On the relation between reconnected magnetic flux and parallel electric fields in the solar corona

Analytical theory and kinematic models are applied to magnetic reconnection in the solar corona. The emphasis of the present investigation is on the relation between the reconnection electric field, the reconnection rate, and the change in magnetic connectivity among photospheric magnetic footpoints. The results are not tied to the presence or absence of specific topological features of the magnetic field, such as a separatrix layer or separators. It is shown that the critical element in determining the location of ribbon-like bright features on the solar surface may be the parallel electric field, integrated along magnetic field lines. A general relation between the change of the reconnected magnetic flux and the integrated parallel electric field is derived. The results of this analysis are applied to the solar coronal case by means of two kinematic models, one of which affords a fully analytical treatment. The results show that reconnection-induced changes of magnetic connectivity on the corona-photosphere interface are directly related to the maximum value of the field line-integrated parallel electric field.