Rotational dependence of turbulent transport coefficients in global convective dynamo simulations of solar-like stars

Abstract

For moderate and slow rotation, magnetic activity of solar-like stars is observed to strongly depend on rotation. These observations do not yet have a solid explanation in terms of dynamo theory. We aim to find such an explanation by numerically investigated the rotational dependency of dynamo drivers in solar-like stars. We ran semi-global convection simulations of stars with rotation rates from 0 to 30 times the solar value, corresponding to Coriolis numbers, Co, of 0 to 110. We measured the turbulent transport coefficients describing the magnetic field evolution with the help of the test-field method, and compared with the dynamo effect arising from the differential rotation. The trace of the $\alpha$ tensor increases for moderate rotation rates with Co$^{0.5}$ and levels off for rapid rotation. This behavior agrees with the kinetic $\alpha$, if one considers the decrease of the convective scale with increasing rotation. The $\alpha$ tensor becomes highly anisotropic for Co$\gtrsim 1$. Furthermore, $\alpha_{rr}$ dominates for moderate rotation (1<Co<10), and $\alpha_{\phi\phi}$ for rapid rotation (Co $\gtrsim 10$). The turbulent pumping effect is dominating the meridional transport of the magnetic field. Taking all dynamo effects into account, we find three distinct regimes. For slow rotation, the $\alpha$ and R\"adler effects are dominating in the presence of anti-solar differential rotation. For moderate rotation, $\alpha$ and $\Omega$ effects are dominant, indicative of $\alpha\Omega$ or $\alpha^2\Omega$ dynamos in operation, producing equatorward-migrating dynamo waves with a qualitatively solar-like rotation profile. For rapid rotation, an $\alpha^2$ mechanism, with an influence from the R\"adler effect appears to be the most probable driver of the dynamo. Our study reveals the presence of a large variety of dynamo effects beyond the classical $\alpha\Omega$ mechanism.