2021ApJ...908..191C

We developed a new selection method of halo stars in the phase-space distribution defined by the three integrals of motion in an axisymmetric Galactic potential (E, L_z, I₃), where I₃ is the third integral of motion. The method is used to explore the general chemodynamical structure of the halo based on stellar samples from SDSS-SEGUE DR7 and APOGEE DR16, matched with Gaia DR2. We found the following. (a) Halo stars can be separated from disk stars by selecting over (1) 0 < L_z < 1500 kpc km s^–1, (2I₃)^1/2> 1000 kpc km s^–1 (orbital angle θ_orb > 15-20 deg), and E < -1.5 x 10⁵ km² s^–2, and (2) L_z < 0 kpc km s^–1. These selection criteria are free from kinematical biases introduced by the simple high-velocity cuts adopted in recent literature. (b) The averaged, or coarse-grained, halo phase-space distribution shows a monotonic, exponential decrease with increasing E and I₃ like the Michie-Bodenheimer models. (c) The inner stellar halo described in Carollo et al. is found to comprise a combination of Gaia Enceladus debris (GE), lowest-E stars (likely in situ stars), and metal-poor prograde stars missed by the high-velocity cut selection. (d) The very metal-poor outer halo, ([Fe/H] < -2.2), exhibits both retrograde and prograde rotation, with an asymmetric L_z distribution toward high retrograde motions and larger θ_orb than those possessed by the GE-dominated inner halo. (e) The Sgr dSph galaxy could induce a long-range dynamical effect on local halo stars. Implications for the formation of the stellar halo are also discussed.