  Magnetic helicity quantifies how globally sheared and/or twisted is the
magnetic field in a volume. This quantity is believed to play a key role in
solar activity due to its conservation property. Helicity is continuously
injected into the corona during the evolution of active regions (ARs). To
better understand and quantify the role of magnetic helicity in solar activity,
the distribution of magnetic helicity flux in ARs needs to be studied. The
helicity distribution can be computed from the temporal evolution of
photospheric magnetograms of ARs such as the ones provided by SDO/HMI and
Hinode/SOT. Most recent analyses of photospheric helicity flux derive an
helicity flux density proxy based on the relative rotation rate of photospheric
magnetic footpoints. Although this proxy allows a good estimate of the
photospheric helicity flux, it is still not a true helicity flux density
because it does not take into account the connectivity of the magnetic field
lines. For the first time, we implement a helicity density which takes into
account such connectivity. In order to use it for future observational studies,
we test the method and its precision on several types of models involving
different patterns of helicity injection. We also test it on more complex
configurations - from magnetohydrodynamics (MHD) simulations - containing
quasi-separatrix layers. We demonstrate that this connectivity-based helicity
flux density proxy is the best to map the true distribution of photospheric
helicity injection.
