Dating young open clusters using delta Scuti stars. Results for Trumpler 10 and Praesepe

Aims. The main goal of this work is to date young open clusters using $\delta$ Sct stars. Seismic indices such as the large separation and the frequency at maximum power can help to constrain the models to better characterise the stars. We propose a reliable method to identify some radial modes, which gives us greater confidence in the constrained models. Methods. We extract the frequency content of a sample of $\delta$ Sct stars belonging to the same open cluster. We estimate the low-order large separation by means of different techniques and the frequency at maximum power for each member of the sample. We use a grid of models built with the typical parameters of $\delta$ Sct stars, including mass, metallicity and rotation as independent variables, and determine the oscillation modes. We select the observed frequencies whose ratios match those of the models. Once we find a range of radial modes matching the observed frequencies, mainly the fundamental mode, we add it to the other seismic parameters to derive the stellar age. Assuming star groups have similar chemistry and age, we estimate their mean age by computing a weighted probability density function fit to the age distribution of the seismically constrained models. Results. We estimate the age of Trumpler 10 to be $30_{-20}{+30}$ Myr, and that of Praesepe to be $580 \pm 230$ Myr. In this latter case, we find two apparent populations of $\delta$ Sct stars in the same cluster, one at $510 \pm 140$ Myr and another at $890 \pm 140$ Myr. This may be due to two different formation events, different rotational velocities of the members in our sample of stars (as rapid rotation may modify the observed large separation), or to membership of unresolved binary systems.
Comment: 20 pages, 25 figure, uses the open-source code MultiModes (see https://github.com/davidpamos/MultiModes). It will be published in A&A