Helicity Fluxes and Hemispheric Helicity Rule of Active Regions Emerging from the Convection Zone Dynamo

Using a 3D non-linear mean-field solar dynamo model, we investigate the magnetic helicity flux and magnetic twist, and tilt parameters of bipolar magnetic regions (BMRs) emerging from the solar convection zone due to the magnetic buoyancy instability. The twist and tilt of the BMR magnetic field are modeled as a result of an effective electromotive force along the rising part of the toroidal magnetic field. This force generates the poloidal field that tilts the whole magnetic configuration. We find that variations of BMR's twist and tilt determine the magnitude and the sign of the magnetic helicity flux on the solar surface. The model shows that the helicity flux associated with the BMR's tilt/twist is the dominant contribution to the BMR helicity at the beginning of the BMR's evolution, while the effect of differential rotation is the main source of the helicity flux at the final stage of the BMR's evolution. We discuss the implications of these effects on the basic properties and variations of the hemispheric helicity rule of active regions on the solar surface.