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Based on the [M/H] versus [Mg/Fe] diagram and distances from APOGEE data release 14, we compare the spatial distributions, the l − Vlos diagram, and the abundance gradients between high-[Mg/Fe] and low-[Mg/Fe] sequences. The two sequences are clearly shown at in the metallicity range of −1.6 < [M/H] < −0.7, where the halo at consists of low-[Mg/Fe] stars only. In the intermediate-metallicity range of −1.1 < [M/H] < −0.7, a [Mg/Fe] gradient is detected for stars at and it flattens out at . The l − Vlos diagram is adopted to separate halo stars from the disk by defining the transition metallicity, which is of [M/H] ∼ −1.1 ± 0.05 dex for the high-[Mg/Fe] sequence and of [M/H] ∼ −0.7 ± 0.05 dex for the low-[Mg/Fe] sequence. The R and distributions for the high-[Mg/Fe] sequence, the thick disk at −1.1 < [M/H] < −0.7 and the in situ halo at −1.6 < [M/H] < −1.1, have a cutoff at R ∼ 15 kpc and , beyond which low-[Mg/Fe] halo stars are the main contributions. In the metallicity range of −1.6 < [M/H] < −0.7, there is a negative metallicity gradient for the high-[Mg/Fe] halo at , while only a marginal or no slope in the [M/H] versus diagram for the low-[Mg/Fe] halo at , beyond which both the high-[Mg/Fe] halo and low-[Mg/Fe] halo flatten out toward . These results indicate a complicated formation history of the Galaxy and we may see a hint of a three-section halo, i.e., the inner in situ halo within , the intermediately outer dual-mode halo at , and the extremely outer accreted halo with . [ABSTRACT FROM AUTHOR]

Red clump stars are fundamental distance indicators in astrophysics, although theoretical stellar models predict a dependence of absolute magnitudes with age. This effect is particularly strong below ∼2 Gyr, but even above this limit a mild age dependence is still expected. We use seismically identified red clump stars in the Kepler field for which we have reliable distances, masses, and ages from the SAGA survey, to first explore this effect. By excluding red clump stars with masses larger than (corresponding to ages younger than 2 Gyr), we derive robust calibrations linking intrinsic colors to absolute magnitudes in the following photometric systems: Strömgren by, Johnson BV, Sloan griz, 2MASS JHKs, and WISE . With the precision achieved we also detect a slope of absolute magnitudes in the infrared, implying that distance calibrations of clump stars can be off by up to in the infrared (over the range from 2 to 12 Gyr) if their ages are unknown. Even larger uncertainties affect optical bands, because of the stronger interdependency of absolute magnitudes on colors and age. Our distance calibrations are ultimately based on asteroseismology, and we show how the distance scale can be used to test the accuracy of seismic scaling relations. Within the uncertainties our calibrations are in agreement with those built upon local red clumps with Hipparcos parallaxes, although we find a tension, which, if confirmed, would imply that scaling relations overestimate the radii of red clump stars by 2 ± 2%. Data releases post Gaia DR1 will provide an important testbed for our results. [ABSTRACT FROM AUTHOR]