Observational determination of the rate of magnetic helicity transport through the solar surface via the horizontal motion of field line footpoints

Magnetic helicity may be transported to the solar corona through the solar surface either via the passage of helical magnetic field lines from below or via the shuffling of footpoints of preexisting coronal field lines. In this Letter, we show how to observationally determine the rate of magnetic helicity transport via photospheric footpoint shuffling from a time series of line-of-sight magnetograms. Our approach is not confined to the previously known shear motions, such as differential rotation, but can be exploited to search for the possible existence of physically significant shear motions other than differential rotation. We have applied the method to a 40 hr run of high-resolution magnetograms of a small active region (NOAA Active Region 8011) taken by the Michelson Doppler Imager on board the Solar and Heliospheric Observatory. In this region, we find that the rate of magnetic helicity transport oscillates with periods of 1 to several hours. Our result suggests that the time-series analysis of the helicity transport rate might be a useful observational diagnostic for the role of photospheric flows in the evolution of coronal magnetic fields in solar active regions.