The relation between the energy conversion rate and reconnection rate in Petschek-type reconnection—Implications for solar flares

The energy conversion rate in Petschek-type reconnection is modeled by parameterizing it with the reconnection rate and a dimensionless factor associated with the structure across the reconnection exhaust. We determine this factor by solving for the magnetic field and density change over the magnetohydrodynamic transitions, which bound the outflow exhaust. With a stronger guide field and/or lower plasma β, the fraction of the reconnecting magnetic field energy, which is transferred into the plasma, can decrease, but is lower-bounded by half of the reconnecting magnetic field energy. The prediction agrees reasonably well with the results in particle-in-cell simulations. We discuss implications to our understanding of energy transfer in reconnection and applications for finding the energy conversion rate in solar flares.