  A detailed spectroscopic study of the ISO-SWS data of the red giant Alpha Tau
is presented, which enables not only the accurate determination of the stellar
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 which
both accurate observations of stellar templates and cool star atmosphere models
are involved to improve the ISO-SWS calibration process as well as the
theoretical modelling of stellar atmospheres. Therefore a sample of cool stars,
covering the whole A0 -- M8 spectral classification, has been observed 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 were
seen between the ISO-SWS data and the generated synthetic spectrum of Alpha
Tau. A study of the influence of various stellar parameters on the theoretical
models and synthetic spectra, in conjunction with the Kolmogorov-Smirnov test
to evaluate objectively the goodness-of-fit, enables us to pin down the stellar
parameters with a high accuracy: Teff = 3850 +/- 70 K, log g = 1.50 +/- 0.15, M
= 2.3 +/- 0.8 Msun, z = -0.15 +/- 0.20 dex, microturbulence = 1.7 +/- 0.3 km/s,
12C/13C= 10 +/- 1, abundance of C = 8.35 +/- 0.20 dex, abundance of N= 8.35 +/-
0.25 dex, abundance of O = 8.83 +/- 0.15 dex and the angular diameter is 20.77
+/- 0.83 mas. These atmospheric parameters were then compared with the results
provided by other authors using other methods and/or spectra.

Astrophysics