Sunspot rotation, flare energetics, and flux rope helicity: The eruptive flare on 2005 may 13

Abstract

We use the Michelson Doppler Imager and TRACE observations of photospheric magnetic and velocity fields in NOAA 10759 to build a three-dimensional coronal magnetic field model. The most dramatic feature of this active region is the 34° rotation of its leading polarity sunspot over 40 hr. We describe a method for including such rotation in the framework of the Minimum Current Corona model. We apply this method to the buildup of energy and helicity associated with the eruptive flare of 2005 May 13. We find that including the sunspot rotation almost triples the modeled flare energy (1.0 × 1031 erg) and flux rope self-helicity (-7.1 × 1042 Mx2). This makes the results consistent with observations: the energy derived from GOES is 1.0 × 1031 erg, the magnetic cloud helicity from WIND is -5×1042 Mx2. Our combined analysis yields the first quantitative picture of the helicity and energy content processed through a flare in an active region with an obviously rotating sunspot and shows that rotation dominates the energy and helicity budget of this event.