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The evolution of stellar metallicity gradients of the Milky Way disk from LSS-GAC main sequence turn-off stars: a two-phase disk formation history?

We use 297 042 main sequence turn-off stars selected from the LSS-GAC to determine the radial and vertical gradients of stellar metallicity of the Galactic disk in the anti-center direction. We determine ages of those turn-off stars by isochrone fitting and measure the temporal variations of metallicity gradients. Our results show that the gradients, both in the radial and vertical directions, exhibit significant spatial and temporal variations. The radial gradients yielded by stars of oldest ages (>11 Gyr) are essentially zero at all heights from the disk midplane, while those given by younger stars are always negative. The vertical gradients deduced from stars of oldest ages (>11Gyr) are negative and show only very weak variations with the Galactocentric distance in the disk plane, $R$, while those yielded by younger stars show strong variations with $R$. After being essentially flat at the earliest epochs of disk formation, the radial gradients steepen as age decreases, reaching a maxima (steepest) at age 7-8 Gyr, and then they flatten again. Similar temporal trends are also found for the vertical gradients. We infer that the assemblage of the Milky Way disk may have experienced at least two distinct phases. The earlier phase is probably related to a slow, pressure-supported collapse of gas, when the gas settles down to the disk mainly in the vertical direction. In the later phase, there are significant radial flows of gas in the disk, and the rate of gas inflow near the solar neighborhood reaches a maximum around a lookback time of 7-8 Gyr. The transition of the two phases occurs around a lookback time between 8 and 11 Gyr. The two phases may be responsible for the formation of the Milky Way thick and thin disks, respectively. And, as a consequence, we recommend that stellar age is a natural, physical criterion to distinguish thin and thick disk stars. ... (abridged)