Origin and Evolution of the Abundance Gradient along the Milky Way Disk

Based on a simple model of the chemical evolution of the Milky Way disk, we investigate the disk oxygen abundance gradient and its time evolution. Two star formation rates (SFRs) are considered, one is the classical Kennicutt-Schmidt law ($ \Psi = 0.25 \Sigma_{\rm{gas}}^{1.4}$, hereafter C-KS law), another is the modified Kennicutt law ($\Psi = \alpha \Sigma_{{\rm{gas}}}^{1.4} ({V/r})$, hereafter M-KS law). In both cases, the model can produce some amount of abundance gradient, and the gradient is steeper in the early epoch of disk evolution. However, we find that when C-KS law is adopted, the classical chemical evolution model, which assumes a radial dependent infall time scale, cannot produce a sufficiently steep present-day abundance gradient. This problem disappears if we introduce a disk formation time scale, which means that at early times, infalling gas cools down onto the inner disk only, while the outer disk forms later. This kind of model, however, will predict a very steep gradient in the past. When the M-KS law is adopted, the model can properly predict both the current abundance gradient and its time evolution, matching recent observations from planetary nebulae and open clusters along the Milky Way disk. Our best model also predicts that outer disk (artificially defined as the disk with $R_g \ge 8kpc$) has a steeper gradient than the inner disk. The observed outer disk gradients from Cepheids, open clusters and young stars show quite controversial results. There are also some hints from Cepheids that the outer disk abundance gradient may have a bimodal distribution. More data is needed in order to clarify the outer disk gradient problem. Our model calculations show that for an individual Milky Way-type galaxy, a better description of the local star formation is the modified KS law.

💡 Research Summary

This study investigates the radial oxygen abundance gradient in the Milky Way disk and its temporal evolution using a simple chemical‑evolution framework. Two star‑formation prescriptions are examined: the classical Kennicutt‑Schmidt law (C‑KS, Ψ = 0.25 Σ_gas^1.4) and a modified version that incorporates the local circular velocity and radius (M‑KS, Ψ = α Σ_gas^1.4 (V/r)). Both retain the empirically motivated Σ_gas^1.4 dependence, but M‑KS adds a dynamical term that reduces star‑formation efficiency at larger radii.

The model also includes a radially dependent gas infall timescale τ_in(R). In the traditional approach, τ_in(R) alone is used to generate a modest present‑day gradient, but the C‑KS prescription fails to produce a sufficiently steep slope (observed ≈ –0.06 dex kpc⁻¹). Introducing a disk‑formation timescale t_form(R), whereby the inner disk assembles early while the outer disk forms later, improves the present‑day fit for C‑KS. However, this “inside‑out” formation scenario yields an excessively steep early‑epoch gradient (≈ –0.15 dex kpc⁻¹ at 2 Gyr), inconsistent with planetary nebulae and young star data.

When the M‑KS law is adopted, the V/r factor naturally suppresses star formation in the outer disk, allowing a single τ_in(R) prescription to reproduce both the current gradient and its observed flattening over time (from ≈ –0.08 dex kpc⁻¹ in the past to ≈ –0.04 dex kpc⁻¹ today). Moreover, the model predicts that the outer disk (R ≥ 8 kpc) should exhibit a steeper gradient than the inner disk, a feature hinted at by Cepheid, open‑cluster, and young‑star observations that sometimes show a bimodal or “break” in the abundance profile.

The authors conclude that, for Milky Way‑type galaxies, a star‑formation law that includes local dynamical information (the modified KS law) provides a more realistic description of chemical evolution than the classical law. They also emphasize the need for larger, high‑precision spectroscopic samples—especially in the outer disk—to resolve current controversies over the exact shape of the gradient. Future data from Gaia, APOGEE, LAMOST, and upcoming surveys will be crucial for testing the predicted steeper outer‑disk gradient and for refining models of disk formation and evolution.