¹ European Southern Observatory, Karl-Schwarzschild-Str. 2, D-85748 Garching bei München, Germany
² Astronomical Institute, Academy of Sciences, CZ-251 65 Ondrejov, Czech Republic
³ Department of Physics & Astronomy, University College London, Gower Street, London WC1E 6BT, UK
⁴ Landessternwarte Königstuhl, D-69117 Heidelberg, Germany
⁵ European Southern Observatory, Casilla 19001, Santiago 19, Chile

After the description and time series analysis of the variability of the circumstellar and stellar lines, respectively, in Papers I and II of this series, this paper sets out to model the stellar variability in terms of multi-mode nonradial pulsation (nrp), but also adds another 109 echelle spectra to the database, obtained in 1999. While the near-circumstellar emission has faded further, the six periods and the associated line profile variabilities (lpv) have remained unchanged. For the modeling, P₁ of the periods P₁-P₄ close to 0.5 day, and P₅ of the two periods P₅ and P₆ near 0.28 day were selected, because they have the largest amplitude in their respective groups, which are characterized by their own distinct phase-propagation pattern. Permissible ranges of mass, radius, effective temperature, projected equatorial rotation velocity, and inclination angle were derived from calibrations and observations available in the literature. A total of 648 different combinations of these parameters were used to compute a number of trial series of line profiles for comparison with the observations. Next to reproducing the observed variability, the primary constraint on all models was that the two finally adopted solutions for P₁ and P₅ had to be based on only one common set of values of these quantities. This was, in fact, accomplished. Townsend's 1997 code BRUCE was deployed to model the pulsational perturbations of the rotationally distorted stellar surface. With the help of KYLIE, from the same author, these perturbations were converted into observable quantities. The local flux and the atmosphere structure were obtained from a grid of ATLAS9 models with solar metallicity, while the formation of 5967 spectral lines was calculated with the LTE code of Bachek et al. (1966). An initial coarse grid of models using all these ingredients was computed for all 12 nrp modes with l  3 and m  0. Comparison with the observed variability of C II 4267, which is the best compromise between contamination by circumstellar emission and significance of the variability, yielded (l = 2, m = +2) for P₁ (and, by implication, P₂-P₄) and (l = 3, m = +3) for P₅ (and P₆) as the best matching nrp modes. At 9M  / 3.4R and 440 km s^-1, respectively, the mass-to-radius ratio and the equatorial velocity are on the high side, but not in fundamental conflict with established knowledge. The photometric variations of all six modes combine at most to a maximal peak-to-peak amplitude of 0.015 mag, consistent with the non-detection of any of the spectroscopic periods by photometry. Without inclusion of additional physical processes, present-day linear nrp models are fundamentally unable to explain major red-blue asymmetries in the power distribution, which however seem to be limited to only some lines and the modes with the highest amplitudes. Nevertheless, the model reproduces very well a wide range of observed details. Most notable among them are: (i) Although all modeling was done on the residuals from the mean profiles only, the mean spectrum predicted by the model closely fits the observed one. (ii) Dense series of high-quality spectra obtained as early as 1987 and as recently as 1999, published independently but not included in the modeling efforts of this paper, are matched in great detail by the multiperiodic nrp model. As in  CMa, the inferred modes are retrograde in the corotating frame and in the observer's frame appear prograde only because of the rapid rotation. This has implications for models of the ejection of matter during line emission outbursts, which in  Cen are correlated with the beating of modes in the 0.5-d group of periods. The length of the corotating periods as well as the horizontal-to-vertical velocity amplitude ratios suggest a g-mode character.

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