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

Abstract

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 (τ gyro ) 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 τ gyro values is evenly spread from very young ages up to a maximum value of a few Gyr, i.e. there is no obvious pileup of stars at very low or very high values of τ gyro 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 τ gyro 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...

The Stellar Obliquity, Planet Mass, and Very Low Albedo of Qatar-2 From K2 Photometry

“…According to this formula and our measured rotation period, the gyrochronological age of Qatar-2 is 1.4±0.3Gyr. Maxted et al (2015) made an independent estimate of the stellar age by fitting stellar-evolutionary models to the observed spectroscopic parameters and apparent magnitudes. Their result was 15.7±1.4Gyr, significantly older than the gyro age.…”

Clusters: Age Scales for Stellar Physics

“…From these panels it is clear the role that both the chemical composition and the physics inside the models are playing. Maxted et al (2015b) concluded that the gyro-ages are significantly younger than isochrone ages for half of their sample. Second order effect might be at play (magnetism, tidal interactions or other), but until we completely understand all sides of stellar evolution, ages would, somehow, remain elusive.…”

“…Maxted et al (2015a) have used a Bayesian approach in order to derive ages based on fits with theoretical models (3.1). They have also derived ages based on gyrochronology (subsection 3.6.1 and Maxted et al 2015b). Figure 24 comes from Maxted et al (2015b), with a caption stating: "Change in the best-fitting masses and ages of transiting exoplanet host stars due to a change in the assumed helium abundance or mixing length parameter.…”

“…They have also derived ages based on gyrochronology (subsection 3.6.1 and Maxted et al 2015b). Figure 24 comes from Maxted et al (2015b), with a caption stating: "Change in the best-fitting masses and ages of transiting exoplanet host stars due to a change in the assumed helium abundance or mixing length parameter. Dots show the best-fitting mass and age for the default values of Y and α MLT and lines show the change in mass and age due to an increase in helium abundance ∆Y = +0.02 (left panel) or a change in mixing length parameter ∆α MLT = +0.2 (right panel).…”

Rotation of Planet-Hosting Stars

“…This study was based on a sample of about 25 transiting systems with published V rot sin i or P rot estimates available at that time. Maxted et al (2015) used Bayesian techniques to compare the age estimates from stellar model isochrones to gyrochronological age estimates for 28 transiting exoplanet host stars with accurate mass and radius estimates and directly measured rotation periods. The gyrochronological age estimate was significantly lower than the isochronal age estimate for about half of the stars in that sample.…”