Inferring Stellar Densities with Flexible Models I: The Distribution of RR Lyrae in the Milky Way with $\textit{Gaia}$ DR3

Abstract

Understanding the formation and evolutionary history of the Milky Way requires detailed mapping of its stellar components, which preserve fossil records of the Galaxy's assembly through cosmic time. RR Lyrae stars are particularly well-suited for this endeavor, as they are old, standard candle variables that probe the Galaxy's earliest formation epochs. In this work, we employ a hierarchical Bayesian Gaussian Mixture Model (GMM) to characterize the three-dimensional density distribution of RR Lyrae stars in the Milky Way over the galactocentric radius ($R$) of $\approx 0.2-120~\rm{kpc}$. This approach provides a flexible framework for modeling complex stellar distributions, particularly in the inner Galaxy where the bulge, disk, and halo components overlap. Our analysis reveals that the inner Galaxy ($R\lesssim10~\rm{kpc}$) is dominated by a distinct prolate stellar population with axis ratio $q$=1.31. Consistent with previous work, we find the halo follows a $r^{-4}$ power-law profile that flattens within 12 kpc of the Galactic center. We also confirm the outer halo ($R\gtrsim10~\rm{kpc}$) is oblate $q$=0.70 with a tilt angle of $18^{\circ}$. We report for the first time that this tilt aligns the halo major axis in the direction of the Sagittarius dwarf galaxy. These results establish GMMs as an effective and flexible tool for modeling Galactic structure and provide new constraints on the distribution of old stars in the inner Galaxy.