tokens: but decrease in an old stellar population (hence, the increase in the abundances of α elements). In Fig. 15 , α-rich stars are highlighted with triangles. However, the AMR for these stars seems to have an unexpected positive trend. To investigate this, we slice [α/M] into six portions and fit a straight line to illustrate the evolution of [M/H] with age in every [α/M] slice, which is shown in Fig. 16 . As the derived age may suffer from a marginal effect, we exclude the oldest stars in the fitting process. They are marked with crosses in Fig. 16 . Figure 16. AMRs for different [α/M] slices. Straight lines are fitted to illustrate the relation between [M/H] and age. Crosses denote the oldest stars, which are not used in the fitting. All six [α/M] slices have a positive slope in the AMR. All the slices have an unexpectedly positive gradient in the AMR with the exception of the highest-α slice, which has a negative gradient of −0.004 dex Gyr −1 . The average of all the gradients is about 0.01 dex Gyr −1 . Notice that there are few stars in the 0.15 > [α/ M ] > 0.10 slice, which is just the watershed between the high-α population and the low-α population. We combine this slice with the highest-α slice, which finally gives a negative gradient of ∼−0.01 dex Gyr −1 . We examined whether the positive gradient does exist in the APOGEE-DR12 data set. In this data set, the three low [α/M] slices ranging from 0.05 to 0.15 also have a positive relation, but the other three [α/M] slices have a negative relation. If these positive correlations in some of the [α/M] slices are real, this may indicate that there is fresh metal-poor gas inflowing during the evolution of the thin Galactic disc. The infall of pristine gas dilutes the gas reservoir, lowering the subsequently formed stars’ metallicities but retaining the [α/M] ratio. These stars contribute a positive trend in the AMR in a given [α/M] slice. Thus, the AMR in different [α/M] slices may give us an opportunity to measure the gas infall rate. Actually, Chiappini, Matteucci Gratton ( 1997 ) and Chiappini, Matteucci Romano ( 2001 ) proved the power of the inflow chemical evolution model. In these references, two main inflow episodes are assumed to form the thin and thick discs. The time-scale for the formation of the thick disc is much shorter than that of the thin disc. The model-predicted metallicity distribution function generally agrees with the observations in the solar neighbourhood [fig. 7 in Chiappini et al. ( 1997 ) and Hayden et al. ( 2015 )]. However, without the aid of a dynamic process to build the Galactic chemical evolution model, it is hard to measure the detailed gas infall rate in this way because it is impossible to confirm which stars are born in situ. Even worse, the potential biases involved in our adopted sample are difficult to measure and they probably play a crucial role when determining the AMR in different [α/M] slices. High-quality spectroscopic data with wide coverage
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