Global Energetics of Solar Flares. X. Petschek Reconnection Rate and Alfven 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 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 lambda of the solar corona, the Alfven Mach number M-A = v(1)/v(A) (the ratio of the inflow speed v(1) to the Alfvenic outflow speed v(A)), and the flare duration tau(f), i.e., where the Alfven 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 Alfven Mach numbers M-A, the reconnection rate, and the total free energy dissipated in solar flares.