Star Formation Timescales of the Halo Populations from Asteroseismology and Chemical Abundances

We combine asteroseismology, optical high-resolution spectroscopy, and kinematic analysis for 26 halo red giant branch stars in the \textit{Kepler} field in the range of $-2.5 -1.7$ into two [{Mg}/{Fe}] groups. While [$\alpha$/{Fe}] and [{Eu}/{Mg}] ratios are different between the two subsamples, [$s$/Eu], where $s$ stands for Ba, La, Ce, and Nd, does not show a significant difference. These abundance ratios suggest that the chemical evolution of the low-Mg population is contributed by type~Ia supernovae, but not by low-to-intermediate mass asymptotic giant branch stars, providing a constraint on its star formation timescale as $100\,\mathrm{Myr}<\tau<300\,\mathrm{Myr}$. We also do not detect any significant mass difference between the two [{Mg}/{Fe}] groups, thus suggesting that their formation epochs are not separated by more than 1.5 Gyr.