Solar Physics

, Volume 290, Issue 2, pp 437–466 | Cite as

A Minimum Energy Fit Method to Reconstruct Photospheric Velocity and Magnetic Diffusivity in Active Regions from Observed Magnetograms and Dopplergrams

  • Benoit Tremblay
  • Alain VincentEmail author


We introduce MEF-R, a generalization of the minimum energy fit (MEF; Longcope, Astrophys. J. 612, 1181, 2004) to a non-ideal (resistive) gas. The new technique requires both vector magnetograms and Doppler velocities as input fields. However, in the case of active regions observed only with the Michelson–Doppler Imager (MDI) onboard the Solar and Heliospheric Observatory (SOHO) such as AR 9077, we have only access to line-of-sight magnetograms. We reconstruct two-dimensional maps of the magnetic diffusivity η(x,y) together with velocity components v x (x,y), v y (x,y), and v z (x,y) under the linear force-free magnetic field approximation. Computed maps for v z (x,y) very well match the Doppler velocities v r (x,y). We find the average value 〈η〉≈108 m2 s−1 with a standard deviation of ≈ 1010 m2 s−1. Such high values of η(x,y) are to be expected at some places since our magnetic diffusivity is actually eddy-diffusivity. Inside AR 9077, the maps of η(x,y) do not resemble closely the maps from classical models of the magnetic diffusivity, but they are closer to η as a function of temperature than to η as a function of electric current density.


Eddy-diffusivity Magnetograms Minimum energy fit Photosphere Velocity fields 



Alain Vincent is supported through NSERC Individual Research Grant. Computations have been done with a modified version of MEF (Longcope 2004). We have used the IDL graphics system and SAO Image DS9 from the Smithsonian Astrophysical Observatory. In this study, we have used SOHO/MDI data archives ( ) as well as Solar Monitor ( ). We thank Frédérique Baron, Léonie Petitclerc, and Benoît Rolland for their initial contributions to data processing. Finally, we thank the anonymous reviewer for her/his constructive remarks.


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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Département de PhysiqueUniversité de MontréalMontréalCanada

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