Global Energetics of Solar Flares. X. Petschek Reconnection Rate and Alfvén Mach Number of Magnetic Reconnection Outflows

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 Ediss in a flare depends on the mean magnetic field component Bf associated with the free energy Ef, the length scale L of the magnetic area, the hydrostatic density scale height λ of the solar corona, the Alfvén Mach number MA = v1/vA (the ratio of the inflow speed v1 to the Alfvénic outflow speed vA), and the flare duration τf, i.e., , where the Alfvén speed depends on the nonpotential field strength Bnp and the mean electron density ne 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 MA, the reconnection rate, and the total free energy dissipated in solar flares.