Abstract
Abstract We investigate physical scaling laws for magnetic energy dissipation in solar flares, in the framework of the Sweet–Parker model and the Petschek model. We find that the total dissipated magnetic energy E diss in a flare depends on the mean magnetic field component B f associated with the free energy E f , the length scale L of the magnetic area, the hydrostatic density scale height λ of the solar corona, the Alfvén Mach number M A = v 1/v A (the ratio of the inflow speed v 1 to the Alfvénic outflow speed v A), and the flare duration τ f , i.e., , where the Alfvén speed depends on the nonpotential field strength B np and the mean electron density n e in the reconnection outflow. Using MDI/Solar Dynamics Observatory (SDO) and AIA/SDO observations and 3D magnetic field solutions obtained with the vertical-current approximation non-linear force-free field code we measure all physical parameters necessary to test scaling laws, which represents a new method to measure Alfvén Mach numbers M A, the reconnection rate, and the total free energy dissipated in solar flares.
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