Determination of the length of coronal loops from the decay of X-ray flares .1. Solar flares observed with Yohkoh SXT

We show how to estimate the size of spatially unresolved solar and stellar coronal flaring regions from the X-ray light curve and time-resolved temperature and emission measure values during the flare decay. By means of extensive hydrodynamic modeling of decaying flaring loops, we propose and test a relationship between the decay time of the light curve in the band of a specific instrument and the slope of the trajectory in the density-temperature diagram. From this relationship, we obtain an expression of the loop length as a function of the decay time, the slope and the flare maximum temperature. The novelty of this approach is that it takes into proper quantitative account, and allows us to estimate, the effect of a prolonged heating during the decay. In view of its application to non-imaged solar flares and to stellar flares, we have tested our relationship on spatially resolved solar flares observed with Yohkoh SXT. The comparison of the predictions to the morphology of the structures in the SXT images proves the reliability of our approach under a wide range of conditions.