Context. The availability of asteroseismic constraints for a large sample of red giant stars from the CoRoT and Kepler missions paves the way for various statistical studies of the seismic properties of stellar populations. Aims. We use the first detailed spectroscopic study of 19 CoRoT red-giant stars (Morel et al 2014) to compare theoretical stellar evolution models to observations of the open cluster NGC 6633 and field stars. Methods. In order to explore the effects of rotation-induced mixing and thermohaline instability, we compare surface abundances of carbon isotopic ratio and lithium with stellar evolution predictions. These chemicals are sensitive to extra-mixing on the red-giant branch. Results. We estimate mass, radius, and distance for each star using the seismic constraints. We note that the Hipparcos and seismic distances are different. However, the uncertainties are such that this may not be significant. Although the seismic distances for the cluster members are self consistent they are somewhat larger than the Hipparcos distance. This is an issue that should be considered elsewhere. Models including thermohaline instability and rotation-induced mixing, together with the seismically determined masses can explain the chemical properties of red-giants targets. However, with this sample of stars we cannot perform stringent tests of the current stellar models. Tighter constraints on the physics of the models would require the measurement of the core and surface rotation rates, and of the period spacing of gravity-dominated mixed modes. A larger number of stars with longer times series, as provided by Kepler or expected with Plato, would help for ensemble asteroseismology.
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