ISO-SWS calibration and the accurate modelling of cool-star atmospheres - I. Method

A detailed spectroscopic study of the ISO-SWS data of the red giant alpha T au is presented, which enables not only the accurate determination of the s tellar parameters of alpha Tau, but also serves as a critical review of the ISO-SWS calibration. This study is situated in a broader context of an iterative process in whic h both accurate observations of stellar templates and cool star atmosphere models are involved to improve the ISO-SWS calibration process as well as t he theoretical modelling of stellar atmospheres. Therefore a sample of cool stars, covering the whole AO - Ms spectral classification, has been observ ed in order to disentangle calibration problems and problems in generating the theoretical models and corresponding synthetic spectrum. By using stellar parameters found in the literature large discrepancies wer e seen between the ISO-SWS data and the generated synthetic spectrum of alp ha Tau. A study of the influence of various stellar parameters on the theor etical models and synthetic spectra, in conjunction with the Kolmogorov-Smi rnov test to evaluate objectively the goodness-of-fit, enables us to pin do wn the stellar parameters with a high accuracy: T-eff = 3850 +/- 70 K, log g = 1.50 +/- 0.15, M = 2.3 +/- 0.8 M., z = -0.15 +/- 0.20 dex, xi (t) = 1.7 +/- 0.3 km s(-1), C-12/C-13: = 10 +/- 1, epsilon (C) = 8.35 +/- 0.20 dex, epsilon (N) = 8.35 +/- 0.25 dex, epsilon (O) = 8.83 +/- 0.15 dex and theta (d) = 20.77 +/- 0.83 mas. These atmospheric parameters were then compared w ith the results provided by other authors using other methods and/or spectr a.