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Abundance analysis for long-period variables II. RGB and AGB stars in the globular cluster 47\,Tuc

Asymptotic giant branch (AGB) stars play a key role in the enrichment of galaxies with heavy elements. Due to their large amplitude variability, the measurement of elemental abundances is a highly challenging task that has not been solved in a satisfactory way yet. Following our previous work we use hydrostatic and dynamical model atmospheres to simulate observed high-resolution near-infrared spectra of 12 variable and non-variable red giants in the globular cluster 47 Tuc. The 47 Tuc red giants are independently well-characterized in important parameters (mass, metallicity, luminosity). The principal aim was to compare synthetic spectra based on the dynamical models with observational spectra of 47 Tuc variables. Assuming that the abundances are unchanged on the upper giant branch in these low-mass stars, our goal is to estimate the impact of atmospheric dynamics on the abundance determination. We present new measurements of the C/O and 12C/13C ratio for 5 non-variable red giants in 47Tuc. The equivalent widths measured for our 7 variable stars strongly differ from the non-variable stars and cannot be reproduced by either hydrostatic or dynamical model atmospheres. Nevertheless, the dynamical models fit the observed spectra of long-period variables much better than any hydrostatic model. For some spectral features, the variations in the line intensities predicted by dynamical models over a pulsation cycle give similar values as a sequence of hydrostatic models with varying temperature and constant surface gravity.