Flux-tube twist resulting from helical turbulence: The Sigma-effect

Recent observational studies suggest that active region magnetic flux emerg es in a twisted state and that the sense of twist depends weakly on solar h emisphere. We propose that this twist is imparted to the flux through its i nteraction with turbulent velocities in the convection zone. This process, designated the Sigma-effect, operates on isolated magnetic flux tubes subje cted to buffeting by turbulence with a non-vanishing kinetic helicity [u . del x u]. The Sigma-effect leads to twist of the same sense inferred from o bservation and opposite to that predicted by the alpha-effect. A series of numerical calculations are performed to estimate the magnitude of the Sigma -effect in the solar convective zone. The results compare favorably with ob servations in both mean value and statistical dispersion. We find a further relationship with total magnetic flux that can be tested in future observa tions. The model also predicts that twist is uncorrelated with the tilt ang le of the active region.