Investigation of Free Magnetic Energy and Magnetic Helicity During M1.2 Solar Flare of 15 March 2015 Using HMI 135-second Vector Magnetograms

We consider a confined solar flare of class M1.2, which occurred on March 15, 2015, accompanied by the acceleration of electrons and plasma heating in a closed magnetic structure (with a strong shear) along the magnetic field polarity inversion line (PIL). The aim of the work is to study the dynamics of magnetic free energy and relative magnetic helicity using high-cadence 135-seconds HMI (Helioseismic Magnetic Imager) vector magnetograms. Such temporal resolution allows us to analyze the dynamics of the magnetic field and quantities derived from these magnetograms on the impulsive phase time scale. To investigate three-dimensional structure of the magnetic field and to compute magnetic free energy and magnetic helicity, we performed 3D magnetic field extrapolations using the non-linear force free field approximation. We found a fast decrease of the magnetic free energy (35 %) and the relative magnetic helicity (24 %) in the active region during the solar flare, while then current helicity decreased by 25%. Our estimates demonstrate that the rapid drop of the magnetic free energy (2x10^31 erg) far exceeded the total energy of the accelerated electrons (10^30 erg) and the maximum internal energy of the heated plasma (3x10^28 erg). It is also shown that the magnetic field lines near the PIL were collapsed during the development of the solar flare becoming shorter and shorter. The analysed event is a good example of a confined solar flare with the pronounced change of the magnetic helicity which is usually assumed to decrease due to eruptive processes.