Tracking Magnetic Footpoints with the Magnetic Induction Equation

The accurate estimation of magnetic footpoint velocities from a temporal sequence of photospheric magnetograms is critical for estimating the magnetic energy and helicity fluxes through the photosphere. A new technique for determining the magnetic footpoint velocities from a sequence of magnetograms is presented. This technique determines the optical flow for magnetic footpoints by applying the magnetic induction equation and an affine velocity profile to a windowed subregion of the magnetogram sequence producing an overdetermined system that can be solved directly by standard least squares or total least squares methods. The resulting optical flow field and associated uncertainties are statistically consistent with the magnetic induction equation and the affine velocity profile within this subregion. The general technique has potential for application to other solar data sets where a physical model for the underlying image dynamics can be applied.