Partitioning the Galactic Halo with Gaussian Mixture Models
  The Galactic halo is supposed to form from merging with nearby dwarf
galaxies. In order to probe different components of the Galactic halo, we have
applied the Gaussian Mixture Models method to a selected sample of metal poor
stars with [Fe/H] $< -0.7$ dex in the APOGEE DR16 catalogue based on
four-parameters, metallicity, [Mg/Fe] ratio and spatial velocity
(\textit{$V_R$, $V_\phi$}). Nine groups are identified with four from the halo
(group 1, 3, 4 and 5), one from the thick disk (group 6), one from the thin
disk (group 8) and one from dwarf galaxies (group 7) by analyzing their
distributions in the ([M/H], [Mg/Fe]), ($V_R$, $V_\phi$), (\textit{Zmax},
\textit{eccentricity}), (\textit{Energy}, \textit{Lz}) and ([Mg/Mn], [Al/Fe])
coordinates. The rest two groups are respectively caused by observational
effect (group 9) and the cross section component (group 2) between the thin
disk and the thick disk. It is found that in the extremely outer accreted halo
(group 1), stars born in the Milky Way can not be distinguished from those
accreted from other galaxies either chemically or kinematically. In the
intermediate metallicity of $-$1.6 $<$ [Fe/H] $< -0.7$ dex, the accreted halo
mainly composed of the Gaia-Enceladus-Sausage substructure (group 5), which can
be easily distinguished from group 4 (the in-situ halo group) in both chemical
and kinematic space. Some stars of group 4 may come from the disk and some disk
stars can be scattered to high orbits by resonant effects as shown in the
\textit{Zmax} versus Energy coordinate. We also displayed the spatial
distribution of main components of the halo and the ratio of accreted
components do not show clear relation to Galactic radius.
