Two-Infall Scenario in the Milky Way Disc

• Two-Infall Scenario is a Galactic chemical-evolution framework where two distinct gas-accretion episodes form the thick (high-alpha) and thin (low-alpha) disc populations.
• The model uses a delayed second infall to dilute an enriched ISM, creating a characteristic abundance loop that explains the observed high-alpha/low-alpha bimodality using asteroseismic age constraints.
• One-zone chemical evolution models employing the Kennicutt–Schmidt law yield predictions for age, metallicity, and vertical structure that refine our practical understanding of Milky Way formation.

The Two-Infall Scenario is a Galactic chemical-evolution framework in which the Milky Way disc is assembled through two main gas-accretion episodes rather than through one smooth, continuous supply. In its modern delayed formulation, the first infall is rapid and produces the old high-$\alpha$ population, identified with the thick disc, whereas the second infall is slower and delayed by roughly $4$–$4.6$ Gyr, producing the younger low-$\alpha$ population, identified with the thin disc. The delayed second episode dilutes a previously enriched interstellar medium (ISM), generates a characteristic loop in abundance space, and thereby explains the observed high-$\alpha$/low-$\alpha$ bimodality in the solar neighbourhood (Spitoni et al., 2018, Spitoni et al., 2022).

1. Conceptual structure and historical reformulation

In the modern literature, the scenario is not merely the statement that there were “two phases” of disc growth. Its defining claim is that the two chemically distinct disc sequences are the imprint of two distinct gas-accretion episodes separated by a substantial lull in accretion and star formation. The first episode forms the high-$\alpha$, thick-disc-like population in a rapid, intense star-forming phase dominated initially by core-collapse supernova enrichment. The second episode begins much later, brings in low-metallicity gas, lowers $[\mathrm{Fe/H}]$ at nearly fixed $[\alpha/\mathrm{Fe}]$, and then forms the low-$\alpha$, thin-disc-like sequence as Type Ia supernova iron accumulates (Spitoni et al., 2018).

A major revision relative to the classical Chiappini-style implementation is the timing of the second infall. The classical version typically placed the second onset after $4$0 Gyr, whereas the revised model constrained by asteroseismic ages requires a much longer delay, $4$1 Gyr, and identifies that delay as the crucial assumption for reproducing both abundances and ages (Spitoni et al., 2018). In this reformulation, the scenario is better described as a delayed-accretion model than as a threshold-driven star-formation-gap model: the key physical ingredient is renewed gas supply after a prolonged reduction in accretion, not necessarily a strictly imposed cessation of star formation.

This formulation was tested directly against the “parallel” alternative, in which the high-$4$2 and low-$4$3 sequences form coevally in independent gas reservoirs. The parallel model can reproduce the bimodality in chemical space qualitatively, but it fails once stellar ages are imposed, especially because it predicts a low-$4$4 population that is too old and lacks the delayed-infall dilution signature (Spitoni et al., 2018).

2. Mathematical formulation in Galactic chemical evolution

The standard implementation is a one-zone chemical-evolution model for the solar annulus or solar vicinity, usually centered at $4$5 kpc. A representative governing equation for the surface density of species $4$6 is

$4$7

where $4$8 is the ISM mass fraction, $4$9 the stellar return term, and $4.6$0 the gas-accretion term (Spitoni et al., 2018).

In the delayed two-infall formulation used for the solar vicinity, the infall law is written as

$4.6$1

with $4.6$2 and $4.6$3 the infall timescales of the first and second episodes, $4.6$4 the onset time of the second accretion episode, and $4.6$5 the Heaviside step function (Spitoni et al., 2022). The normalizations are fixed so as to reproduce the present-day total surface mass density of $4.6$6 in the solar neighbourhood (Spitoni et al., 2022).

Star formation follows a Kennicutt–Schmidt law,

$4.6$7

with $4.6$8 the star-formation efficiency and $4.6$9 the gas surface density. In the APOGEE-constrained ES21 realization, the adopted efficiencies are $\alpha$0 and $\alpha$1 for the high-$\alpha$2 and low-$\alpha$3 phases, respectively (Spitoni et al., 2022). In the APOKASC age-constrained revised two-infall model, the preferred parameters are $\alpha$4, $\alpha$5, $\alpha$6, $\alpha$7, $\alpha$8, and $\alpha$9 (Spitoni et al., 2018).

