Cross helicity at the solar surface by simulations and observations

A result of the quasilinear mean-field theory for driven magnetohydrodynamic (MHD) turbulence is that the observed cross helicity ⟨u·b⟩ may directly yield the magnetic eddy diffusivity ηT of the quiet Sun. In order to model the cross helicity at the solar surface, magnetoconvection under the presence of a vertical large-scale magnetic field is simulated with the nonlinear MHD code Nirvana. The very robust result of the calculations is that ⟨uzbz⟩ ≃ 2⟨u·b⟩ independent of the applied magnetic field amplitude. The correlation coefficient for the cross helicity is about 10%. Of similar robustness is the finding that the rms value of the magnetic perturbations exceeds the mean-field amplitude (only) by a factor of five. The characteristic helicity speed uη as the ratio of the eddy diffusivity and the density scale height for an isothermal sound velocity of 6.6 km s-1 prove to be 1 km s-1 for weak fields. This value coincides well with empirical results obtained from the data of the Hinode satellite and the Swedish 1-m Solar Telescope (SST) providing the cross-helicity component ⟨uzbz⟩. Both simulations and observations thus lead to the numerical value of ηT ≃ 1012 cm2/s as characteristic for the surface of the quiet Sun.