The existence of the Λ effect in the solar convection zone as indicated by SDO/HMI data

Abstract

The empirical finding with data from the Helioseismic and Magnetic Imager instrument onboard the Solar Dynamics Observatory of positive (negative) horizontal Reynolds stress at the northern (southern) hemisphere for solar giant cells is discussed for its consequences on the theory of solar/stellar differential rotation. By solving the nonlinear Reynolds equation for the angular velocity Ω when neglecting the meridional circulation, we show that the horizontal Reynolds stress of the northern hemisphere is always negative at the surface but positive in the bulk of the solar convection zone by the action of the Λ effect. The Λ effect, which describes the angular momentum transport of rigidly rotating anisotropic turbulence and which avoids a rigid-body rotation of the convection zones, is in the horizontal direction of cubic power in Ω and proves to be always positive (negative) in the northern (southern) hemisphere in both theory and simulations. In contrast, theories without the Λ effect, which may provide the observed solar rotation law only by the action of a meridional circulation, will lead to a horizontal Reynolds stress with signs that are not observed.