These models adopt the Scalo (1986) IMF, constant in time and space, and standard delayed enrichment from Type Ia supernovae in the Matteucci formalism (Spitoni et al., 2018, Spitoni et al., 2022). In the local disc realizations discussed here, galactic winds are not included, and radial migration is not included in the model proper (Spitoni et al., 2018, Spitoni et al., 2022).

The abundance-space morphology follows directly from this setup. After the second infall begins, low-metallicity gas dilutes the ISM and produces a nearly horizontal excursion in $\alpha$0–$\alpha$1, because dilution lowers metallicity more directly than the abundance ratio. Renewed star formation then raises $\alpha$2 through core-collapse enrichment, and later Type Ia supernovae lower $\alpha$3 again, creating the loop that populates the low-$\alpha$4 branch (Spitoni et al., 2018). For comparison with APOKASC, one implementation uses

$\alpha$5

following Salaris et al. (1993) (Spitoni et al., 2018).

3. Empirical support from ages, abundance planes, and metallicity distributions

The decisive observational shift in favour of the revised delayed scenario came from asteroseismic ages. In the APOKASC sample analyzed in this context, the high-$\alpha$6 population peaks at about $\alpha$7 Gyr, while the low-$\alpha$8 population peaks at about $\alpha$9 Gyr (Spitoni et al., 2018). After kinematic pruning and selection-function corrections, the final APOKASC sample used for the age test contains $\alpha$0 red giants (Spitoni et al., 2018).

The revised two-infall model reproduces several observables simultaneously once age and metallicity uncertainties are convolved into the synthetic predictions. These include the $\alpha$1–$\alpha$2 relation at different Galactic epochs, the age–metallicity relation, the time evolution of $\alpha$3, the age distributions of the high-$\alpha$4 and low-$\alpha$5 populations, and the metallicity distribution function (Spitoni et al., 2018). Quantitatively, the observed median age of the high-$\alpha$6 population is $\alpha$7 Gyr, compared with $\alpha$8 Gyr in the synthetic revised two-infall model; for the low-$\alpha$9 population, the observed median is $\alpha$0 Gyr, compared with $\alpha$1 Gyr in the model (Spitoni et al., 2018).

The same age information disfavors the parallel scenario. Its synthetic low-$\alpha$2 age distribution has median $\alpha$3 Gyr, substantially older than the observed $\alpha$4 Gyr, and it lacks the horizontal dilution signature that the delayed second infall produces in the abundance plane (Spitoni et al., 2018).

A recurrent misconception is that the delayed two-infall picture requires an explicitly imposed star-formation threshold or a strict hiatus. The revised local model tested against APOKASC does not include a star-formation threshold; rather, it uses a delayed second gas-accretion event to mimic a period of substantially lowered gas accretion, which is sufficient to generate the observed age-separated chemical structure (Spitoni et al., 2018).

4. Vertical chemo-dynamical signatures

A further development tests whether the same delayed-infall mechanism that explains the abundance bimodality also predicts the vertical distribution of $\alpha$5. In this extension, the chemistry is first computed in the solar vicinity and then linked to vertical structure by assigning each simple stellar population (SSP) an age, chemical composition, mass, vertical action, and maximum height $\alpha$6 above the plane (Spitoni et al., 2022).

The SSPs are defined as “an assembly of coeval and chemically homogeneous stars,” formed with time-step $\alpha$7, yielding $\alpha$8 SSPs in total (Spitoni et al., 2022). The age–vertical action relation is taken from Ting & Rix (2019),

$\alpha$9

and each SSP orbit is integrated in the static Galactic potential MWPotential2014 from galpy, consisting of bulge, Miyamoto–Nagai disc, and NFW halo (Spitoni et al., 2022). Scatter in the empirical action relation is modeled with Gaussian perturbations, using $[\mathrm{Fe/H}]$0 and $[\mathrm{Fe/H}]$1 as test cases (Spitoni et al., 2022).

