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.