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 ($ Ψ= 0.25 Σ_{\rm{gas}}^{1.4}$, hereafter C-KS law), another is the modified Kennicutt law ($Ψ= αΣ_{\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.