Constraining Metallicity-dependent Mixing and Extra Mixing using [C/N]
  in Alpha-Rich Field Giants
  Internal mixing on the giant branch is an important process which affects the
evolution of stars and the chemical evolution of the galaxy. While several
mechanisms have been proposed to explain this mixing, better empirical
constraints are necessary. Here, we use [C/N] abundances in 26097 evolved stars
from the SDSS-IV/APOGEE-2 Data Release 14 to trace mixing and extra mixing in
old field giants with -1.7< [Fe/H] < 0.1. We show that the APOGEE [C/N] ratios
before any dredge-up occurs are metallicity dependent, but that the change in
[C/N] at the first dredge-up is metallicity independent for stars above [Fe/H]
~ -1. We identify the position of the red giant branch (RGB) bump as a function
of metallicity, note that a metallicity-dependent extra mixing episode takes
place for low-metallicity stars ([Fe/H] <-0.4) 0.14 dex in log g above the
bump, and confirm that this extra mixing is stronger at low metallicity,
reaching $\Delta$ [C/N] = 0.58 dex at [Fe/H] = -1.4. We show evidence for
further extra mixing on the upper giant branch, well above the bump, among the
stars with [Fe/H] < -1.0. This upper giant branch mixing is stronger in the
more metal-poor stars, reaching 0.38 dex in [C/N] for each 1.0 dex in log g.
The APOGEE [C/N] ratios for red clump (RC) stars are significantly higher than
for stars at the tip of the RGB, suggesting additional mixing processes occur
during the helium flash or that unknown abundance zero points for C and N may
exist among the red clump RC sample. Finally, because of extra mixing, we note
that current empirical calibrations between [C/N] ratios and ages cannot be
naively extrapolated for use in low-metallicity stars specifically for those
above the bump in the luminosity function.
