An equation for the evolution of solar and stellar flare loops

Abstract

An ordinary differential equation describing the evolution of a coronal loop subjected to a spatially uniform but time-varying heating rate is discussed. We assume that the duration of heating is long compared to the sound transit time through the loop, which is assumed to have uniform cross section area. The form of the equation changes as the loop evolves through three stages: "strong evaporation," "scaling law behavior," and "strong condensation." Solutions to the equation may be used to compute the time dependence of the average coronal temperature and emission measure for an assumed temporal variation of the flare heating rate. The results computed from our model agree reasonably well with recent published numerical simulations and may be obtained with far less computational effort. We then use our model to study the 1980 May 21 solar flare observed by SMM and the giant 1985 April 12 flare observed on the star AD Leo.