Many of the bright sources in the XUV are late-type dwarf active stars with very strong chromospheric emission. These stars have quiescent XUV/bolometric luminosity ratios many orders of magnitude greater than the Sun. They also present recurrent flares. The physical characteristics of the stellar transition regions (TRs) and coronae provide important observational constraints on the modeling of the thermal structure of their outer atmospheres (see, e.g., Jordan 2000). It is important to determine: the thermal structure of the stellar outer atmospheres, in terms of the differential emission measure DEM or emission measure EM; the chemical composition of the TR and corona; electron densities (or pressures); radiative losses. At present, these physical characteristics are poorly known for active stars. It is important to measure them, because they seem to vary from star to star, and to be different from the Sun. For example, EUV observations indicate that some stars have coronal abundances similar to the Sun, while other stars do not (see, e.g., the review of Feldman & Laming 2000). This could have important implications for our understanding of the various processes taking place in stellar atmospheres.
Spectroscopic diagnostics can be applied to XUV observations to determine the above physical characteristics. Until recently, low- to medium-resolution XUV spectroscopy provided measurements which were subject to large uncertainties, with approximate methods being used to analyse them. For example: electron densities were estimated from emission measures; the emission measures were estimated assuming an isothermal or a two-temperature coronal plasma; elemental abundances were estimated using global fits to the spectra. The advent of high-resolution XUV spectroscopy in the past few years (summarised in Sect. 2) provides an excellent opportunity to determine these physical parameters more directly and more accurately.
A large body of literature has been written on the subject of spectroscopic diagnostics (for a general review see, e.g., Mason & Monsignori Fossi 1994) and applications to solar and stellar observations. Unfortunately, in many studies, particularly those based on stellar observations, incorrect physical parameters have been obtained. This has in turn led to unnecessary physical conjectures that we believe should now be revisited. In this paper, we are primarily concerned with pointing out the reasons why wrong results have been obtained. We illustrate this with some examples and suggest the correct methodologies that should be applied to high-resolution XUV stellar spectra. In many cases, inaccurate atomic calculations have been used. The problematics discussed here are more generally applicable, both for solar and stellar atmospheres.
It is important to realise that some of the physical parameters are inter-related. For example, an accurate knowledge of the DEM is necessary to estimate elemental abundances (see Sect. 3), and both the DEM and the chemical composition are important factors in the calculation of the radiative losses (cf. Cook et al. 1989). The DEM and the relative element abundances can only be directly obtained to a high accuracy from the line intensities if the spectral lines:
Regarding point (f), anomalous behaviour of lines emitted by some ions from the Li and Na isoelectronic sequences has now been reported by several authors (see Sect. 3.1). However, in most of the literature (see, e.g., Brown et al. 1984b; Brown et al. 1984a; Hartmann et al. 1985; Jordan et al. 1985; Byrne et al. 1987; Jordan et al. 1987; Linsky et al. 1989; Quin et al. 1993; Maran et al. 1994; Linsky et al. 1995; Doschek 1997; Griffiths & Jordan 1998; Brandt et al. 2001), these lines have been used for solar and stellar emission measure analyses, since they are among the most prominent ones in the FUV. In this paper we show that erroneous results are obtained if these lines are used, in particular in terms of DEM, elemental abundances and electron densities. For example, many authors have used the EM loci method (see Sect. 3.3 for details) and lines with anomalous behaviour to determine electron densities. The values derived from the EM loci method are often one order of magnitude higher than those derived with the line ratio technique. In the majority of cases the authors adopt the results obtained from the EM loci method, because of the weakness of the lines used in the density-sensitive line ratios, and the various uncertainties due to blending and atomic data. The discrepancy in the electron densities derived from the two different methods is often explained with unnecessary conjectures, for example by assuming that the emission was formed in distinct types of atmospheric structures, having different densities (see, e.g., Linsky et al. 1995; Pagano et al. 2000). In this paper we show that the lower densities found by the line ratio technique should be adopted and that the two methods are fully consistent if the correct EM is obtained.
In Sect. 2 we briefly discuss some of the limitations and diagnostic possibilities offered by observations with previous and current XUV spectroscopic instruments, from the the TR through to the corona. Section 3 contains a discussion of diagnostics in the far ultraviolet spectral region (FUV: 900-1700 Å) for the determination of the physical parameters of the transition regions in active stars. In Sect. 4 we consider multi-wavelength observations of the quiescent phase of the dMe star AU Mic as a benchmark case. Section 5 presents the results, including a detailed discussion of densities, and a revision of some previous solar and stellar measurements. Section 6 draws the conclusions.
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