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.
