A Blueprint for the Milky Way's Stellar Populations. III. Spatial
  Distributions and Population Fractions of Local Halo Stars
  We analyze the observed spatial, chemical and dynamical distributions of
local metal-poor stars, based on photometrically derived metallicity and
distance estimates along with proper motions from the Gaia mission. Along the
Galactic prime meridian, we identify stellar populations with distinct
properties in the metallicity versus rotational velocity space, including Gaia
Sausage/Enceladus (GSE), the metal-weak thick disk (MWTD), and the Splash
(sometimes referred to as the "in situ" halo). We model the observed
phase-space distributions using Gaussian mixtures and refine their positions
and fractional contributions as a function of distances from the Galactic plane
($|Z|$) and the Galactic center ($R_{\rm GC}$), providing a global perspective
of the major stellar populations in the local halo. Within the sample volume
($|Z|<6$ kpc), stars associated with GSE exhibit a larger proportion of
metal-poor stars at greater $R_{\rm GC}$ ($\Delta \langle{\rm[Fe/H]}\rangle
/\Delta R_{\rm GC} =-0.05\pm0.02$ dex kpc$^{-1}$). This observed trend, along
with a mild anticorrelation of the mean rotational velocity with metallicity
($\Delta \langle v_\phi \rangle / \Delta \langle{\rm[Fe/H]} \rangle \sim -10$
km s$^{-1}$ dex$^{-1}$), implies that more metal-rich stars in the inner region
of the GSE progenitor were gradually stripped away, while the prograde orbit of
the merger at infall became radialized by dynamical friction. The metal-rich
GSE stars are causally disconnected from the Splash structure, whose stars are
mostly found on prograde orbits ($>94\%$) and exhibit a more centrally
concentrated distribution than GSE. The MWTD exhibits a similar spatial
distribution to the Splash, suggesting earlier dynamical heating of stars in
the primordial disk of the Milky Way, possibly before the GSE merger.
