Inferring a Photospheric Velocity Field from a Sequence of Vector Magnetograms: The Minimum Energy Fit

Abstract

We introduce a technique for inferring a photospheric velocity from a sequence of vector magnetograms. The technique, called the minimum energy fit, demands that the photospheric flow agree with the observed photo-spheric field evolution according to the magnetic induction equation. It selects from all consistent flows the one with the smallest overall flow speed by demanding that it minimize an energy functional. Partial or imperfect velocity information, obtained independently, can be incorporated by demanding a velocity consistent with the induction equation that minimizes the squared difference with flow components otherwise known. The combi-nation of low velocity and consistency with the induction equation are desirable when using the magnetogram data and associated flow as boundary conditions of a numerical simulation. The technique is tested on synthetic magnetograms generated by specified flow fields and is shown to yield reasonable agreement. It also yields believable flows from magnetograms of NOAA Active Region 8210 made with the Imaging Vector Magnetogram at the Mees Solar Observatory.