  For the first time we reconstruct the magnetic helicity density of global
axisymmetric field of the Sun using method proposed by Brandenburg et al.
(2003) and Pipin et al. (2013). To determine the components of the vector
potential, we apply the gauge which is typically employed in mean-field dynamo
models. This allows for a direct comparison of reconstructed helicity with the
predictions from the mean-field dynamo models. We apply the method to two
different data sets: the synoptic maps of line-of-sight (LOS) magnetic field
from the Michelson Doppler Imager (MDI) on board of Solar and Heliospheric
Observatory (SOHO) and vector magnetic field measurements from Vector
Spectromagnetograph (VSM) on Synoptic Optical Long-term Investigations of the
Sun (SOLIS) system. Based on the analysis of 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 helicity of 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 in early and late phases
of cycle 23. Furthermore, the data indicate an imbalance in magnetic helicity
between the northern and southern hemispheres. This imbalance seem to correlate
with the total level of activity in each hemisphere in cycle 23. Magnetic
helicity for 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.
