Absolute Magnitudes of Seismic Red Clumps in the Kepler Field and SAGA:
  the age dependency of the distance scale
  Red clump stars are fundamental distance indicators in astrophysics, although
theoretical stellar models predict a dependence of absolute magnitudes with
ages. 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 1.6 Msun (corresponding to ages younger
than 2 Gyr), we derive robust calibrations linking intrinsic colors to absolute
magnitudes in the following photometric systems: Str\"omgren $by$, Johnson
$BV$, Sloan $griz$, 2MASS $JHK_s$ and WISE $W1W2W3$. With the precision
achieved we also detect a slope of absolute magnitudes 0.020(0.003) mag per
Gyrin the infrared, implying that distance calibrations of clump stars can be
off by up to 0.2 mag in the infrared (over the range from 2 Gyr 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 clump with Hipparcos} parallaxes, although we find a
tension which if confirmed would imply that scaling relations overestimate
radii of red clump stars by 2(+-20%. Data-releases post Gaia DR1 will provide
an important testbed for our results.
