Evolution of Magnetic Helicity in Solar Cycle 24

We propose a novel approach to reconstruct the surface magnetic helicity density on the Sun or Sun-like stars. The magnetic vector potential is determined via decomposition of vector magnetic-field measurements into toroidal and poloidal components. The method is verified using data from a non-axisymmetric dynamo model. We apply the method to vector field synoptic maps from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory to study the evolution of the magnetic helicity density during solar cycle 24. It is found that the mean helicity density of the non-axisymmetric magnetic field of the Sun evolves in a way similar to that reported for the current helicity density of the solar active regions. It predominantly has a negative sign in the northern hemisphere, while it is mainly positive in the southern hemisphere. Also, the hemispheric helicity rule for the non-axisymmetric magnetic field showed the sign inversion at the end of cycle 24. The evolution of the magnetic helicity density of a large-scale axisymmetric magnetic field is different from what is predicted by dynamo theory. On one hand, the mean large- and small-scale components of magnetic helicity density display the hemispheric helicity rule of opposite signs at the beginning of cycle 24. However, later in the cycle, the two helicities exhibit the same sign, in contrast with theoretical expectations.