This construction yields a nontrivial result: the delayed-infall model reproduces not only the high-$[\mathrm{Fe/H}]$2/low-$[\mathrm{Fe/H}]$3 bimodality in the $[\mathrm{Fe/H}]$4–$[\mathrm{Fe/H}]$5 plane, but also a corresponding vertical dichotomy in $[\mathrm{Fe/H}]$6–$[\mathrm{Fe/H}]$7 (Spitoni et al., 2022). For stars younger than $[\mathrm{Fe/H}]$8 Gyr, which are mostly low-$[\mathrm{Fe/H}]$9 thin-disc stars and for which the Ting relation is directly applicable, the predicted $[\alpha/\mathrm{Fe}]$0–$[\alpha/\mathrm{Fe}]$1 relation agrees with the APOGEE DR16 plus astroNN data, especially for the $[\alpha/\mathrm{Fe}]$2 kpc and $[\alpha/\mathrm{Fe}]$3 kpc samples. When high-$[\alpha/\mathrm{Fe}]$4 stars are included, the model reproduces the existence of the vertical dichotomy for the $[\alpha/\mathrm{Fe}]$5 kpc sample (Spitoni et al., 2022).

The main tension concerns the high-$[\alpha/\mathrm{Fe}]$6 regime. The model predicts too flat a growth of $[\alpha/\mathrm{Fe}]$7 with $[\alpha/\mathrm{Fe}]$8 for high-$[\alpha/\mathrm{Fe}]$9 stars compared with the observed median trend. Proposed explanations in the study include halo contamination in the $\alpha$0 kpc sample, external perturbations such as minor mergers, dynamical heating associated with events such as Gaia-Enceladus, the inadequacy of extrapolating the Ting relation to old high-$\alpha$1 stars, the limitations of a static-potential approximation, and sizable observational uncertainties in vertical action estimates (Spitoni et al., 2022). If the data are dissected chemically into high-$\alpha$2 and low-$\alpha$3 populations, the observed $\alpha$4 distributions agree much better with the model, especially for $\alpha$5 (Spitoni et al., 2022).

5. Gaia DR3 and the three-infall refinement

Gaia DR3 introduced a sharper test of the scenario by exposing a population of young, often massive, low-$\alpha$6 disc stars with unexpectedly low metallicity and low $\alpha$7 values for several $\alpha$8-elements. In the solar vicinity, the comparison sample is restricted to giant stars with $\alpha$9 and guiding radii $4$00 kpc, with ages from the Gaia DR3 catalogue of Kordopatis et al. (2022) and relative age errors $4$01 (2206.12436). The abundance planes examined are $4$02 versus $4$03 for $4$04 (2206.12436).

The modern delayed two-infall model remains broadly successful for the classical high-$4$05/low-$4$06 dichotomy, but it fails specifically for the youngest age bins. Gaia DR3 shows many young stars with under-solar metallicity and low $4$07, $4$08, $4$09, and similar low-$4$10 behaviour; Recio-Blanco et al. (2022b), as summarized in this context, identified many massive stars with under-solar $4$11, especially Ca-poor objects with $4$12 as low as $4$13 dex over $4$14 (2206.12436). The older two-infall model, when projected into young age bins, forms too many young stars at too high metallicity.

The proposed response is not a rejection of the Two-Infall Scenario but an explicit extension of it. The three-infall model keeps the first two infalls essentially identical to the delayed two-infall baseline and splits the low-$4$15 disc formation into two distinct gas-accretion episodes (2206.12436). The infall law becomes a sum of three exponentials with Heaviside onsets, corresponding to high-$4$16, low-$4$17 part I, and low-$4$18 part II (2206.12436). The first infall remains very rapid, with $4$19; the second has $4$20 and onset $4$21; the third begins at $4$22, i.e. about $4$23 Gyr ago for $4$24 Gyr, and has $4$25 (2206.12436). The star-formation efficiencies are $4$26, $4$27, and $4$28, with $4$29, so the low-$4$30 mass split is about $4$31 in low-$4$32 part I and $4$33 in low-$4$34 part II (2206.12436).

Physically, the third infall is interpreted as a recent dilution event: fresh primordial or mildly enriched gas lowers the ISM metallicity and forms chemically impoverished young stars. The model also uses mild pre-enrichment for the two low-$4$35 infalls, setting their gas composition to the high-$4$36-phase model abundance at $4$37 dex divided by a factor of five (2206.12436). In abundance space, the first two infalls preserve the standard explanation for the main bifurcation, while the third introduces a second, smaller loop inside the low-$4$38 regime. The central conclusion is therefore precise: Gaia DR3 pushes the field beyond the two-infall model by extending its logic, not by replacing its foundation (2206.12436).

