  Spectroscopic parameters (effective temperature, metallicity, etc) were
determined for a large sample of ~100 red giants in the Kepler field, for which
mass, radius, and evolutionary status had already been asteroseismologically
established. These two kinds of spectroscopic and seismic information suffice
to define the position on the "luminosity versus effective temperature" diagram
and to assign an appropriate theoretical evolutionary track to each star.
Making use of this advantage, we examined whether the stellar location on this
diagram really matches the assigned track, which would make an interesting
consistency check between theory and observation. It turned out that
satisfactory agreement was confirmed in most cases (~90%, though appreciable
discrepancies were seen for some stars such as higher-mass red-clump giants),
suggesting that recent stellar evolution calculations are practically reliable.
Since the relevant stellar age could also be obtained by this comparison, we
derived the age-metallicity relation for these Kepler giants and found the
following characteristics: (1) The resulting distribution is quite similar to
what was previously concluded for FGK dwarfs. (2) The dispersion of metallicity
progressively increases as the age becomes older. (3) Nevertheless, the maximum
metallicity at any stellar age remains almost flat, which means the existence
of super/near-solar metallicity stars in a considerably wide age range from
~(2--3)x 10^8~yr to ~10^10~yr.
