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 [$\alpha$/{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.
