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

TL;DR

This paper examines whether δ Sct stars can date open clusters through asteroseismology by focusing on Kepler and TESS targets near the red edge of the instability strip. It uses a grid of 1D stellar models with varying mass, metallicity, and rotation, and derives the large frequency separation $Δν$ from observed pulsation spectra to infer ages via a weighted PDF. The method is validated on a synthetic sample of 20 δ Sct stars and applied to 35 observed stars, finding that dating beyond about 1 Gyr is unreliable with current 1D treatments; only a few stars marginally exceed this limit. The results imply that dating older open clusters with δ Sct asteroseismology requires more sophisticated convection and rotation physics beyond 1D models.

Abstract

Aims. The aim of this work is to determine the maximum ages that can be unambiguously established for $δ$ 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 $δ$ 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 $δ$ 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 $δ$ Sct stars with varying metallicities and ages, generated by randomly selecting models. The analysis indicates that $δ$ 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 $δ$ Sct stars with 1D models, at least not without a more complete treatment of convection and a non-linear treatment of rotation.

Figures (7)

• Figure 1: HR diagram showing 64 $\delta$ Sct candidates observed in various Kepler sectors (orange) and 53 $\delta$ Sct candidates observed in TESS sectors (green), all located near the red edge of the instability strip. Targets from both samples selected for seismic analysis are highlighted with circles.
• Figure 2: Top: Periodogram of KIC 6123324. Bottom: Periodogram of TIC 121729614.
• Figure 3: Top: Estimated large separation for KIC 8827821, $\Delta\nu$ = 61 $\mu$Hz = 5.27 d$^{-1}$. Top Left: Fourier Transform (FT), Autocorrelation (AC) and the Histogram of Frequency Differences (HFD). Top Right: Echélle Diagram (ED). Bottom: Frequency ranges corresponding to radial modes with radial orders $n=1$ to $n=8$, based on the estimated large separation.
• Figure 4: Histograms and WPDFs of twenty simulated stars, with different metallicities: when Z is used (red) and not used (blue) as an observational constraint. The green solid line represents the real age of the model.
• Figure 5: Left panel: Seismically constrained stellar models for the Kepler sample of $\delta$ Sct stars, using large separation, spectroscopic temperatures, and metallicities. Right panel: Same as left, but for the TESS sample.