Cross helicity at the solar surface by simulations and observations

¹ Leibniz-Institut für Astrophysik Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany
e-mail: gruediger@aip.de; mkueker@aip.de
² Dept. of Astronomy,Stockholm University, Alba Nova University Center, 10691 Stockholm, Sweden

Received: 22 March 2012
Accepted: 24 July 2012

Abstract

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 η_T 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 ⟨u_zb_z⟩ ≃ 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 u_η 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 ⟨u_zb_z⟩. Both simulations and observations thus lead to the numerical value of η_T ≃ 10¹² cm²/s as characteristic for the surface of the quiet Sun.