent improvements in our understanding of the rotational evolution of single stars and a substantial increase in the number of exoplanet host stars with accurate rotation period measurements make it worthwhile to revisit this question. Aims. Our aim is to determine whether the gyrochronological age estimates for transiting exoplanet host stars with accurate rotation period measurements are consistent with their isochronal age estimates, and whether this is indicative of tidal interaction between the planets and their host stars. Methods. We have compiled a sample of 28 transiting exoplanet host stars with measured rotation periods, including two stars (HAT-P-21 and WASP-5) for which the rotation period based on the light curve modulation is reported here for the first time. We use our recently developed Bayesian Markov chain Monte Carlo method to determine the joint posterior distribution for the mass and age of each star in the sample. We extend our Bayesian method to include a calculation of the posterior distribution of the gyrochronological age estimate that accounts for the uncertainties in the mass and age, the strong correlation between these values, and the uncertainties in the mass-rotation-age calibration. Results. The gyrochronological age estimate (τgyro) is significantly lower than the isochronal age estimate for about half of the stars in our sample. Tidal interactions between the star and planet are a reasonable explanation for this discrepancy in some cases, but not all. The distribution of τgyro values is evenly spread from very young ages up to a maximum value of a few Gyr, i.e. there is no obvious pile-up of stars at very low or very high values of τgyro as might be expected if some evolutionary or selection effect were biasing the age distribution of the stars in this sample. There is no clear correlation between τgyro and the strength of the tidal force on the star due to the innermost planet. There is clear evidence that the isochronal age estimates for some K-type stars are too high, and this may also be the case for some G-type stars. This may be the result of magnetic inhibition of convection. The densities of HAT-P-11 and WASP-84 are too high to be reproduced by any stellar models within the observed constraints on effective temperature and metallicity. These stars may have strongly enhanced helium abundances. There is currently no satisfactory explanation for the discrepancy between the young age for CoRoT-2 estimated from either gyrochronology or its high lithium abundance, and the extremely old age for its K-type stellar companion inferred from its very low X-ray flux. Conclusions. There is now strong evidence that the gyrochronological age estimates for some transiting exoplanet host stars are significantly lower than the isochronal age estimates, but it is not always clear that this is good evidence for tidal interactions between the star and the planet