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 $-2.5<[\mathrm{{Fe}/{H}}]<-0.6$. After applying theoretically motivated corrections to the seismic scaling relations, we obtain an average mass of $0.97\pm 0.03\,\mathrm{M_{\odot}}$ for our sample of halo stars. Although this maps into an age of $\sim 7\,\mathrm{Gyr}$, significantly younger than independent age estimates of the Milky Way stellar halo, we considerer this apparently young age is due to the overestimation of stellar mass in the scaling relations. There is no significant mass dispersion among lower red giant branch stars ($\log g>2$), which constrains a relative age dispersion to $<18\%$, corresponding to $<2\,\mathrm{Gyr}$. The precise chemical abundances allow us to separate the stars with [{Fe}/{H}]$>-1.7$ into two [{Mg}/{Fe}] groups. While [$α$/{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 $100\,\mathrm{Myr}<τ<300\,\mathrm{Myr}$. 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.