6. Current challenges from large stellar age catalogues

Large age catalogues across the disc have tightened the allowed parameter space of the scenario considerably. In a multi-zone VICE implementation spanning $4$39 kpc in annuli of width $4$40 pc, with stellar migration, APOGEE DR17 abundances, and age catalogues from Leung et al. (2023) and Roberts et al. (2025, submitted), the Two-Infall Scenario still reproduces the existence of the $4$41 bimodality, but it struggles with several features of the age–abundance structure (Dubay et al., 1 Aug 2025).

The first challenge is the age–metallicity relation of the thin disc. Because the second infall introduces a large quantity of low-metallicity gas, the model generically predicts a substantial dilution event followed by several Gyr of re-enrichment. The data, however, show that the mode of the stellar metallicity distribution is remarkably constant over much of the past $4$42–$4$43 Gyr, and more broadly that the thin-disc epoch is much flatter in age–metallicity than a strong dilution-reset event would predict (Dubay et al., 1 Aug 2025). In the solar annulus, the fiducial models underpredict the metallicity of $4$44–$4$45 Gyr old stars by up to $4$46–$4$47 dex (Dubay et al., 1 Aug 2025).

The second challenge is the age distribution of local metal-rich stars. In the two-infall picture, the most metal-rich stars at fixed radius should arise either from the metal-rich tip of the first sequence or from the very late endpoint of the second, so the model predicts a bimodal age distribution. By contrast, in APOGEE with neural-network ages, local metal-rich stars with $4$48 have a broad, mostly unimodal age distribution peaking around $4$49 Gyr, with very few older than $4$50 Gyr (Dubay et al., 1 Aug 2025).

A third generic issue is an extra intermediate-$4$51 overdensity near the turnover after the second infall, around $4$52 and $4$53–0.2 depending on parameters. The models predict this feature, whereas APOGEE shows a trough there (Dubay et al., 1 Aug 2025).

Several modifications mitigate but do not remove these tensions. Longer $4$54 smooths the low-$4$55 loop, larger thick/thin mass ratios reduce dilution, stronger migration broadens local distributions, and pre-enrichment of the second infall to $4$56 or $4$57 weakens dilution to about the $4$58-dex level (Dubay et al., 1 Aug 2025). Yet the age structure of local metal-rich stars remains fundamentally incorrect in the tested models. The resulting assessment is not that the scenario is ruled out, but that it remains viable only in modified and tightly restricted form (Dubay et al., 1 Aug 2025).

7. Extensions, reinterpretations, and terminological scope

The two-infall logic has also been extended beyond the local Galactic disc. In a bulge-specific one-zone OMEGA++ implementation constrained by more than $4$59 Galactic chemical-evolution models and machine learning, the preferred solution for the Milky Way bulge consists of an early rapid collapse with $4$60 Gyr, $4$61 Gyr, and $4$62, followed by a delayed second episode at $4$63 Gyr with $4$64 Gyr, $4$65, and reduced efficiency $4$66 (Miller et al., 8 Dec 2025). In that reinterpretation, the first phase builds the majority of the bulge and the second is chemically required to reproduce the metal-rich peak of the bulge metallicity distribution function and the decline in $4$67 at high $4$68. The study explicitly emphasizes that the posterior supports more than one gas-supply episode, but not necessarily exactly two sharply separated physical events; in a one-zone model, multiple minor late inflows would be absorbed into the effective second episode (Miller et al., 8 Dec 2025).

The phrase “two infall” also appears in other astrophysical settings, but these uses are conceptually distinct. In circumstellar-disk hydrodynamics, late inclined infall onto an already formed star–disk system can create a second-generation outer disk that is misaligned with respect to the primordial inner disk, or even counter-rotating in retrograde cases; this is a physically concrete two-stage accretion picture, but it is not the Galactic chemical-evolution Two-Infall Scenario (Kuffmeier et al., 2021). Conversely, methanol studies of high-mass star-forming regions use a modified two-layer radiative-transfer model to infer inward motions from redshifted absorption; those results support large-scale inward collapse and, in W31C, possibly hierarchical or multi-layer infall, but they do not identify two temporally separate infall episodes and should not be conflated with the Galactic chemical-evolution usage of the term (Yang et al., 2022).

Within Galactic archaeology, the Two-Infall Scenario therefore remains best understood as an effective description of Milky Way enrichment history in which the main high-$4$69/low-$4$70 dichotomy arises from two major gas-accretion episodes, with the modern debate centered less on whether two episodes are useful than on how delayed, how chemically disruptive, and how literally discrete those episodes must be.