Determination of the length of coronal loops from the decay of X-ray flares II. Stellar flares observed with ROSAT/PSPC

We illustrate a procedure to estimate the length of stellar coronal loops from the decay of X-ray flares observed with ROSAT/PSPC. As we did in the first paper of this series for solar flares, we use extensive hydrodynamic modeling, and the synthesis of observable quantities from the model results, to obtain an expression for the loop length in terms of parameters readily derivable from spectrally-resolved X-ray light curves, such as those of ROSAT/PSPC. The length estimate takes into account the effect of possible sustained heating during the decay and is derived from a quantity measuring PSPC spectral shape variations (Spectral Shape Index, SSI), which is a temperature indicator, and from the global light curve. Self-consistency tests on models have shown that the loop length estimation should not suffer from systematic errors, and that its uncertainty ranges from ∼ 20% for ∼ 40000 counts in the flare observation to ∼ 70% for ∼ 1000 counts. The effect of interstellar absorption is discussed and the appropriate corrections derived. As test applications, we derive the loop length for two flares, one on the M star AD Leo and the other on the M star CN Leo.