Abstract Accurate measurements of stellar metallicity gradients in the radial and vertical directions of the disk and their temporal variations provide important constraints on the formation and evolution of the Milky Way disk. We use 297 042 main sequence turn-off stars selected from the LAMOST Spectroscopic Survey of the Galactic Anti-center (LSS-GAC) to determine the radial and vertical gradients of stellar metallicity, ∆[Fe/H]/∆R and ∆[Fe/H]/∆|Z| of the Milky Way disk in the direction of the anti-center. We determine ages of those turn-off stars by isochrone fitting and measure the temporal variations of metallicity gradients. We have carried out a detailed analysis of the selection effects resulting from the selection, observation and data reduction of LSS-GAC targets and the potential biases of a magnitude limited sample on the determinations 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 with the 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 with the oldest ages (≿ 11 Gyr) are negative and only show very weak variations with 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 maximum (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 assembly 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 between 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’s thick and thin disks, respectively. Also, as a consequence, we recommend that stellar age is a natural, physical criterion to distinguish stars from the thin and thick disks. From an epoch earlier than 11 Gyr to one between 8 and 11 Gyr, there is an abrupt, significant change in magnitude of both the radial and vertical metallicity gradients, suggesting that stellar radial migration is unlikely to play an important role in the formation of the thick disk.
Keywords Galaxy: abundances — Galaxy: disk — Galaxy: evolution – Galaxy: formation — techniques: spectroscopic
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