Estimating Flare-Related Photospheric Lorentz Force Vector Changes Within Active Regions

It is shown that expressions for the global Lorentz force associated with a flaring active region derived by Fisher et al. (Solar Phys. 277, 59, 2012) can be used to estimate the Lorentz-force changes for strong fields in large structures over photospheric subdomains within active regions. Gary's (Solar Phys. 203, 71, 2001) model for the stratified solar atmosphere is used to demonstrate that in large-scale structures with typical horizontal magnetic length scale >= 300 km and with strong magnetic fields (>= 1 kG at the tau=1 opacity layer at 5000 ), the Lorentz force acting on the photosphere may be approximated by a surface integral based on photospheric boundary data alone. These conditions cover many of the sunspot fields and major neutral lines that have been studied using Fisher et al.'s (2012) expressions over the past few years. The method gives a reasonable estimate of flare-related Lorentz-force changes based on photospheric magnetogram observations provided that the Lorentz-force changes associated with the flare have a lasting effect on the observed fields, and they are not immediately erased by post-flare equilibration processes.