The cross helicity at the solar surface by simulations and observations

TL;DR

This study combines simulations and observations to analyze the cross helicity at the solar surface, providing a robust estimate of magnetic eddy diffusivity in the quiet Sun, which aligns with empirical data.

Contribution

It demonstrates that the cross helicity can be used to directly estimate magnetic eddy diffusivity, supported by nonlinear MHD simulations and observational data.

Findings

Cross helicity <u  b> is approximately twice <u old b>

The correlation coefficient of cross helicity is about 10%

Magnetic eddy diffusivity 12 cm^2/s estimated for the quiet Sun surface

Abstract

The quasilinear mean-field theory for driven MHD turbulence leads to the result that the observed cross helicity <u \cdot b> may directly yield the magnetic eddy diffusivity \eta_{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_z b_z >\simeq 2 < u\cdot 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_{\eta} as the ratio of the eddy diffusivity and the density scale height for an isothermal sound velocity of 6.6 km/s proves to be 1 km/s for weak fields. This value well coincides 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_z b_z >. Both simulations and observations thus lead to a numerical value of \eta_{T} \simeq 10^12 cm^2 /s as characteristic for the surface of the quiet Sun.