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

TL;DR

This paper leverages RR Lyrae stars as precise, old tracers to map the Milky Way's three-dimensional structure using a hierarchical Bayesian Gaussian Mixture Model. It introduces two coupled GMMs (inner Galaxy and halo) with a rotated halo to capture tilt, fitting to Gaia DR3 RR Lyrae distances while accounting for a detailed selection function. The analysis finds the inner Galaxy dominated by a prolate component with $q=1.31$, and the halo following a $r^{-4}$ law that flattens inside $12$ kpc with $q=0.70$ and a tilt of $\alpha=18^{\circ}$ toward Sagittarius, implying the halo major axis aligns with the Sagittarius dwarf. This work demonstrates the flexibility of GMMs for modeling complex Galactic structure and provides new constraints on the distribution of ancient stars in the inner Galaxy, with future work planned to explore metallicity dependence and larger RR Lyrae samples.

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. 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 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 halo 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.

Figures (6)

• Figure 1: The sky distribution in Galactic coordinates ($l,b$) of our RR Lyrae sample. stars in our sample. The top panel shows the log density for the entire sample of 128,353 RR Lyrae. After removing the XMCs with a cut in RA and DEC, there are 105,325 RRL that we use in our analysis as shown in the middle panel. The bottom panel shows the sky distribution of our final sample colored by the Gaia G magnitude, which, because of their standard-candle nature, is strongly correlated with the distance.
• Figure 2: Empirical Completeness Maps of the RR Lyrae sample in Galactic Coordinates at distances of 5 kpc (top left), 10 kpc (middle left), and 20 kpc (bottom left). We show corresponding slices of the data in distance bins of 1 kpc in the right panels. At small distances, the completeness is degraded because of the bright limits of surveys. The dominant structure in the completeness map is consistent with the Gaia scanning law.
• Figure 3: Comparison of the sky projected densities of our model to the data in Galactic coordinates ($l, b$). The top left panel is sky projection of our model where the darkest patches indicate the highest density of RRL. The top right panel shows the same but convolved with our model for the selection function. The bottom panel shows the equivalent sky projection of the RRL sample used in this work. In general, the sky projected model is similar to the data when convolved with the selection.
• Figure 4: The normalized halo density profile of RR Lyrae as a function of distance from the Galactic center ($r$) for our GMM. The light purple dotted lines indicate the 5 components of the inner Galaxy GMM while the dark purple dotted lines show the halo GMM components. The dark blue solid line is their sum. For comparison, we also show results from the literature for halo profiles including Horta2025, Han2022, Yang2022 and Pietrukowicz2015. The works from Horta2025, Han2022, and Yang2022 use red giant stars while Pietrukowicz2015 utilize only RRL.
• Figure 5: The inferred Galactic distribution of RRL as a GMM. The face-on distribution evaluated at Z=0 kpc is shown in the left panel. The middle and right panels show the edge-on distributions evaluated at X=0 kpc and Y=0 kpc, respectively. The location of the Sun is shown as a black star in the left and middle panels. In all panels, we include an ellipse (red-dashed line) which demonstrates the shape and tilt of the halo model from Han2022. We also show the direction to Sagittarius which is located at (17.9, 2.6, $-$6.6) kpc Vasiliev2021.