The magnetic helicity driven solar-type dynamo

Abstract

(1)The previous theoretical studies showed that in the presence of the small-scale dynamo the large-scale vorticity can produce the the divergent-type helicity flux breaking the equatorial reflection symmetry of the magnetic fluctuations in the stellar convection zone. This effect was called the new Visniac flux (hereafter the NV flux). Similarly to the $α$ effect, the NV flux is able to maintain the large-scale turbulent dynamo. 2) Methods:Using the mean-field dynamo model we study the effect of the NV flux on the solar type dynamos. We found that the NV flux results to a increase of the dynamo efficiency for the turbulent generation of the large-scale poloidal magnetic field of the Sun. The dynamic effect of the NV flux on the magnetic field evolution results into concentrating the dynamo waves toward the equator. Using the numerical simulations of the mean-field dynamo model we compare the helicity production rates by the turbulent dynamo effects, like the $α$ effect and the NV flux. We found that the new dynamo source can produce the large-scale dynamo even if the kinetic $α$ effect is zero.3) Conclusions:The new findings suggest the crucial role of the large-scale vorticity and fluctuating magnetic field in the large-scale dynamo inside the stellar convection zones.

Figures (5)

• Figure S1: a) The meridional circulation (streamlines) and the angular velocity distributions; the magnitude of circulation velocity is of 13 m/s on the surface at the latitude of 45$^{\circ}$; b) the $\alpha$-effect tensor distributions at the latitude of 45$^{\circ}$, the dash line shows the convection zone boundary; b) radial dependencies of the total, $\eta_{T}+\eta_{||}$, and the rotational induced part, $\eta_{||}$, of the eddy magnetic diffusivity, the eddy viscosity profile, $\nu_{T}$; d) streamlines of the effective drift velocity of large-scale toroidal magnetic field due to the turbulent pumping and the meridional circulation for the case of equipartition between the intensity of the magnetic fluctuations and turbulent motions, $\epsilon=1$; e) the same as d) when the energy of the magnetic fluctuations is less by factor two than the energy of turbulent flows; f) streamlines of the effective drift velocity of large-scale poloidal magnetic field. We use numpy/scipyharris2020array2020SciPyNMeth together with matplotlib Hunter2007and pyvista sullivan2019pyvistafor post-processing and visualization.
• Figure S2: Panels a) and b) show the components large-scale vorticity as due to the differential rotation of the Sun. It is noteworthy that $W_{r}$ and $W_{\theta}$ are antisymmetric and symmetric about the equator, respectively; c) the small-scale helicity transport velocity by $-\nabla\cdot F_{\mathrm{RA}}$.
• Figure S3: Snapshots of the models M0 and M1 for the decaying phase of the magnetic cycle: a) the large-scale magnetic field distribution, color image shows the toroidal magnetic field and the streamlines show the poloidal magnetic field; b) the small-scale magnetic helicity density generation rate by the large-scale dynamo ; c) the same as b) for the $\alpha$ effect contribution; d) the radial profiles of the $\alpha$ effect, $\alpha_{\phi\phi}^{M}$ shows the contribution of the small-scale magnetic helicity.
• Figure S4: The same as \ref{['fig3']} for the models M2 and M3. Here, the column d) show the new Vishniac flux contribution, $-\boldsymbol{\nabla}\cdot F_{\mathrm{NV}}$. Note the substantial changes of the alpha effect near the bottom of the convection zone and at high latitude near the surface. Animations of this figure show variations of the magnetic field and the helicity generation rate distributions, as well as variations of the $\alpha$ effect profiles during 3 magnetic cycles of the runs M2 and M3.
• Figure S5: a) The time latitude diagrams of the large-scale magnetic field in the model M0, contours show the toroidal magnetic field at $r=0.9R$; b) the time latitude diagram of the small-scale helicity density evolution at the surface; c) and d) show the same for the run M2.