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

TL;DR

This paper derives and tests scaling laws for magnetic energy dissipation in solar flares, focusing on the Petschek reconnection model and measuring key parameters like the Alfvén Mach number using observational data.

Contribution

It introduces a new method to measure the Alfvén Mach number, reconnection rate, and free energy dissipation in solar flares using combined observational and magnetic field modeling techniques.

Findings

Derived a scaling law for magnetic energy dissipation in flares.

Measured reconnection parameters using SDO observations and magnetic field models.

Provided estimates for the reconnection rate and energy release in solar flares.

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 $\lambda$ of the solar corona, the Alfv\'en Mach number $M_A=v_1/v_A$ (the ratio of the inflow speed $v_1$ to the Alfv\'enic outflow speed $v_A$), and the flare duration $\tau_f$, i.e., $E_{diss} = (1/4\pi) B_f^2\ L\ \lambda\ v_A\ M_A\ \tau_f$, where the Alfv\'en speed depends on the nonpotential field strength $B_{np}$ and the mean electron density $n_e$ in the reconnection outflow. Using MDI/SDO and AIA/SDO observations and 3-D magnetic field solutions obtained with the vertical-current approximation nonlinear force-free field code (VCA-NLFFF) we measure all physical parameters necessary to test scaling laws, which represents a new method to measure Alfv\'en Mach numbers $M_A$, the reconnection rate, and the total free energy dissipated in solar flares.