Deep mixing in stellar variability: improved method, statistics, and applications
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 {sub 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{sub 2})−log(τ{sub 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 τ {sub 1} and τ {sub 2} to the timescales τ {sub lam1} and τ {sub lam2} of laminar convection in the deep stellar layers reveals the proximity of both τ {sub lam1} and τ {sub lam2} to the turnover time τ {sub MLT} of standard mixing length theory. Considering this result, we use the obtained stellar variability timescales instead of τ {sub MLT} in our analysis of the relation between stellar activity and the Rossby number P/τ {sub MLT}. Comparison of our diagrams with previous results and theoretical expectations shows that best-fit correspondence is achieved for τ {sub lam1}, which can therefore be used as an analog of τ {sub 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.