Magnetic helicity of the global field in solar cycles 23 and 24

For the first time we reconstruct the magnetic helicity density of the global axisymmetric field of the Sun using the method proposed by Brandenburg et al. and Pipin et al. To determine the components of the vector potential, we apply a gauge which is typically employed in mean-field dynamo models. This allows for a direct comparison of the reconstructed helicity with the predictions from the mean-field dynamo models. We apply this method to two different data sets: the synoptic maps of the line-of-sight magnetic field from the Michelson Doppler Imager (MDI) on board the Solar and Heliospheric Observatory (SOHO) and vector magnetic field measurements from the Vector Spectromagnetograph (VSM) on the Synoptic Optical Long-term Investigations of the Sun (SOLIS) system. Based on the analysis of the MDI/SOHO data, we find that in solar cycle 23 the global magnetic field had positive (negative) magnetic helicity in the northern (southern) hemisphere. This hemispheric sign asymmetry is opposite to the helicity of the solar active regions, but it is in agreement with the predictions of mean-field dynamo models. The data also suggest that the hemispheric helicity rule may have reversed its sign during the early and late phases of cycle 23. Furthermore, the data indicate an imbalance in magnetic helicity between the northern and southern hemispheres. This imbalance seems to correlate with the total level of activity in each hemisphere in cycle 23. The magnetic helicity for the rising phase of cycle 24 is derived from SOLIS/VSM data, and qualitatively its latitudinal pattern is similar to the pattern derived from SOHO/MDI data for cycle 23.