EUV spectroscopy of cool stars. III. Interpretation of EUVE spectra in terms of quasi-static loops.

We discuss the limitations of coronal spectroscopy to derive physical parameters of stellar magnetic loops. We distinguish between the intrinsic non-uniqueness of emitted spectra for models of quasi-static coronal loops, and the supplemental ambiguity introduced by both instrumental effects and spectral line formation. We demonstrate that the spectrum emitted by loops with constant cross-sections is the same for a large range of values of the conductive flux at the base when the apex temperature is fixed. Because it is impossible to estimate the conductive flux at the base from observations, it is also impossible to determine the volume heating rate and the loop length uniquely. For geometrically expanding (tapered) loops, the emitted spectrum depends on the expansion and on the conductive flux at the base, and there is a trade off between them without significant changes in the spectrum. We show that loop length and heating rate can only be derived if the density is known, but that even then a large intrinsic uncertainty remains for these loop parameters. We conclude that there is no unambiguous relationship between loop parameters and emitted spectra: modeling the spectra as the sum of spectra from discrete loops cannot result in a unique determination of coronal structure. Based on spectra observed with the Extreme Ultra Violet Explorer (EUVE) we find that quasi-static loop models allow adequate modeling of stellar coronal spectra. We show that coronal loops on active cool stars must expand with height. The minimum required areal expansion between base and apex is not very large, lying between 2 and 5. For three stars (α Cen, Capella and ξ UMa) the observations suggest the presence of two distinct, dominant loop populations, while for χ^1^ Ori a single population, characterized by a single apex temperature, suffices. The high electron densities (10^12^-10^13^cm^-3^) for coronal components on Capella and ξ UMa require abnormally large heating rates. It is likely that these high densities are related to a multitude of small volumes that are temporarily excited.