Constraints on the structure of the core of subgiants via mixed modes: the case of HD 49385

Context. The solar-like pulsator HD 49385 was observed with the CoRoT* satellite over a period of 137 days. The analysis of its oscillation spectrum yielded precise estimates of the mode frequencies over nine radial orders and distinguished some unusual characteristics, such as some modes outside the identified ridges in the echelle diagram and that the curvature of the l = 1 ridge differs significantly from that of the l = 0 ridge. Aims. We search for stellar models that can reproduce the peculiar features of the oscillation spectrum of HD 49385. After showing that they can be accounted for only by a low-frequency l = 1 avoided crossing, we investigate the information provided by the mixed modes about the structure of the core of HD 49385. Methods. We propose a toy-model to study the case of avoided crossings with a strong coupling between the p-mode and g-mode cavities in order to establish the presence of mixed modes in the spectrum of HD 49385. We then show that traditional optimization techniques are ill-suited to stars with mixed modes in avoided crossing. We propose a new approach to the computation of grids of models that we apply to HD 49385. Results. The detection of mixed modes leads us to establish the post-main-sequence status of HD 49385. The mixed mode frequencies suggest that there is a strong coupling between the p-mode and g-mode cavities. As a result, we show that the amount of core overshooting in HD 49385 is either very small (0 < alpha(ov) < 0.05) or moderate (0.18 < alpha(ov) < 0.20). The mixing length parameter is found to be significantly lower than the solar one (alpha(CGM) = 0.55 +/- 0.04 compared to the solar value alpha(circle dot) = 0.64). Finally, we show that the revised solar abundances of Asplund ensure closer agreement with the observations than the classical ones of Grevesse & Noels. At each step, we investigate the origin and meaning of these seismic diagnostics in terms of the physical structure of the star. Conclusions. The subgiant HD 49385 is the first star for which a thorough modeling has been attempted to reproduce all the properties of an avoided crossing. It has provided the opportunity to show that the study of the coupling between the cavities in these stars can provide valuable insight into open questions such as core overshooting, the efficiency of convection, and the abundances of heavy elements in stars.