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

We constrain the formation history of the Milky Way bulge using a two-infall galactic chemical evolution (GCE) algorithm implemented in the N’OMEGA+ code. We recover a best-fit scenario in which the bulge forms through an early, rapid starburst (t1 ∼ 0.1 Gyr, τ1 ∼ 0.09 Gyr, and star formation efficiency (SFE) ∼ 3 Gyr−1), followed by a delayed, lower-mass second infall (t2 ∼ 5.1 Gyr, τ2 ∼ 1.7 Gyr, and σ2 ∼ 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, SFE, mass partitioning, initial mass function upper mass, and type Ia supernova normalization, optimized via a hybrid genetic algorithm with Markov Chain Monte Carlo refinement. The later infall features a reduced SFE (ΔSFE ∼ 0.72), reproducing the metal-rich peak of the bulge metallicity distribution function (MDF) and the decline in [α/Fe] at high [Fe/H]. Our model naturally favors the M. Joyce et al. age–metallicity relation over the ages in T. Bensby et al. Degeneracy and principal component analyses 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—an early, rapid collapse builds the majority of the mass, while a younger component is required to match the late-stage enrichment.