Asteroseismology of 35 Kepler and TESS $\delta$ Scuti stars near the red edge of the instability strip. The limitations of $\delta$ Scuti stars for dating open clusters

Abstract

Aims. The aim of this work is to determine the maximum ages that can be unambiguously established for $\delta$ Sct stars using seismic observables, and, by extension, the oldest open clusters that can be dated using this type of star. Methods. I estimate the large frequency separation using various techniques applied to two samples of $\delta$ Sct located near the red edge of the instability strip. One sample consists of 18 targets observed by the Kepler mission, and the other comprises 17 targets observed by TESS. I employ a grid of stellar models representative of typical $\delta$ Sct parameters, incorporating mass, metallicity, and rotation as independent variables, and compute the first eight radial modes for each model. Using the observed spectroscopic temperature, and the estimated large separation, I estimate the age of each star by fitting a weighted probability density function to the age distribution of the models that best match the seismic constraints. Results. To evaluate the performance of the fitting method, it was applied to a synthetic population of 20 $\delta$ Sct stars with varying metallicities and ages, generated by randomly selecting models. The analysis indicates that $\delta$ Sct stars older than 1 Gyr, but still prior to reaching the terminal-age main sequence, can in principle be reliably age-dated. Nevertheless, when the method is applied to the observational sample, only three out of the 35 stars considered marginally exceed an estimated age of 1 Gyr. Conclusions. From these results, I can say that open clusters older than approximately 1 Gyr cannot be reliably dated using astero-seismology of $\delta$ Sct stars with 1D models, at least not without a more complete treatment of convection and a non-linear treatment of rotation.