The Two-Infall Model Revisited: Constraints on Milky Way Bulge Assembly from >30,000 Galactic Chemical Evolution Models and Machine Learning

TL;DR

This study uses an extended two-infall galactic chemical evolution framework (OMEGA++) to constrain the Milky Way bulge's formation history. By exploring a broad parameter space with a hybrid genetic algorithm and DEMC refinement, the authors find a best-fit scenario with a rapid initial infall ($t_1 \approx 0.1$ Gyr, $\tau_1 \approx 0.09$ Gyr, SFE $\approx 3$ Gyr$^{-1}$) followed by a delayed second infall ($t_2 \approx 5.1$ Gyr, $\tau_2 \approx 1.7$ Gyr, $\sigma_2 \approx 0.69$) and reduced second-phase SFE ($\Delta$SFE $\approx 0.72$). The model successfully reproduces the bulge MDF bimodality and the alpha-element trends, and it yields an age–metallicity relation broadly consistent with Joyce2023 bulge ages, though not with all Bensby17 ages. The analysis reveals strong degeneracies among infall timing, SFE, and mass partitioning, implying that only combinations of parameters are constrained, not individual values. Overall, the results support a composite bulge origin: a dominant classical, rapid-collapse component and a younger, metal-rich contribution from later gas supply, likely linked to bar-driven inflows or merger debris. The work highlights the need for spatially resolved, chemodynamical modeling to capture gradients and dynamical processes shaping the bulge’s chemical evolution.

Abstract

We constrain the formation history of the Milky Way bulge using a two-infall Galactic Chemical Evolution (GCE) framework implemented in the OMEGA++ code. We recover a best-fit scenario in which the bulge forms through an early, rapid starburst (t1 ~ 0.1Gyr, tau1 ~ 0.09Gyr, star-formation efficiency (SFE) ~ 3Gyr^-1 followed by a delayed, lower mass second infall (t2 ~ 5.1Gyr, tau2 ~ 1.7Gyr, sigma2 ~ 0.69). Our model adopts mass- and metallicity-dependent nucleosynthetic yields from modern stellar grids and explores a wide GCE parameter space in infall timing, star formation efficiency, mass partitioning, IMF upper mass, and SN Ia normalization, optimized via a hybrid genetic algorithm with MCMC refinement. The later infall features a reduced star formation efficiency (Delta SFE ~ 0.72), reproducing the metal-rich peak of the bulge metallicity distribution function (MDF) and the decline in [alpha/Fe] at high [Fe/H]. Our model naturally favors the Joyce et al. (2023) age -- metallicity relation over the ages in Bensby et al. (2017). Degeneracy and principal component analysis show that the infall history, SFE, and mass partitioning are strongly covariant -- the bulge's observed MDF, abundance trends, and age distribution constrain only their combinations, not each parameter independently. The results support a composite bulge origin -- a classical collapse builds the majority of the mass, while a younger component is required to match the late stage enrichment.

Figures (12)

• Figure 1: Schematic illustration of the two--infall framework used in this work. Left: Face-on (looking down the Galaxys rotation axis) view of the early bulge depicting the first infall (Shown by the blue arrows), represented as a rapid, centrally directed collapse that builds the classical bulge (Orange circle) in the absence of a bar or extended disk. Right: Diagonal view of the later galactic bulge during the second infall, where gas may be funneled inward along the existing bar (Orange rectangle) and disk (Yellow ellipse represents thin disk and grey ellipse represents thick disk), while additional material can arrive along more radial paths consistent with a GSE-like accretion event (Purple bar with red dots represents the GSE merger). All of the channels supply fuel to the same central region but differ in geometry and angular momentum, motivating the distinct evolutionary signatures explored in this study.
• Figure 2: The figure shows the $\mathrm{[Fe/H]}$ distribution for the Milky Way bulge. Dashed lines indicate individual MDF fits from APOGEE DR16 across various Galactic latitude bands '$|\mathrm{b}|$'. The APOGEE Composite (thick black line) is the latitude-weighted average of the APOGEE fits. The BDBS MDF (blue line) is derived from red clump stars Johnson2022. The composite MDF (thick red line) represents the final, equally-weighted composite observational target ($50\%$ APOGEE, $50\%$ BDBS) used for the Galactic Chemical Evolution (GCE) model optimization in this study. The target exhibits the characteristic bimodal distribution with peaks near $\mathrm{[Fe/H]} \sim -0.3$ and $\mathrm{[Fe/H]} \sim +0.3$.
• Figure 3: Corner plot of posterior showing 1D histograms (diagonals) and 2D density (off–diagonals) continuous parameter groups. The black cross indicates the maximum a posteriori (MAP). The red square highlights the Highest Density Interval (HDI)
• Figure 4: Parameter dependency analysis. Left: Fitness-weighted Pearson correlation matrix. Right: Mutual information matrix which highlights both linear and nonlinear dependencies. Parameter pairs with high mutual information but low correlation indicate strong nonlinear coupling.
• Figure 5: Principal component analysis of the top-performing models. Left: Parameter loadings on the first six principal components, showing which parameters contribute most strongly to each mode of variation. Right: The variance explained by each principal component. The first six PCs capture approximately 77.5% of the total variance, indicating substantial degeneracy in the parameter space.