2016ApJ...826...35A

The preliminary results on deep-mixing manifestations in stellar variability are tested using our improved method and extended data set. We measure the timescales τ_ m_ of the stochastic change in the spectral power of rotational harmonics with numbers m <= 3 in the light curves of 1361 main-sequence stars from the Kepler mission archive. We find that the gradient [log(τ_{2})-log(τ_{1})]/[log(2)-log(1)] has a histogram maximum at -2/3, demonstrating agreement with Kolmogorov's theory of turbulence and therefore confirming the manifestation of deep mixing. The squared amplitudes of the first and second rotational harmonics, corrected for integral photometry distortion, also show a quasi-Kolmogorov character with spectral index ≃-5/3. Moreover, the reduction of τ₁ and τ₂ to the timescales τ_lam1 and τ_lam2 of laminar convection in the deep stellar layers reveals the proximity of both τ_lam1 and τ_lam2 to the turnover time τ_MLT of standard mixing length theory. Considering this result, we use the obtained stellar variability timescales instead of τ_MLT in our analysis of the relation between stellar activity and the Rossby number P/τ_MLT. Comparison of our diagrams with previous results and theoretical expectations shows that best-fit correspondence is achieved for τ_lam1, which can therefore be used as an analog of τ_MLT. This means that the laminar component (giant cells) of stellar turbulent convection indeed plays an important role in the physics of stars. Additionally, we estimate the diffusivity of magnetic elements in stellar photospheres.